text:
\section{Abstract}
\label{SECabstract}
Micro-bubbles are of significant interest due to the long-living signature they leave behind naval ships. In order to numerically model and predict these bubbles in naval applications, subgrid-scale models are required because of the extreme separation of length- and time-scales between the macroscopic geometries and the physical processes leading to the formation of these bubbles. Yet, there is much that is unknown about the mechanism behind the entrainment of such bubbles. Furthermore, quantitative information regarding their size distribution and dependence on flow parameters is very limited. Impact events are hypothesized to be the main contributor to the generation of micro-bubbles. This is due to a phenomenon known as Mesler entrainment, which has been observed in the context of the drop-pool impact problem. Namely, when a water droplet with diameter of $\mathcal{O}(1mm)$ impacts a deep water pool with an impact velocity of $\mathcal{O}(1m/s)$, hundreds of air micro-bubbles are entrained into the pool. These bubbles have been found to be remnants of a very thin air film entrapped between the two liquid bodies. These films have extremely high aspect ratios and after being punctured, shed micro-bubbles while retracting on time scales much shorter than the outer flow time scales.

This separation of time-scales, along with a lacking of studies on retracting thin gas films has motivated us to study this fundamental problem with numerical simulations in two and three dimensions. Using a diffuse interface method, we perform two-phase simulations of retracting thin gas films in initially static liquid backgrounds to gain understanding regarding this problem and gather statistics that can be potentially used in a subgrid-scale model to predict micro-bubble shedding from a thin gas film. Coupling a model like this to a model that predicts the thin film characteristics resulting from an impact event, and a real-time impact detection algorithm, allows for predicting micro-bubbles within large scale two-phase flow simulations of naval interest.
\section{Introduction}
\label{SECintroduction}
A wide range of bubbles can be found in the wake of naval ships (Trevorrow \textit{et al.} 1994, Reed \& Milgram, 2002). Among these bubbles, bubbles in the range of $10\mu m-100\mu m$ are of particular interest as they neither dissolve nor rise to the surface (via buoyancy) fast enough to disappear from the trail of ships. In fact these bubbles, which we denote as micro-bubbles, remain under water for hours, leading to an easily detectable trail behind ships.

Within literature, the Mesler entrainment phenomenon in the context of the drop-pool impact problem is the best known instance where air micro-bubbles can be observed (Esmailzadeh \& Mesler 1986, Thoroddsen \textit{et al.} 2003, Saylor \& Bounds 2012, Thoroddsen \textit{et al.} 2012). Mesler entrainment happens when a water drop with diameter of $\mathcal{O}(1mm)$ impacts a deep water pool with an impact velocity of $\mathcal{O}(1m/s)$, to leave hundreds of air micro-bubbles in the pool. For such drop-pool impact events, there are multiple stages and different possible outcomes. First, as the air mediating the drop and pool is squeezed out and the gas layer becomes thin enough to around $\mathcal{O}(1\mu m)$, a high pressure zone builds up in the center of the film, "pumping" air out of the thin gas film. It is well known from experiments (Thoroddsen \textit{et al.} 2003, Tran \textit{et al.} 2013) and numerical simulations (Hicks \& Purvis 2011, Hendrix \textit{et al.} 2016) that this high pressure deforms the drop and pool, leading to two "kinks" that move radially away from the center. In Figure \ref{timeevltn} the formation of the kinks and deformation of the two liquid surfaces can be seen from a numerical simulation using boundary integral method (Mirjalili \& Mani, 2014). Experimental evidence from Thoroddsen \textit{et al.} (2012) shows that Mesler entrainment happens when the thin gas film prevents coalescence of the drop and pool while spreading around the drop such that a very thin hemispherical cap with thickness of the order of $\mathcal{O}(100nm)$ separates the two liquid bodies. At this stage, the very thin gas film ruptures due to intermolecular forces. The thin air film then retracts from the rupture points due to capillary forces and sheds micro-bubbles along the way. Some of the remnant air also form micro-bubbles when films from different rupture points come together to form threads of micro-bubbles. These steps can be clearly seen from experimental images of Thoroddsen \textit{et al.} (2012) .
\begin{figure}[H]
\centering
\includegraphics[width=\linewidth]{timeevltn.png}
\caption{Evolution of the water-air interfaces for a drop impacting a deep pool obtained from boundary integral method. Drop diameter is $D=3.4mm$ and impact velocity is $U=1m/s$.}
\label{timeevltn}
\end{figure}
Naval ships can induce bow waves, transom waves and waves due to turbulent boundary layers along the ship hull. Such waves often become turbulent breaking waves, resulting in entrainment of air in complicated processes occurring at a wide range of time scales and length scales. Recent numerical studies of breaking waves have been successful at resolving scales down to below the Hinze scale (Mortazavi \textit{et al.} 2016, Wang \textit{et al.} 2016, Deike \textit{et al.} 2016), enhancing our understanding of such flow structures. However, the smallest micro-bubbles cannot be captured via such simulations as they often involve scales multiple orders of magnitude below the Hinze scale. The dynamics of breaking waves take place on $\mathcal{O}(1m)$ and $\mathcal{O}(1s)$ length and time scales respectively. The resolved Hinze scale, indicating the scale at which turbulent forces are in competition with surface tension forces,  is on the order of $\mathcal{O}(1mm)$, with time scale $\mathcal{O}(1ms)$. On the other hand, the events during liquid-liquid impacts and the subsequent Mesler entrainment at least require resolving events happening at length scales of $\mathcal{O}(100nm)$ and time scales of $\mathcal{O}(100ns)$. As such, subgrid-scale (SGS) models such as the proposed method by Chan \textit{et al.} (2016) and Chan \textit{et al.} (2017) are necessary to capture and predict micro-bubbles in turbulent breaking waves simulations. Based on the assumption that Mesler entrainment is the mechanism responsible for micro-bubble generation, this type of SGS model uses the drop-pool impact problem as a model problem to predict the micro-bubbles in the flow. Particularly, such SGS algorithms would map any collision between two liquid bodies to a drop-pool impact event via relevant non-dimensional numbers. For a water-air system, the non-dimensional parameters that can describe a drop-pool impact event are the Weber ($We={\rho}_{l}{U}^{2}D/\sigma$) number and Stokes ($St={\rho}_{l}UD/{\mu}_{g}$) number, where subscripts of "l" and "g" denote properties of the liquid and gas, respectively, $U$ is the impact velocity, $D$ is the diameter of the drop, $\sigma$ is the surface tension, $\rho$ is density and $\mu$ is viscosity.

As mentioned before, numerical and experimental efforts focused on capturing the thin gas film entrapped during drop-pool impact are available in the literature. We have also investigated this problem via a diffuse interface interface-capturing scheme introduced in Mirjalili \textit{et al.} (2018a). Figure \ref{table_self_similar} shows the outcome of such simulations across a wide range of $St$ and $We$ numbers relevant to the Mesler entrainment regime. From these simulations and experimental evidence, the film thickness in drop-pool impact events in the Mesler entrainment regime is from $\sim 100nm$ to $\sim 1\mu m$. With that, the only step of the process that is still not well-understood is the shedding or generation of micro-bubbles when these films retract. Hence, in this work we will focus on the dynamics of a retracting gas film in a background liquid.
\begin{figure}[H]
\centering
\includegraphics[width=\linewidth]{table_self_similar.png}
\caption{Thin entrapped film after contact for a drop impacting a deep pool in an air-water system is plotted as a function of $St$ and $We$ of impact. In each plot the right boundary represents the axis of symmetry. Results obtained from high resolution diffuse interface calculations introduced in Mirjalili \textit{et al.} (2018b). } \label{table_self_similar}
\end{figure}
After rupture of the thin gas film, a very high surface tension force field at the rim of the film causes film retraction on time-scales much smaller than the background flow time scale. It is thus justified to disregard the effects of the background flow. Moreover, since the film thickness is multiple orders of magnitude smaller than the radius of the drop, which is of the order of the film length, the curvedness of the film can also be neglected. Thus, we can effectively study the post-rupture dynamics of the hemispherical thin gas film entrapped during drop-pool impact events via analyzing a planar gas film retracting in an initially quiescent liquid. It is important to point out that the reverse of this problem, the retracting liquid film, is a well-studied classical problem that has received attention due to its role in formation of fingers and secondary drops in impact problems and atomization (Brenner \& Gueyffier 1999, S\"{u}nderhauf \textit{et al.} 2002, Roisman \textit{et al.} 2006, Savva \& Bush 2009, Krechetnikov 2010, Agbaglah \textit{et al.} 2013). Nevertheless, there is little to no quantitative understanding on the problem of a retracting gas film in a liquid. These two problems are significantly different. In the case of retracting liquid films, the effects of the background gas phase on the momentum transport can be and has been ignored in most analyses. For retracting gas films, however, the high-inertia flow in the background liquid drives the evolution of the film. In the present study we numerically study this problem. These simulations help us gain understanding of the relevant instabilities and the mechanism leading to micro-bubble shedding.

In the following, we will first formulate the problem and describe the numerical approach we have taken in this work for studying retracting thin gas films in liquid surroundings. Next, we will analyze 2D retracting gas films with aid from numerical simulations. After establishing the necessity for considering 3D effects, we will present our analysis and numerical results from high-fidelity 3D simulations of retracting gas films. Finally, we conclude this work with a summary of our findings.

\section{Problem Formulation and Numerical Approach}
\label{SECpfna}
As explained above, we disregard the curvature of the film and the effect of background flow in our study of retracting thin gas films. Thus, we examine a planar retracting thin gas film with thickness $h$ and length $L$ in an initially stationary liquid surrounding. From experiments and numerical results, the thin gas films have very high aspect ratios such that $L\gg h$. The dynamics of a long thin air film in a background of water is determined only by its thickness. Thus, there is only one non-dimensional number that controls this problem for a given pair of working fluids (i.e. density and viscosity ratios). In this work, similar to literature on retracting liquid films, we have chosen to use the Ohnesorge number ($Oh={\mu}_{l}/\sqrt{{\rho}_{l}h\sigma}$) as the key dimensionless parameter to differentiate between different settings. In all our simulations we ensure that the domain and film length are large enough to correctly capture the evolution of the edge (rim) of the retracting gas film. In all simulations, the film is aligned with the x axis and retracts towards the negative x direction, the y axis is normal to the top and bottom sides of the film and the z direction is in the span-wise direction, as shown by a simulation snapshot in Figure \ref{sample_image}. This figure also shows a typical domain size used for our simulations. We will explain initial conditions, boundary conditions and mesh requirements for each simulation as we present the results in the following sections.
\begin{figure}[H]
\centering
\includegraphics[width=\linewidth]{sample_image_thin_film.png}
\caption{A sample snapshot of thin gas film simulations showing the axis and typical domain size.} \label{sample_image}
\end{figure}

We examine the evolution of retracting thin gas films through incompressible two-phase flow simulations using a phase field method introduced in Mirjalili \textit{et al.} (2018a). The conservative phase field equation given by
 \begin{equation}
\frac { \partial \phi  }{ \partial t } +\nabla \cdot \left(\vec{ u } \phi \right)=\nabla \cdot \left[\gamma \left(\epsilon \nabla \phi -\phi \left(1-\phi \right)\frac { { \nabla \phi  }  }{ \left| { \nabla \phi  }  \right|  }  \right) \right],
\label{phitrans}
\end{equation}
is discretized using central differences on staggered grids where $\phi$ represents the volume fraction of liquid in each phase such that $\phi=1$ in pure water and $\phi=0$ in pure air. $\epsilon$ and $\gamma$ are the free parameters of the numerical setup, respectively representing the interface thickness and interface formation speed. Realistic air-water interfaces are sharp and are formed at speeds much faster than the outer hydrodynamic scale; directly capturing their scale would lead to enormously stiff numerical systems. An alternative asymptotic approach is to select finite $\epsilon$ and $\gamma$ such that the numerical interfacial thickness, while resolvable, remains much smaller than any hydrodynamic geometrical scale, and its formation speed remains much faster than the flow scale. Mirjalili \textit{et al.} (2018a) developed a detailed investigation of the $\epsilon$-$\gamma$ parameter space and identified zones leading to robust, bounded, and well-posed numerical models for interfaces. Following their recommendation, we selected a fine mesh with $\epsilon/\Delta x=\gamma/{|\vec{u}|}_{max}=1$. This choice guarantees the boundedness of the phase field and obviates clipping or mass redistribution, as explained in Mirjalili \textit{et al.} (2018a). Continuity for incompressible flow is expressed by
\begin{equation}
\nabla\cdot\vec{u}=0,
\label{continuity}
\end{equation}
and the Navier-Stokes equations can be written as
\begin{equation}
\frac{\partial \vec{u}}{\partial t}+\nabla\cdot(\vec{u}\otimes\vec{u})=\frac{1}{\rho}\left(-\nabla P+\nabla\cdot[\mu(\nabla \vec{u}+\nabla^{T}\vec{u})]+\sigma\kappa\nabla\phi\right)
\label{NS},
\end{equation}
where curvature ($\kappa$) is computed via
\begin{equation}
\kappa=\nabla\cdot\vec{n},
\label{curvature}
\end{equation}
and both density and viscosity are linear with respect to $\phi$,
\begin{equation}
\rho=(\rho_{l}-\rho_{g})\phi+\rho_{g},
\label{rho}
\end{equation}
\begin{equation}
\mu=(\mu_{l}-\mu_{g})\phi+\mu_{g}.
\label{mu}
\end{equation}
Equations \ref{NS} to \ref{mu} are time-integrated along with Equation \ref{phitrans} using a second order fractional step method requiring only one Poisson solve per time-step (Le \& Moin, 1991). The Poisson solve is performed using an efficient state of the art in-house parallel multigrid solver (Esmaily \textit{et al.}, 2017). The accuracy, efficiency and robustness of this fully-coupled two-phase solver was studied in Mirjalili \textit{et al.} (2018b).
\section{2D Retracting thin gas films}
\label{SEC2D}
2D simulations are much cheaper than their 3D counterparts, but offer valuable information and important understandings of retracting thin gas films. We first use 2D simulations to compare the dynamics of retracting gas films with liquid films. Then, looking at the retraction of long films we explore the possibility of micro-bubble shedding from 2D films and their retraction speed. By varying the $Oh$ number, we examine how the film thickness affects the dynamics for a water/air system. It is noteworthy that by mesh refinement in 2D, we also extract the resolution requirements for our 3D studies.

In our 2D simulations, we initiate the simulations with a thin and long film closed on one side with $\vec{u}=0$ everywhere. The numerical conditions imposed on all exterior boundaries are slip boundary conditions as the domain is sufficiently far away from the long film and its retracting edge. Figure \ref{2D_gas_film} shows a thin gas film with $h=2\mu m$ retracting in a 2D domain. This 2D film does not leave behind any shedding bubbles, and the gas keeps accumulating near the edge as it retracts. If we switch the phases, the retraction of thin liquid film does not leave any drops behind either, as can be observed from Figure \ref{2D_liquid_film}. In these figures, the streamlines are plotted on top of pressure values. In both scenarios, the pressure gradients are much larger in the liquid phase and in fact the pressure in the gas phase is almost uniform. In the liquid phase of either scenario, ${Re}_{l}=\mathcal{O}(100)$ and pressure gradients predominantly balance inertial terms in the momentum equation. Moreover, a growing rim is formed in both cases with a narrow neck to its left. In the gas film problem (Figure \ref{2D_gas_film}), scaling arguments can be used to show that due to the high density and viscosity ratios of water to that of air, only very small pressure gradients can be sustained in the gas film. Thus, variation in the curvature of the film induces high and low pressure zones in the liquid phase which form a pair of counter-rotating vortices at the rim of the film. These vortices travel with the rim and displace the liquid from its neck (left of rim) to behind the rim (right of rim), causing the film to retract and the rim to grow as it collects air. For the liquid film retraction (Figure \ref{2D_liquid_film}), however, the high pressure in the rim drives the liquid towards the film, accumulating more liquid along its way and causing the rim to grow.
\begin{figure}[H]
\centering
\includegraphics[width=\linewidth]{Collages1_small.jpg}
\caption{Thin air film retracting in water. Pressure is shown in color and velocity field is drawn on top. Counter rotating vortices drive the film to the left of the domain.}
\label{2D_gas_film}
\end{figure}
\begin{figure}[H]
\centering
\includegraphics[width=\linewidth]{LIQUID_FILM_small.jpg}
\caption{ Thin water film retracting in air. Pressure is shown in color and velocity field is drawn on top. Surface tension force pulls the liquid film to the left.}
\label{2D_liquid_film}
\end{figure}

The edge shape evolution for gas and liquid films with $Oh=0.072$ (the films from Figures \ref{2D_gas_film} and \ref{2D_liquid_film}) are plotted against dimensionless coordinates (${x}^{*}=x/h$ and ${y}^{*}=y/h$) centered at the film tip in Figures \ref{gas_edge_overlay} and \ref{liquid_edge_overlay}, respectively.

\begin{figure}[H]
\centering
\includegraphics[width=\linewidth]{gas_edge_overlay.pdf}
\caption{Evolution of the thin gas film edge as it retracts plotted against dimensionless coordinates. The contours are shifted such that the rightmost point of the film is at ${x}^{*}={y}^{*}=0$.}
\label{gas_edge_overlay}
\end{figure}
\begin{figure}[H]
\centering
\includegraphics[width=\linewidth]{liquid_edge_overlay.pdf}
\caption{Evolution of the thin liquid film edge as it retracts plotted against dimensionless coordinates. The contours are shifted such that the rightmost point of the film is at ${x}^{*}={y}^{*}=0$.}
\label{liquid_edge_overlay}
\end{figure}
 It is quite clear that the edge of the liquid film attains a much more cylindrical shape compared to the thin gas film. This observation can be intuitively explained by noting that for surface tension to create a minimal surface in the gas film case (Figure \ref{2D_gas_film}), it would need to displace much more liquid compared to the case where it only moves the flow inside the retracting liquid film (Figure \ref{2D_liquid_film}). The retraction of a very long air film in water with $Oh=0.072$ can be observed in Figure \ref{long_film_retraction}. It is clear that this film does not shed any bubbles in 2D.
 \begin{figure}[H]
\centering
\includegraphics[width=\linewidth]{gas_film_not_shifted_oh072.pdf}
\caption{The evolution of a thin retracting air film in background water simulated using DI in 2D. The thin film has Oh=0.072 and all lengths are normalized by film thickness.}
\label{long_film_retraction}
\end{figure}
Experiments (Thoroddsen \textit{et al.} 2002, Thoroddsen \textit{et al.} 2012, Tran \textit{et al.} 2013) and numerical simulations (Figure \ref{table_self_similar}) inform the relevant film thicknesses in the context of Mesler entrainment. For air/water systems, the film thicknesses are $h=\mathcal{O}(100 nm)-\mathcal{O}(1\mu m)$. As such, we consider film thicknesses of $h=100nm, 200nm, 800nm, 2\mu m$, corresponding to $Oh=0.320, 0.224, 0.113, 0.072$ respectively. Air film retraction simulations with these $Oh$ values are performed in 2D keeping resolution per film thickness the same. All simulations retracted throughout the domain without leaving any bubbles behind. The interfacial profiles of two thin films with different $Oh$, corresponding to different film thicknesses for a water-air system are shown in Figure \ref{2D_profiles_oh_113_32}. In this figure, the interface for simulations at $Oh=0.113$ and $Oh=0.320$ are plotted in red and black respectively. It seems that at lower $Oh$, where capillary effects dominate viscous effects, the rim is more cylindrical and essentially rounder. This is expected, as capillarity tends to minimize the surface of the film while retracting. Retracting liquid films (S\"{u}nderhauf \textit{et al.} 2002) exhibit a similar behavior. Further examination of this shape dependence on $Oh$ is worthwhile but out of the scope of this study.
\begin{figure}[H]
\centering
\includegraphics[width=\linewidth]{oh_32_113_contours_edited.pdf}
\caption{Interfacial profile evolution of retracting thin gas films with $Oh=0.113$ and $Oh=0.320$ plotted in dimensionless coordinates in red and black respectively.}
\label{2D_profiles_oh_113_32}
\end{figure}
Comparing retracting gas and liquid films, shown in Figures \ref{2D_gas_film} and \ref{2D_liquid_film} respectively, reveals the lower retraction velocity of the gas film. An analysis of momentum balance for the growing mass in the edge by the surface tension force reveals that for $Oh<1$, liquid film retraction speed is given by the Taylor-Culick velocity (Taylor 1959, Culick 1960)
\begin{equation}
{V}_{TC}=\sqrt{\frac{2\sigma}{{\rho}_{l}h}}.
\label{taylor_culick}
\end{equation}

On the other hand, the retraction speed of the edge of a gas film in a background liquid is not as simple to derive analytically. Oguz \& Prosperetti (1989) numerically showed that a relation similar to \ref{taylor_culick} holds for the retraction speed of the edge of thin gas films,
\begin{equation}
{V}_{OP}=C\sqrt{\frac{\sigma}{{\rho}_{l}h}},
\label{oguz_prosperetti}
\end{equation}
where $C$ is a constant taking a value of approximately $1$. Experiments by Thoroddsen \textit{et al.} (2002) confirmed this relation by measuring the retraction rate of thin gas sheets in drop-pool impacts. If we denote the edge location as $R$, then dimensionless velocity and time can be defined as
\begin{equation}
{u}^{*}=\frac{dR/dt}{{V}_{OP}},
\end{equation}
and
\begin{equation}
{t}^{*}=\frac{t{V}_{OP}}{h}.
\end{equation}

Figure \ref{retraction_speed_all_Oh} shows the normalized dimensionless retraction speeds against time for different thin gas films. From this figure, the normalized retraction speeds (${u}^{*}=(dR/dt)/{V}_{OP}$) for different cases seem to be relatively similar and slowly varying. In fact, after an earlier transience the retraction speed is approximated by \ref{oguz_prosperetti} with $C\sim 1$. Thus, a thin gas film retracting in a liquid background retracts about $\sqrt{2}$ times slower than a thin liquid film with the same thickness retracting in the gas. The minor effect of $Oh$ number can be used in conjunction with experimental images to estimate the gas film thickness at rupture time. For a pair of liquid-gas working fluids, the film thickness is the only parameter that influences the film retraction dynamics. Considering Figure \ref{retraction_speed_all_Oh}, giving the scaling of ${u}^{*}\approx 1$, the film thickness can be found to be
\begin{equation}
h\approx \frac{\sigma}{{\rho}_{l}{(dR/dt)}^{2}},
\label{using_op}
\end{equation}
where the retraction rate ($dR/dt$) can be measured experimentally. This relationship is only valid for films where viscous effects are not dominant. In other words, as long as $Oh<1$, we can use Equations \ref{oguz_prosperetti} and \ref{using_op}. We will expand upon experimental techniques for measuring film thickness in the next section. A more careful inspection shows that there is a slight decrease in ${u}^{*}$ as the $Oh$ number is increased. This can be justified by acknowledging that higher $Oh$ values result in higher viscous dissipation, reducing the total energy of the system. As mentioned above, Equations \ref{taylor_culick} and \ref{oguz_prosperetti} were both derived while neglecting viscous effects. In fact, it has been shown in literature that liquid film retraction rates normalized by ${V}_{TC}$ from Equation \ref{taylor_culick} also decrease as $Oh$ is increased (S\"{u}nderhauf \textit{et al.} 2002).
\begin{figure}[H]
\centering
\includegraphics[width=\linewidth]{gas_film_speed_all_Oh_10_edited.pdf}
\caption{Dimensionless retraction speed plotted against dimensionless time. ${u}^{*}\sim 1$ is equivalent to $C\sim 1$ in Equation \ref{oguz_prosperetti}.}
\label{retraction_speed_all_Oh}
\end{figure}
While \ref{oguz_prosperetti} gives a good approximation on the retraction speed for films with $Oh<1$, the long term evolution of the retraction speed of these thin films sheds light on an important distinction between retracting thin gas films and liquid films. Figure \ref{retraction_speed} clearly shows that after an initial transitory phase, the edge velocity slowly decreases with time. This observation can be justified using conservation of momentum. For a control volume containing the edge and large enough that liquid and gas velocities vanish at the boundaries, external forces must be balanced by the rate of change of fluid momentum. For large density ratios, the inertia of the gas inside the film can be ignored. Thus, the drag force on the film which is equal (with opposite sign) to the rate of change of momentum of the liquid must balance the surface tension forces acting at the surface of the control volume. After the edge grows to become much larger than the film thickness, we can assume that the drag force on the film is dominated by the drag on its edge. The $Re$ numbers of the flow around the edge of the films of interest to us are $\mathcal{O}(100)$, and as a result the drag on the nearly cylindrical edge of these thin films can be written as ${\rho}_{l}H{(dR/dt)}^{2}{C}_{D}$ per unit length, where H is the edge diameter and ${C}_{D}$ can be approximated as a constant at such $Re$ numbers. Equating this with the surface tension force, and using mass conservation,
$H(dH/dt)\sim (dR/dt)h$, we obtain $dR/dt \sim {t}^{-1/5}$ and ${H}\sim {t}^{2/5}$. This power law is verified in Figure \ref{retraction_speed_power_law} and a similar observation was made in experiments on anti-bubbles by \cite{Sobyanin2015}. We later show that this inverse relationship between retraction speed and edge diameter plays an important role in the 3D mechanism underlying micro-bubble shedding from gas films.

\begin{figure}[H]
\centering
\includegraphics[width=\linewidth]{gas_film_speed_long_time_oh072.pdf}
\caption{Long-term dimensionless retraction speed plotted against dimensionless time for an Oh=0.072 air film retracting in water. ${u}^{*}\sim 1$ is equivalent to $C\sim 1$ in Equation \ref{oguz_prosperetti}.}
\label{retraction_speed}
\end{figure}

\begin{figure}[H]
\centering
\includegraphics[width=\linewidth]{retraction_speed_power_law.png}
\caption{Long-term dimensionless retraction speed plotted against dimensionless time for an Oh=0.072 air film retracting in water, demonstrating how the speed of the film edge obeys a power law in time.}
\label{retraction_speed_power_law}
\end{figure}

Considering the 2D retracting air films, there are no significant qualitative differences between different $Oh$ cases. The rim shape and normalized retraction speeds are similar in all $Oh$ number simulations. More importantly, none of the cases we examined in our 2D calculations resulted in micro-bubbles, while experiments on Mesler entrainment have shown micro-bubbles shedding from gas films with similar $Oh$ values. In fact, we observe that the rim finds a self-similar profile as shown in Figure \ref{self_similar}. In this figure, the edge profiles shown in Figure \ref{long_film_retraction} are shifted and then scaled based on the time in accordance with the scaling law found for the growth of the rim thickness, $H$. This confirms that 3D instabilities in the span-wise direction must be responsible for micro-bubble generation, as was also illustrated by Thoroddsen \textit{et al.} (2012). In that work, "sawtooth" instabilities were found to cause micro-bubble shedding. We will study such instabilities in the following sections.
\begin{figure}[H]
\centering
\includegraphics[width=\linewidth]{gas_film_collapse_oh072_t04_zoomed.pdf}
\caption{The evolution of a thin retracting air film in background water with Oh=0.072 simulated using DI in 2D. The edge profiles shown in Figure \ref{long_film_retraction} are shifted and scaled according to the power law dictating the growth of $H$.}
\label{self_similar}
\end{figure}

Based on the geometrical similarities between the results of 2D simulations of gas films at various $Oh$ numbers, it is justified to use a common mesh for 3D calculations at different $Oh$ values. From our 2D simulations, after mesh refinement, we observe that the film thickness can be resolved by 20 cells. Isotropic uniform meshes around the interfacial regions are also found to yield best results. We take advantage of these cost-effective learnings in our high-fidelity 3D simulations, presented in the proceeding sections of this paper.

\section{3D retracting thin gas films}

As explained in the previous section, our 2D simulations result in stable self-similar growing rims, indicating that 3D mechanisms are in play for break-up of micro-bubbles. In the context of drop-pool impact experiments, Thoroddsen \textit{et al.} (2002) and
Thoroddsen \textit{et al.} (2012) observed instabilities in the span-wise direction of retracting thin gas films. Such instabilities seemingly triggered micro-bubble shedding from the thinner, higher aspect ratio gas films in Thoroddsen \textit{et al.} (2012). In Thoroddsen \textit{et al.} (2002), the wave length of the undulations in the span-wise direction were found to be consistent with the maximum growth wavenumber from Rayleigh-Plateau instability. Indeed, in this section we will theoretically explain and numerically confirm that a Rayleigh-Plateau type instability in the span-wise direction of the rim of a high aspect ratio (thin and long) retracting gas film can induce micro-bubble shedding.

Rayleigh-Plateau (RP) instability is an axisymmetric mechanism that breaks cylindrical features like liquid jets into drops with lower total free surface energy (Chandrasekhar, 2013). This capillary instability can also break up hollow cylinders into bubbles. In practice, the "hollow" cylinder can be occupied by a very low inertia fluid like a gas. As the thin gas film in our problem retracts, the size of the rim increases by accumulation of the gas volume. Overtime, the rim starts to resemble a hollow cylinder, vulnerable to RP instability. The inviscid version of this instability can be applied here as per Chandrasekhar (2013). For a hollow cylinder with radius ${R}_{cyl}$, the mode of maximum instability occurs at
\begin{equation}
{\lambda}_{RP}=\frac{2\pi}{0.484}{R}_{cyl},
\label{wave_length_RP}
\end{equation}
and the growth rate is given by
\begin{equation}
{\omega}_{RP}=0.820\sqrt{\sigma/({\rho}_{l}{R}_{cyl}^3)}.
\label{RP_growth_rate}
\end{equation}
These relations can provide experimentalists with a simple method, requiring just a few images, for computing the thickness of retracting thin gas films, for instance in drop-pool experiments. Measuring the thickness of the thin gas films entrapped during Mesler entrainment has been found to be rather cumbersome. Thoroddsen \textit{et al.} (2012) relied on images of the micro-bubble cloud after retraction terminated as a direct way of estimating the air film thickness at rupture. Alternatively, Tran \textit{et al.} (2013) used a technique based on colour interferometry to extract the thickness of the film. Their method, however, was limited to a narrow region around the center of the drop due to limited field of view. We have already mentioned that for $Oh<1$, a practical way to estimate film thickness is based on the retraction speed and Equation \ref{oguz_prosperetti}. This method also fails for viscous liquids, where $Oh\geq1$. Equation \ref{wave_length_RP} has a weak dependence on viscosity of the liquid, which allows the following method to be also applicable to more viscous liquids such as the ones used in the experiments of Thoroddsen \textit{et al.} (2012) and Tran \textit{et al.} (2013). The steps for our proposed method are:
\begin{itemize}
\item Measure wavelength of edge instability, ${\lambda}_{exp}$, from the experimental images
\item Use Rayleigh-Plateau most unstable wavelength from Equation \ref{wave_length_RP} to estimate the effective diameter of the rim, ${H}_{exp}=0.484{\lambda}_{exp}/\pi$.
\item Measure distance of edge from rupture point, ${\Delta}_{exp}$
\item Use conservation of mass to obtain the average film thickness, ${h}_{exp}=\pi{H}_{exp}^{2}/(2{\Delta}_{exp})$.
\end{itemize}
Applying this method to the images provided by Thoroddsen \textit{et al.} (2012), results in thin film thickness of about $120nm$, which is close to the estimates provided by the authors.

As the film retracts, the rim continually receives air and grows. From Equations \ref{wave_length_RP} and \ref{RP_growth_rate} it is quite clear that as the rim grows, the most critical wavelength increases and the growth rate decreases. Figure \ref{wave_growth_time} shows the evolution of the unstable RP modes and their growth rate as the rim grows in time. The growing rim becomes unstable to perturbations at larger wavelengths with smaller growth rates. Therefore, growth of the rim which happens on the timescale of film retraction can stabilize Rayleigh-Plateau instability. In particular, two time scales are in competition: the time
scale associated with growth of the rim radius (${T}_{ret}$), and the RP instability in the span-wise direction (${T}_{RP}$). Bubbles can only be shed when the RP instability is much faster than the edge growth, ${T}_{RP}\ll{T}_{ret}$. If we denote the "diameter" of the rim at a given time to be given by $H$, then we have
\begin{equation}
{T}_{RP}\sim \sqrt{\frac{\rho{H}^{3}}{\sigma}}.
\end{equation}
For films with $Oh<1$, corresponding to film thicknesses of about $100nm$ and above for water-air systems, the retraction speed can be approximated to be of the order of ${V}_{OP}$ from Equation \ref{oguz_prosperetti}, by which we are ignoring the weak time-dependence of retraction velocity. Additionally, conservation of mass dictates the scaling $H dH/dt\sim h{V}_{OP}$, yielding the time scale of retraction defined as ${T}_{ret}=H/(dH/dt)$ to be
\begin{equation}
{T}_{ret}\sim \sqrt{\frac{\rho{H}^{4}}{\sigma h}}.
\end{equation}
For ${T}_{RP}\ll{T}_{ret}$ to hold, the thin film must satisfy $\sqrt{h/H}\ll1$. For a film with retraction length L, given ${H}^{2}\sim hL$, once can write this condition as:
\begin{equation}
\sqrt[4]{h/L}\ll1.
\label{requirement_inviscid}
\end{equation}
From this observation, we conclude that for films with $Oh<1$, micro-bubble shedding is only possible for films with very high aspect ratios such that even the fourth root of the aspect ratio is a small number. This explains why for disk type films such as the one shown in Figure 2.b of Thoroddsen \textit{et al.} (2002) displaying the outcome of a water drop impacting with $D=4.24mm$ and $U=0.49m/s$, azimuthal undulations stabilize and shed no bubbles. On the other hand, Figure 8.a of the same paper, shows that a thinner and longer film obtained for similar impact parameters ($D=4.24mm$ and $U=0.6m/s$), results in hundreds of micro-bubbles. This is in accordance with our scaling analysis since in the latter case a much longer and thinner film was generated before the two liquid bodies made contact.
\begin{figure}[H]
\centering
\includegraphics[width=\linewidth]{growth_rate_growing_edge_edited.pdf}
\caption{Growth rate of RP instability at unstable wave numbers plotted for a growing rim. The curves move to the left of the plot as time progresses and the rim increases in size.}
\label{wave_growth_time}
\end{figure}
While we do not concern ourselves with more viscous fluids such as the silicon oils frequently used in Mesler entrainment experiments (Saylor \& Bounds 2012, Thoroddsen \textit{et al.} 2012, Tran \textit{et al.} 2013), we briefly note that in such cases the thin gas film retracts with the capillary-viscous velocity given by ${V}_{cap-visc}=\sigma/{\mu}_{l}$ (Reyssat \& Quere 2006, Aryafar \& Kavehpour 2008, Thoroddsen \textit{et al.} 2012) which is independent of the film thickness and slower than ${V}_{OP}$ (Equation \ref{oguz_prosperetti}. This increases the retraction time scale (${T}_{ret}$), while not affecting the scaling of ${T}_{RP}$, since viscous effects at such $Oh$ numbers just slightly decrease the constant behind the maximum growth rates (Ashgriz, 2011). In order to have ${T}_{RP}\ll{T}_{ret}$ it suffices to have
\begin{equation}
\frac{1}{Oh}\sqrt[4]{\frac{h}{L}}\ll1,
\label{requirement_viscous}
\end{equation}
where of course $Oh>1$. Comparing Equation \ref{requirement_inviscid} and \ref{requirement_viscous}, one can recognize that increasing the viscosity of the liquid phase can enhance the likelihood of the RP instability leading to micro-bubble shedding.
\subsection{3D Simulations}
We take advantage of high resolution 3D simulations of retracting thin gas films to verify the formation of edge (rim) instabilities, and study how they eventually lead to micro-bubbles. By varying $Oh$ number of the films, which is the only dimensionless parameter controlling this problem for a water/air system, we explore how the film thickness affects the dynamics and outcome of this process.

For our 3D simulations, we perform two types of simulations. First, we use a static frame of reference with a very long film, as shown in Figure \ref{sample_image}. In this simulation the edge moves towards the negative $x$ axis, until it almost reaches the boundary. In the second type of simulation which runs for a much longer time and is cheaper, a smaller length is simulated as the domain moves with the edge, allowing for the edge to remain within the bounds at all times. This is made possible by the approximately constant retraction velocity, ${V}_{OP}$, given by Equation \ref{oguz_prosperetti}. We must note that the shedding of micro-bubbles does cause the retraction speed to drift from ${V}_{OP}$, for which we account for by adjusting the frame of reference speed accordingly. We explore the role of $Oh$ using the second type of simulation.

\subsection{Static Domain Simulations}
\label{SECstaticdomain}
For the 3D simulation using static domains, slip boundary conditions are used in the $x$ and $y$ boundaries, while employing periodic boundary conditions in the $z$ direction. The domain must be long enough in the $x$ direction to satisfy Equation \ref{requirement_inviscid}, and wide enough to capture the unstable wavelengths from Equation \ref{wave_length_RP}. Moreover, similar to our 2D simulations, the domain height in the y-direction is kept large enough so as to not influence the dynamics of the thin film. To be specific, for a water film retracting in air with $h=2\mu m$, which we will denote as the nominal case, we use ${L}_{x}=200\mu m$, ${L}_{y}=50\mu m$ and ${L}_{z}=100\mu m$. Our Cartesian mesh is stretched in $x$ and $y$ such that it has the highest concentration around the edge, and resolves the film thickness with at least $20$ mesh points. The mesh at the beginning of the simulation is shown in Figure \ref{mesh_and_ic}. It must be noted that one of the downsides of this type of simulation is that the mesh has to be altered after the film has retracted past the refinement zone.
\begin{figure}[H]
\centering
\includegraphics[width=0.9\linewidth]{mesh_and_ic.png}
\caption{The mesh is shown at the beginning of the static domain simulation, stretched to capture the rim dynamics accurately (top). Initial film profile obtained from extruding 2D results and shifting the fields in the $x$ direction is shown in the bottom.}
\label{mesh_and_ic}
\end{figure}
Initial phase and velocity fields for this simulation are extrusions of 2D simulation results perturbed in the spanwise direction as also shown in Figure \ref{mesh_and_ic}. These perturbations are periodic waves with random small amplitudes and random phases that shift a 2D snapshot in the $x$ direction. Once the instability is triggered, self sustaining shedding phenomena is observed over the long-term simulation.

The evolution of this simulation is shown in Figure \ref{3D_sim_type_1}. Figure \ref{3D_sim_type_2} also shows the $x-z$ plane view of the same images. For visualization, the simulation results are repeated in the span-wise direction in both figures. The temporal order of the panels are indicated with numbers. As shown in these figures, there are multiple steps involved in the shedding of a micro-bubble. First (panel 1,2), a span-wise edge instability causes punctures in the film that was retracting stably in 2D simulations. Next (panel 2), the hole grows such that a gas filament remains at the edge of the film. The gas filament breaks in a manner similar to primary atomization (Ashgriz, 2011), giving birth to mother and satellite bubbles (hardly visible on panel 3). The geometry of the thin film edge is severely disturbed at this stage. We will later demonstrate that this is in fact the norm for a retracting thin gas film, because once the uniform profile is broken, the retraction speed is variable for different points on the edge, depending on the local thickness. The thinner parts of the film retract with a larger speed than the thicker parts, as was explained before, leaving the larger parts of the edge behind. As gas fills the thick part of the edge another rupture occurs (panel 4), leading to another filament and its subsequent break-up (panel 5, 6). Eventually (panels 7-8), the thickest part of the edge is connected to the film via a filament that thins out as the film retracts with higher velocity until it breaks up and leaves a large micro-bubble behind (panel 9). It is clear that this mechanism is very different from how droplets pinch-off from the edge of unstable liquid sheets (Agbaglah \textit{et al.}, 2013).
\begin{figure*}
\centering
\includegraphics[width=0.7\textwidth]{collage6.jpg}
\caption{The time-progression of static domain results for a retracting air film with $Oh=0.072$ in an initially static background of water, with the numbers indicating the order in time. Note that for visualization, the results are copied once in the z direction.}
\label{3D_sim_type_1}
\end{figure*}
\begin{figure*}
\centering
\includegraphics[width=0.8\textwidth]{collage5.jpg}
\caption{A top view of the time-progression of static domain results for a retracting air film with $Oh=0.072$ in an initially static background of water, with the numbers indicating the order in time. Note that for visualization, the results are copied once in the z direction.}
\label{3D_sim_type_2}
\end{figure*}
\subsection{Moving Domain Simulations}
\label{SECmovingdomain}
The requirement for very high aspect ratio films (Equation \ref{requirement_inviscid}) renders static domain simulations expensive. Moreover, as the edge retracts, the mesh has to be modified periodically as to situate the refinement region around the edge. Given the almost constant retraction velocity of these films, it is possible to perform simulations where the frame of reference is moving with ${V}_{OP}$, given by Equation \ref{oguz_prosperetti} plus appropriate small correction as observed in Figure \ref{retraction_speed_all_Oh}. For these simulations we have inflow and outflow boundary conditions in the $x$ direction, while slip and periodic boundary conditions are imposed in $y$ and $z$, respectively. Compared to the static domain simulations, the domain has been abridged in the $x$ direction, but is long enough such that the inflow can be assumed to be given by ${V}_{OP}$ in both phases. For outflow, we use convective boundary conditions. The initial conditions are from the static domain simulations, where we continue simulating the flow around the edge after the events shown in Figure \ref{3D_sim_type_1} and \ref{3D_sim_type_2}. We performed these simulations on different $Oh$ value films, given by $Oh=0.320, 0.224, 0.113, 0.072$, while fixing the density and viscosity ratios. All simulations presented up to this point were from the nominal case, $Oh=0.072$, corresponding to a $h=2\mu m$ film. Snapshots for moving domain simulations of this nominal case are shown in Figure \ref{3D_sim_mm}. Once again, the simulation results are repeated in the $z$ direction for visualization purposes. It is clear that the mechanism for formation of micro-bubbles is further repetition of the static domain simulations. Namely, the thicker parts of the rim retract with a slower velocity than the rest of the film while continuing to grow due to accumulation of air. This relative growth of the thicker parts of the perturbed edge eventually causes puncture in the film. The hole then grows to separate one side of the thick feature. At this stage, the thick feature is connected to the film via a filament and surface tension forces act towards making the feature more spherical or bubble-like. This, in addition to the slower retraction rate of the feature thins the connecting filament until the micro-bubble is separated. In these simulations, since the domain size is smaller in the $x$ direction, we often do not capture a whole micro-bubble at its break-up time. In the following, we analyze the results of these simulations and the steps leading to micro-bubbles in detail. Finally, we conclude this section by studying the effect of varying $Oh$ number.
\begin{figure*}
\centering
\includegraphics[width=0.7\textwidth]{collage_bw_mm_rotated.jpg}
\caption{The time-progression of moving domain results for a retracting air film with $Oh=0.072$ with the numbers indicating the order in time. Note that for visualization, the results are copied once in the z direction.}
\label{3D_sim_mm}
\end{figure*}
\subsection{Edge Instability}
\label{SECedgeinstability}
Initial conditions for the 3D simulations were obtained by extruding 2D results in the $z$ direction and perturbing them by displacing all fields in the x direction (Figure \ref{mesh_and_ic}). As the film retracts, undulations appear on the rim. Figure \ref{undulations} shows how these undulations grow for a perturbed thin air film retracting in water with $h=2\mu m$. The left and right images in Figure \ref{undulations} show before and after the growth of the undulations, respectively. The wavelength of these undulations are about $\lambda=28\mu m$. These undulations start to appear as the thickness of the rim reaches $H\approx9 \mu m$. From Rayleigh-Plateau instability, the smallest unstable wavelength is given by $\pi H\approx28\mu m$ and the maximum growth, as given by Equation \ref{wave_length_RP} happens at a wavelength of ${\pi H}/{0.484}\approx58.3\mu m$. The instability governing a growing rim connected to a thin film is different from a RP instability for a hollow cylinder. Moreover, it is difficult to establish the rim thickness when the linear phase of the instability is active. In Thoroddsen \textit{et al.} (2003), they modeled the rim as a cylinder where $H\approx 2h$ and found the measured wavelengths to match the maximum growth wavelengths for that particular rim thickness. In a similar manner, if we assume that the instability kicks in when $H\approx 2h$, the maximum growth rate would happen at a wavelength of around $26\mu m$, which is very close to the wavelength of the undulations we see in our numerical results. Regardless of these details, it is reasonable to conclude that a Rayleigh-Plateau type capillary instability is responsible for the undulations we see in Figure \ref{undulations}.
\begin{figure}[H]
\centering
\includegraphics[width=\linewidth]{RP_undulations.pdf}
\caption{Growth of undulations from left to right showing how the rim is susceptible to a capillary instability reminiscent of Rayleigh-Plateau instability.}
\label{undulations}
\end{figure}
\subsection{Hole Formation}
From Figures \ref{3D_sim_type_1}, \ref{3D_sim_type_2} and \ref{3D_sim_mm}, we see that the formation of holes in the neck region of the rim is one of the necessary steps for micro-bubble shedding from thin retracting gas films. This is in contrast to how drops pinch off from unstable liquid sheets (Agbaglah \textit{et al.}, 2013) or how ligament or finger break-up leads to drops in atomization processes. Recently, Zaleski \textit{et al.} (2017) performed high fidelity numerical simulations of turbulent two-phase mixing layers and observed that the formation of holes and their rapid growth can also be responsible for generating droplets (primary atomization). For thin gas films at scales relevant to Mesler entrainment, the formation of these holes is critical in the process of micro-bubble shedding, and the thin films will remain semi-stable if such events do not happen.

For small $Oh$ number films such as the nominal case studied here, capillary waves connect the thick rim to the uniform thickness film region. A prominent feature of these waves is a narrow neck region just before the rim connection to the film. This neck region, which is also observable in 2D simulations, can be seen in Figure \ref{capillary_wave} which is showing a typical $x-y$ plane of the thin film from the 3D simulations.
\begin{figure}[H]
\centering
\includegraphics[width=\linewidth]{capillary_wave_sample3.png}
\caption{A sample zoom-in image on the thin gas film, showing the capillary waves and thin neck region of the rim.}
\label{capillary_wave}
\end{figure}
As the rim becomes unstable in the span-wise direction, the neck of the film at different $z$ values attains different axial positions and thicknesses. The superposition of variation of the film thickness due to capillary waves induced by the RP instability with the 2D mechanism that induces the neck results in regions with minimum film thickness that are most hospitable to puncture.
\begin{figure}[H]
\centering
\includegraphics[width=\linewidth]{capillary_wave_3D.png}
\caption{Slices on a snapshot of the thin film prior to hole formation, showing how the interplay between the capillary waves and the film topology can lead to puncture of the film.}
\label{capillary_wave_3D}
\end{figure}
 Figure \ref{capillary_wave_3D} shows a snapshot before a hole is formed indicating variation of film thickness on two perpendicular x-y and y-z planes. This point is where the minimum thickness of the unstable span-wise wave coincides with the minimum thickness region of the film in the stream-wise direction (the film neck), causing film rupture. After such holes are formed, they grow radially outwards until they form a filament at the edge of the film that eventually breaks, resulting in major disturbances to the shape of the rim (Figures \ref{3D_sim_type_1}, \ref{3D_sim_type_2}, \ref{3D_sim_mm}). Such disturbances cause non-uniformity in the thickness of the rim and consequent non-uniform retraction velocities that lead to micro-bubble shedding in the long run.

\subsection{Filament Break-up}
\label{SECfilamentbreakup}
The break-up of liquid filaments plays an important role in combustion and atomization. There have been many studies focused on the non-linear mechanism leading to the formation of mother and satellite drops (Tjahjadi \textit{et al.} 1992, Ashgriz \& Mashayek 1995, Ashgriz 2011). Satellite bubbles have been observed experimentally, especially in the context of the singular process of bubble pinch off (Burton \textit{et al.} 2005, Keim \textit{et al.} 2006, Thoroddsen \textit{et al.} 2007). The dynamics of a thinning gas filament have been found to be significantly different from that of a thinning liquid filament (Burton \textit{et al.}, 2005). Thoroddsen \textit{et al.} (2007) observed the formation of a thin neck as a gas filament becomes very thin. This thin neck attained higher aspect ratios as the viscosity of the liquid was increased. In Gordillo \& Fontelos (2007), the authors performed numerical simulations of the process of separation of two identical bubbles placed in shear flow. Similar to the experiments of Thoroddsen \textit{et al.} (2007), a thin filament formed, which later turned into an elongated satellite bubble. Numerical results in Gordillo \& Fontelos (2007) also revealed that the size of the bubble decreased as the density ratio (${\rho}_{l}/{\rho}_{g}$) was increased, explaining why it is much more difficult to observe satellite bubbles compared to satellite drops. Moreover, the numerical simulations in that work showed that the ratio of the satellite bubbles to the original bubbles (mother bubbles in our case) is of the order of ${10}^{-3}$.

In our simulations, filaments are formed when growing holes in the film approach the rim (e.g. panels 2,5 and 8 in Figures \ref{3D_sim_type_1} and \ref{3D_sim_type_2}). In Figure \ref{zoom-in-filament} a zoom-in on a filament at different times is presented.
\begin{figure}[H]
\centering
\includegraphics[width=\linewidth]{zoom-in-filament.png}
\caption{Gas filament formation and break-up shown.}
\label{zoom-in-filament}
\end{figure}
In all cases we first see an elongated bubble break from both ends, disconnecting it from the rest of the film (middle panel in Figure \ref{zoom-in-filament}). This bubble resembles the elongated drops in liquid jet break-up events (Tjahjadi \textit{et al.} 1992, Ashgriz 2011), and the elongated satellite bubble in simulations of Gordillo \& Fontelos (2007). Surface tension then, gives this bubble a spherical shape, and occasionally satellite bubbles on its sides. We find the diameter of the mother bubble (main bubble remaining from the filament) to be about $1\mu m$ for our nominal simulations ($h=2\mu m$ air film in water). These bubbles are resolved with about 10 cells but their size is not consistent with the predictions of Gordillo \& Fontelos (2007), possibly due to the low resolution in the preceding elongation stage, and also the necessity for including Van der Waals forces to capture such dynamics correctly. In any case, these bubbles are very small and their high dissolution rates render them unimportant to the Mesler entrainment process which is primarily focused on micro-bubbles in the range of $10\mu m-100\mu m$. An important feature we see in our simulation results is the formation of flattened, ragged ends on the locations where the filament was connected to the film (middle and right panels in Figure \ref{zoom-in-filament}). These features were also observed in experiments for low viscosity ambient liquids such as water (Burton \textit{et al.}, 2005, Thoroddsen \textit{et al.} 2007). This topological feature in fact plays an important role in the subsequent formation of holes and bubbles in the film as can be seen in Figure \ref{3D_sim_mm}.

\subsection{Micro-bubble Statistics}
\label{SECmicrobubble}
The main motivation of this work is to understand how micro-bubbles are shed from thin retracting gas films and to gain a predictive capability with regards to their size and rate of production. In this vein, we examine the micro-bubbles that are separated from the thin film as shown in Figures \ref{3D_sim_type_1}, \ref{3D_sim_type_2} and \ref{3D_sim_mm}. Note that by micro-bubbles we do not refer to the very small bubbles remnant from the broken filaments, but rather the larger bubbles that have diameters of $\mathcal{O}(10\mu m)$, such as the bubble formed in panel 9 of Figures \ref{3D_sim_type_1} and \ref{3D_sim_type_2}. So far, in our simulations of the nominal case, we have seen 3 micro-bubbles shed from the thin gas film corresponding to a $h=2\mu m$ thick air film retracting in water. Snapshots showing the separation of the first bubble are provided in panel 9 of Figures \ref{3D_sim_type_1} and \ref{3D_sim_type_2}. The other two micro-bubbles are separated in panels 5 and 13 of Figure \ref{3D_sim_mm}. Table \ref{table_microbubbles} summarizes the statistics regarding these bubbles. The diameter of the bubbles (${D}_{bubb}$), in addition to the time it took them to be shed (${\Delta t}_{bubb}$) is presented in dimensional and dimensionless form in the table. Bubble diameters are obtained from the volume of the bubbles, which can be computed via calculating the volume left in the film at a given time, and by using the known rate of gas entering the domain to determine the amount of gas leaving the film in the form of micro-bubbles.
\begin{table}[H]
\centering
\begin{tabular}{c|c|c|c|c}
Bubble  & ${D}_{bubb}(\mu m)$ & ${\Delta t}_{bubb}(\mu s)$ & ${D}_{bubb}/h$ & ${\Delta t}_{bubb}{V}_{OP}/h$ \\ \hline
1 &  26.7   &    19.9  &    13.35 &  61.4  \\
2 &  31.8   &    10.5  &    15.9  &  32.36 \\
3 &  34.2   &    20.6  &    17.1  &  63.5  \\
\end{tabular}
\vspace{4mm}
\caption{Bubble statistics and time intervals taken for shedding enlisted in dimensional and non-dimensional form.}
\label{table_microbubbles}
\end{table}

Based on the results so far it seems that for the nominal case ($Oh=0.072$), the diameter of the bubbles is approximately given by ${D}_{bubb}\approx15h$, as evident from the fourth column of Table \ref{table_microbubbles}. Interestingly, the interval for their shedding is not necessarily similar as can be seen from the third and fifth columns of the table. These simulations are still in progress, and by capturing more bubbles we can obtain reliable statistics, from which we can draw conclusions regarding the bubble size distribution and shedding rates from this film.
\subsection{Dependence on Ohnesorge (Oh) Number}
For a water-air system, only one dimensionless number is required to parameterize the thin retracting gas film. We have chosen the Ohnesorge number ($Oh$) for this purpose. By changing the viscosity values of both phases while maintaining the viscosity ratio, we are able to alter $Oh$ and study its effect on the 3D dynamics of the film. So far we have presented 3D results for the nominal case, with $Oh=0.072$, which corresponds to a $h=2\mu m$ air film retracting in water. We use the same mesh and moving domain as the nominal case for all $Oh$ value simulations. The initial conditions and the boundary conditions are also the same as the nominal case. In particular, given the weak dependence of the retracting velocity on viscosity, the inflow velocity is the same for different $Oh$ value simulations. In Figure \ref{3D_sim_oh113} simulation results for $Oh=0.113$ are shown. This case corresponds to a $h=800nm$ air film in water and the initial conditions are the same as the nominal case moving domain simulation (Figure \ref{3D_sim_mm}). In Figure \ref{3D_sim_oh113}, a comparison of the evolution of the $Oh=0.113$ and $Oh=0.072$ films (on the left and right, respectively) is shown at the same non-dimensional times.
\begin{figure}[H]
\centering
\includegraphics[width=0.8\linewidth]{collage_113_vs_072_cropped_rotated.png}
\caption{The time-progression of moving domain results for retracting air films with $Oh=0.113$ and $Oh=0.072$ on the left and right respectively. Note that for visualization, the results are copied once in the z direction.}
\label{3D_sim_oh113}
\end{figure}
It seems that that viscous forces are more dominant in the $Oh=0.113$ simulations compared to the nominal case with $Oh=0.072$. These effects reduce the amplitude of the capillary waves (also observed in 2D, Figure \ref{2D_profiles_oh_113_32}) and make the interface smoother in general. Based on the mechanism explained for hole formation, holes are formed with less frequency in higher $Oh$ films, as can be seen in Figure \ref{3D_sim_oh113}. This may explain why these holes have not been explicitly observed in experiments where more viscous fluids are used to visualize microbubble shedding (Thoroddsen \textit{et al.} 2012). Moreover, the filaments are thicker for these films and seem to be more robust, causing delay of break-up and micro-bubble shedding. While the simulation is running, based on the volume in the film and the amount of time passed we have found a lower bound for the size of the micro-bubble resulting from the $Oh=0.113$ film:
\begin{equation}
{D}_{bubb,Oh=0.113}>18.4h
\label{Oh113_bubb_size}
\end{equation}
For a water-air system, the film thickness would be $800nm$, meaning that this micro-bubble has at least a diameter of $15\mu m$. We know from experiments that even thinner films result in micro-bubbles in the range of $10-100$ microns (Thoroddsen \textit{et al.}, 2012), therefore we expect ${D}_{bubb}/h$ to increase as $Oh$ is increased. Based on Equation \ref{Oh113_bubb_size}, our simulations are so far in line with this expectation. This simulation is also currently in progress, in addition to more expensive simulations at $Oh=0.226$ and $Oh=0.320$. By covering this wide range of $Oh$ numbers, we can deduct scaling laws and propose models for micro-bubble shedding from thin retracting gas films.

\section{Conclusions}
\label{SECconclusions}
In this work, we presented high resolution 2D and 3D numerical simulations of very long and thin retracting air films surrounded by water. For this pair of working fluids that are of interest for naval applications, the only parameter controlling the evolution of the film is its thickness. By fixing the density and viscosity ratios to match those of air and water, we studied the effect of the film thickness by varying the Ohnesorge ($Oh$) number of the film in the range of $0.072\le Oh\le 0.32$, corresponding to film thicknesses of $100nm\le h\le 2\mu m$ which are relevant based on drop-pool experimental measurements. From our 2D simulations we observed that bubbles do not shed from the gas films and 3D mechanisms must be responsible for micro-bubble shedding from thin gas films entrapped in drop-pool experiments. We also found that contrary to thin liquid films, the retraction speed of thin gas films does not reach a steady value and decreases with time as the rim becomes thicker. Based on the found retraction speed power law, we discovered that the 2D edge follows a similarity shape as it grows. Moreover, these 2D simulations enabled us to study the dependence of the rim shape and retraction speed on $Oh$ number. We found that in the range of $Oh$ numbers we studied, viscous effects do not cause significant variations in the two-dimensional dynamics. We then provided scaling arguments and referred to experiments to show that a capillary instability similar to the Rayleigh-Plateau instability can act upon the growing rim of these thin films if they have very high aspect ratios (long and thin films). Our 3D simulations confirmed this analysis, and showed that span-wise undulations appear on the rim of the film that cause puncture of the film. These rapidly growing holes distort the shape of the rim significantly and the slower retraction speed of larger parts of the rim eventually leads to their separation from the film, in the form of micro-bubbles. The process of micro-bubble shedding was thus found to be different from fragmentation of liquid films. These micro-bubbles were found to have diameters of around $15$ times the thickness of the film for $Oh=0.072$. Simulations at $Oh=0.113$ revealed that viscous effects delay hole formation by reducing capillary waves around the rim, resulting in larger bubbles with respect to the film thickness. In other words, our simulations indicate that micro-bubble size is a sub-linear function of film thickness. The 3D simulations are still in progress, from which we will be able to extract scaling laws and models that can be used for subgrid-scale modeling of micro-bubbles in practical two-phase simulations of flows around naval vessels.

\section{Acknowledgements}
\label{SECacknowledgements}
This work was supported by Office of Naval Research (Grant No. 119675). The authors gratefully acknowledge discussions and comments by Prof. Bud Homsy on an earlier version of our results.

redpajama_set_name: RedPajamaArXiv


Czech Koruna will gradually become cheaper. At least on the graphical analysis it is clearly visible. Although, I must pay tribute to the crown: for the countries of the former Soviet bloc, she looks very well and cheerfully. In any case, it is necessary to work with stop orders and not to give everything in one transaction.
Consider the graph in the time interval. The currency pair CHF/CZK is in a narrow channel between the support levels and 22,59 22,54 actively trying to break through the lower boundary of the channel.The indicator RSI is almost at the 50 mark. The makd indicator indicates a weak upward movement of prices. On H4 the situation is something different, and to makd have the opportunity to get in purchase to the resistance level of 22,57 and it will be a small profit, then it can be fixed.
The currency pair CHF/CZK on the hourly chart went down, breaking through the resistance level 22,805 with a successful break below this level. The indicator RSI is in area below 50. The makd indicator indicates a weak downward price movements. While you should refrain from work for the couple until a more favorable market conditions. On the H4 to be sideways and yet it continues. Indicators go to the neutral zone.
Analysis CHF/CZK on the hourly chart. The price for this pair turned North from a level of support 22.601. Moving on the chart is in the oversold pair. Arrow indicator indicators and bill Williams gave signals to buy the pair. There is a possibility of price movement to the North from a level of support to level 22.746 mark.
thirty minute bars expect the southern movement of the pair.
On the daily chart, CHF/CZK formed a double bottom that will support the buyers in their attack on the enemy's defenses. The percent of Williams indicate bullish divergence. Our assumptions: prices will continue to rise against the market from the current level 22.553 with the aim of breaking up the resistance level of bullish 22.636.
Analysis CHF/CZK on the hourly chart. The price for this pair is at the resistance level 22.614. Moving on the chart located in the overbought zone pair. Arrow indicator indicators and bill Williams gave a signal to sell the pair. There is a possibility of price movement to the South from the resistance level to the level at 22.527.
Analysis CHF/CZK on the daily chart for longer term trading. The price for this pair turned North from the support level of 22.521. Moving on the chart is in the oversold pair. Arrow indicator indicators and bill Williams gave signals to buy the pair. There is a possibility of price movement to the North from a level of support to the level at 22.848.
Analysis CHF/CZK on the hourly chart. The price for this pair is at the resistance level 22.794. Moving on the chart located in the overbought zone pair. Arrow indicator indicators and bill Williams gave a signal to sell the pair. There is a possibility of price movement to the South from the resistance level to the level at 22.652.
Consider the graph in the time interval. The currency pair CHF/CZK went down breaking the support level 22,686 with a successful break below this level. The indicator RSI is almost at the level of 23.6, which indicates that sales begin. The makd indicator indicates a strong downward movement of prices. On H4, MACD has entered the zone of purchases and costs to consider the sale of small lots.
Analysis CHF/CZK on the hourly chart. The price for this pair is at the resistance level 22.723. Moving on the chart located in the overbought zone pair. Arrow indicator indicators and bill Williams gave sell signals. There is a possibility of price movement to the South from the resistance level to the level at around 22.617.
Analysis CHF/CZK on the hourly chart. The price for this pair turned South from the new resistance level 22.793. Moving on the chart located in the overbought zone pair. Arrow indicator indicators and bill Williams gave sell signals. There is a possibility of price movement to the South from the resistance level to the level at 22.647.
Analysis CHF/CZK on the hourly chart. The price for this pair turned North from a level of support 22.531. Moving on the chart is in the oversold pair. Arrow indicator indicators and bill Williams gave signals to buy the pair. There is a possibility of price movement to the North from a level of support to the level at 22.604.
Analysis CHF/CZK on the hourly chart. The price for this pair turned South from the resistance level 22.6222. Moving on the chart located in the overbought zone pair. Arrow indicator indicators and bill Williams gave a signal to sell the pair. There is a possibility of price movement to the South from the resistance level to the level at the level of 22.552.


Sweet, juicy fruit is refreshing, tasty and satisfying. However, I'm so disappointed when I open up an orange and it is dry and tasteless. Or, when I expectantly cut into a cantaloupe and find out it is hard and almost bitter. So disappointing. I was anticipating a sweet, juicy cantaloupe – instead, I wasted my money.
The outside can appear good. It can smell okay when it is surrounded by good fruit. But, when you open it up, there is no substance.
Not only were you chosen for a particular place, time and job, but you were appointed. Think about this.
So many times we (me included) are either waiting for that perfect time, wishing we were somewhere else or had what others had that we miss the appointments God has for us now. When God appoints us, He also prepares hearts and provides for us – nothing happens by accident.
One day a couple of years ago, I was in Mardels buying a Jesus Calling book for my doctor. While there, I felt a very strong urge to purchase two additional copies for my doctor's office assistants. I didn't feel they would receive them well but sensed God was directing me to purchase them anyway.
The following day at the doctor's office I handed each assistant a gift bag with the books and waited for my appointment.
You see, I was chosen and appointed. It was not about me. It was about God and His Kingdom.
I can't just appear good on the outside – act like a Christian. I have to be obedient to the Father and respond to His leading.
I also know that the fruit He is producing in these two assistants may take time, but they do know that God is real.
1. What has God chosen for you?
2. Is your appearance deceiving?
3. How good is your fruit?


text:
Book Review: Hella by David Gerrold
Title: Hella
Author: David Gerrold
Publisher: DAW
Source: Review copy courtesy of the publisher via NetGalley
Rating: 3.5 out of 5.
A master of science fiction introduces a world where everything is large and the problems of survival even larger in this exciting new novel.
Hella is a planet where everything is oversized—especially the ambitions of the colonists.
The trees are mile-high, the dinosaur herds are huge, and the weather is extreme—so extreme, the colonists have to migrate twice a year to escape the blistering heat of summer and the atmosphere-freezing cold of winter.
Kyle is a neuro-atypical young man, emotionally challenged, but with an implant that gives him real-time access to the colony's computer network, making him a very misunderstood savant. When an overburdened starship arrives, he becomes the link between the established colonists and the refugees from a ravaged Earth.
The Hella colony is barely self-sufficient. Can it stand the strain of a thousand new arrivals, bringing with them the same kinds of problems they thought they were fleeing?
Despite the dangers to himself and his family, Kyle is in the middle of everything—in possession of the most dangerous secret of all. Will he be caught in a growing political conspiracy? Will his reawakened emotions overwhelm his rationality? Or will he be able to use his unique ability to prevent disaster?
Hella is a hella big place. It's a large planet where, due to lower gravity as compared to Earth, living things grow to crazy huge size. And there are dinosaurs. And they're HELLA gigantic. Herbivorous leviathans migrate across the plains, slowly stomping over everything in their path, and hungry carnosaurs attack them in groups, feasting for days on the huge carcasses that they manage to bring down.
Hella is not the most hospitable environment for humans, but these few thousand colonists are there to make it home. It's already been a hundred years since the First Hundred made landfall, and since then, additional migrations of humans have helped the colony to grow and expand.
Caution is the highest priority. Everything is studied and planned for, because it's crucial that the human population avoid cross-contamination with the Hella natural world. All food is grown within the enclosed colonies, and care is taken never to allow human-produced microbes or plants out into the planet's own natural environment.
We get to know the world of Hella through main character Kyle, a neuro-atypical teen (roughly 13 years old in Earth years, or 5 years old in Hella years). Kyle is smart and detail-oriented, devoted to his family, but has challenges understanding nuance and reading other people's emotions, doesn't like to be touched, and is unable to leave a topic until he's shared everything (and I do mean EVERYTHING) he knows about it. He's gifted and his talents can benefit the colony, but there are some who view Kyle as a freak and treat him that way.
While the colony seems to function on the principle of communal service toward the greater good, there are those who thirst for power, just like in any human society. When the chief power-hungry representative gets an opportunity to seize control, he takes it.
Hella is an interesting book, although I have some issues with it. At the beginning, the focus is on getting to know the planet and the colony. Kyle goes out on an expedition for the first time, and through his experiences, we get to see the plants, trees, strange creatures, and huge dinosaurs that roam the land.
We're also introduced to the daily routines, the concept of work that's at the foundation of this human society, and the myriad factors that go into maintaining safety and self-sufficiency.
We learn more about how human society has changed and evolved over the years since our own time as well. For example, gender is fluid and easily changeable. Kyle's mother was born biologically male, but changed to female so she could experience pregnancy (which is in itself a fairly unusually choice, as many people prefer to have their babies bottle-grown rather than womb-grown). Kyle himself was born biologically female, but decided to change when his older brother did, largely because he too wanted to be able to pee standing up. Changing doesn't have to be permanent; later in the book, Kyle has cause to rethink his decision and considers changing again in order to please his boyfriend (which is a frustrating reason to change, but fortunately, his boyfriend sees it that way too.)
By the second half of the book, the emphasis is less on the natural world outside the human habitats and much more on the political maneuvering within the human colony. There's a conspiracy afoot, and Kyle and his friends may be in the best position to try to stop it. There's plenty of danger and excitement as they chase through tunnels, hack networks, and try to avoid or defeat the bad guys.
My feelings about Hella are mixed. First off — cool planet! I really liked learning about this world, its dangers and its beauty, and what it takes for humans to adapt and survive there.
But, there's just so much time spent with Kyle on the details! Granted, this is a piece of who Kyle is, but his need to go down the rabbit hole chasing every detail doesn't always make for great reading, and I felt that the plot tended to bog down in detours.
At almost 450 pages, this book is longer than it needs to be. I think if 50-75 pages had been trimmed, the pacing might have improved, keeping the plot more on track and letting momentum build. As is, I didn't truly feel caught up or swept along by the story until the 2nd half, and that's too bad, as there are elements of a great story here.
As I said, I did really enjoy the (literal) world-building the author accomplishes in introducing us to the human society in this large and frightening world, and explaining how they find ways to improve their resources bit by bit, even while always protecting themselves from the dangers just outside their fences.
I was a bit startled looking at the author's Goodreads profile when I realized that some of the characters in Hella appear in his earlier works. This made me wonder how much I was missing and whether a familiarity with other books would enhance the reading experience.
This is me being persnickety, but the author's writing style got on my nerve in places. He has a tendency to throw commas into sentences to connect clauses. Random example:
Outside, the northeast slope was a rumpled landscape, hundreds of layers of lava flows had hardened here.
Just a little pet peeve of mine. Use a period! Separate your sentences! Or, you know, give semicolons a try!
Hella has a conclusion that ties up the major action of the story, but there's certainly room for more storytelling about the colony, its people, and its politics — plus, it would be fun to get to see what happens next for Kyle, his family, and his friends.
I do recommend Hella, but wished that it was just a little tighter and faster overall. Still, it's a fun and engaging story set in a really fascinating world, and I'm glad I read it.
2020 new release, book review, dinosaurs, human space travel, life in space, new planets, science fiction, space colonization, space exploration	5 Comments
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5 thoughts on "Book Review: Hella by David Gerrold"
I had no idea that he's written about some of these characters before. Interesting! You and I had very similar thoughts, and I agree, a lot could have been shaved off to make the pacing better.
When I looked at his Goodreads page, I saw that he's written about HARLIE before, and that Charlie and his family have a couple of books about them as well. I didn't look at everything, but I do wonder whether other characters appear in earlier books too!
I like the premise. I like imagining different worlds. Great title. See how I'm using periods? 😉 (I agree with you!)
I'm glad I'm not alone! It felt like a picky thing to mention, but he uses commas that way throughout the book, and it made me a little batty.
I get that 🙂

redpajama_set_name: RedPajamaCommonCrawl


Rajiv Gandhi International Airport is the only airport in Hyderabad. It is also referred to as Shamshabad Airport and can be reached from the heart of the city traveling about 22 kms. This airport has been made as a replacement for Begumpet Airport for the convenience of the passengers.
The airport was inaugurated on 23rd March 2008 and marked the beginning of its operation with receiving a flight from Frankfurt at 12.25. Smt. Sonia Gandhi had cut the ribbon to mark the process of inauguration at the airport. She was accompanied by the Chief Minister Late Dr. Y. S. Rajasekhara Reddy and Minister of Civil Aviation Mr. Praful Patel.
The Hyderabad International Airport is India's first green-field airport. And as per public-private partnership in the area of airport infrastructure is concerned, it occupies second position after Cochin International Airport.


text:
Tag Archives: Rob Witcomb
THE WIND IN THE WILLOWS
New Vic Theatre, Newcastle under Lyme, Saturday 24th November, 2018
This brand-new adaptation of Kenneth Grahame's classic children's novel is written by the New Vic's genius-in-residence, Theresa Heskins, and is directed by Peter Leslie Wild. It bears all the hallmarks of a great New Vic Christmas show, with the Workshop and technical crew all flexing their creative muscles to translate fantastic worlds onto the stage. And so, Laura Willstead's set has painted branches, like illustrations, and sprigs of greenery draped all around. Tree trunks made of cloth descend from above, like roots probing into soil, to create the Wild Woods… while Lis Evans's Edwardian costumes give us the pre-WWI period while emphasising the anthropomorphism of Grahame's characters; ears on hats and tails protruding from trouser seats are all that differentiate species.
With original music by Matt Baker, performed by the cast, the story unfolds, beginning with Alicia McKenzie's inquisitive Mole setting off on adventure. She encounters Richard Keightley's dapper Ratty and their voyage in his boat is positively lovely, with Daniella Beattie's lighting and projections creating a captivating illusion. Emma Manton's Badger, younger and more female than is traditional, is schoolma'am-ish and forthright, but it's Matthew Burns's long-suffering Horse who delights the most. Burns later appears as a cheerfully macabre Jailer, when Rob Witcomb's ebullient Toad falls foul of the Law.
This Toad is sweet-natured despite his manic obsessions. Witcomb makes him more of an Ed Balls figure than a Boris Johnson, while Kieran Buckeridge's villainous Fox is more exploitative and, yes, more than a bit scary. Even scarier is Sophia Hatfield's strident Mrs Otter; you would not like to tangle with her.
The whole enterprise is played with exuberance by the talented ensemble. Their choral singing is enough to melt your heart. Peter Leslie Wild's direction keeps things moving, and very much in the New Vic in-house style, with cast members holding up shelves, car wheels and so on, to keep the scenery flowing. The sequence involving the train is breath-takingly executed, a remarkable piece of physical theatre.
Heskins tweaks the ending a little to give us a timely nudge in these dark days of austerity and isolationism. Wealth is better shared, Toad demonstrates, better when it's put to use creating opportunities for the marginalised. It's subtly done, augmenting the heart-warming feelings the show has engendered from the start.
Cosy, charming and consistently amusing, this is a family show that makes you feel as warm and fuzzy as the woodland creatures it portrays.
A car getting toad. Rob Witcomb, poop poop!
Leave a comment	| tags: Alicia McKenzie, Daniella Beattie, Emma Manton, Kenneth Grahame, Kieran Buckeridge, Laura Willstead, Lis Evans, Matt Baker, Matthew Burns, New Vic Theatre, Newcastle under Lyme, Peter Leslie Wild, review, Richard Keightley, Rob Witcomb, Sophia Hatfield, The Wind in the Willows, Theresa Heskins	| posted in Review, Theatre Review
39 Steps to Heaven
The REP, Birmingham, Tuesday 1st March, 2016
Having only recently ended its West End run of almost a decade, one of my favourite shows comes to town for a week in this exuberant touring production; I am delighted to have the chance to see it again and be tickled by its silliness and comic invention.
This is a show that celebrates theatricality – it wallows in it, in fact, archly satirising its own artificiality while at the same time making us marvel at the skills and cleverness involved to pull off its tricks and stunts. The script is by Patrick Barlow, adapted from an original concept by Simon Corble and Nobby Dimon (I believe I saw the show's first incarnation many moons ago) but the spark that generated the show is the John Buchan spy thriller as distilled through the cinematic eye of Alfred Hitchcock. (The show is peppered with references to Hitch's films, for added laffs).
But you don't need to know all that in order to enjoy yourself. This is quite simply one of the funniest shows it has ever been my pleasure to witness and, I'm pleased to say, its ability to amuse does not diminish with repeated viewings. The inventiveness of director Maria Aitken is still admirable – the audience gasps at the cheeky breaking of the fourth wall, and the speed at which the ideas keep coming. Part of the enjoyment comes from seeing how the effects are pulled off; another part is appreciation of the performers. The success of each flash of brilliance is dependent on the skill and unflagging energy of the cast of four, a versatile quartet whose verve and comic timing keep the show running like well-oiled, overwound clockwork.
Olivia Greene plays three of the female roles, ranging from a Germanic femme fatale, to a lonely Scottish farmer's wife, and the platinum blonde love interest Pamela. If anyone says women can't be funny they have never seen this show (or crawled out from under their rock).
Andrew Hodges and Rob Witcomb work devilishly hard as Man 1 and Man 2 – providing all the other characters, sometimes at the switch of a hat (miraculously, no hats are dropped during the high-speed changes). As a double act or working singly, this pair are breath-takingly good. Broad characterisations, quick changes, vocal dexterity and accomplished physical comedy, these two have them all. In spades. And so does Greene. And so does the man of the match, our hero Richard Hannay – I squealed in excitement to learn that Richard Ede has returned to the role I think he was born to play. Tall and dashing (literally, for the most part) Ede consolidates his status in my view as the funniest man in British theatre. Hardly ever off, Ede hurtles around the stage, jumping from train roof, falling from railway bridge, climbing a cliff face, or just pelting through the Scottish countryside. You can't take your eyes off him in case you miss a reaction. Utterly charming and relentlessly hilarious, Ede is supported by an equally talented cast – every cog in the clockwork relies on others in order to do its job – and a production that is unerringly laugh-out-loud funny.
An unadulterated joy.
Not to be mist! Olivia Greene and Richard Ede (Photo: Dan Tsantilis)
Leave a comment	| tags: ALfred Hitchcock, Andrew Hodges, John Buchan, Maria Aitken, Olivia Greene, Patrick Barlow, review, Richard Ede, Rob Witcomb, Simon Corble and Nobby Dimon, The 39 Steps, The REP Birmingham	| posted in Theatre Review


LEGAL ISSUES: IBNA members can get free answers to questions concerning open meetings, public records, and court proceedings. IBNA is also a First Amendment Member of the Iowa Freedom of Information Council.
AWARDS: IBNA recognizes outstanding work done by its members. During the annaul IBNA convention, an awards banquet is held to honor news reports in several categories. IBNA also awards the Jack Shelley Award, given to someone who has made substantial contributions to electronic media journalism in Iowa. Money raised through the contest is used to support IBNA activities.
SCHOLARSHIPS: IBNA is committed to helping aspiring electronic media journalists. Each year at the annual convention, the IBNA Grant Price Scholarship for $1,000 is awarded to a student from one of Iowa's colleges or universities.
GET INVOLVED: The major event for IBNA is its spring convention, a time for electronic media journalists and others from across the state to gather and discuss issues, get performance tips, socialize and meet newsmakers. Active members vote on issues brought up at the annual meeting and elect members to serve on the IBNA Board of Directors.


text:
Hote Hote Pyaar Ho Gaya ist ein Bollywood-Liebesfilm von Firoz Irani aus dem Jahr 1999.

Handlung
Pinky und Atul alias Bunty haben sich im College verliebt und wollen nun ihr Leben gemeinsam verbringen. Doch deren Eltern haben ganz andere Pläne mit den beiden: Pinkys Vater hat bereits einen ehrlichen Polizisten Arjun als würdevollen Schwiegersohn ausgewählt. Auch Buntys Vater will Shobha, die Tochter eines Familienfreundes, zur Schwiegertochter.

Pinky und Bunty können die arrangierten Ehen nicht verweigern, da Bunty enterbt und Pinky verstoßen würde. Es gibt keinen anderen Ausweg als der Heirat mit den jeweiligen Partnern zuzustimmen, jedoch wollen sie Arjun und Shobha derart verärgern, dass sie sich freiwillig scheiden lassen wollen.

Dies erweist sich als schwieriger als gedacht, denn Arjun und Shobha zeigen sich sehr verständnisvoll und überschütten sie mit ihrer Liebe. Doch irgendwann sind auch sie mit der Situation überfordert, dass sie sich wirklich scheiden lassen wollen.

Für Pinky ändert sich alles, als Arjun ihr Leben rettet und sein eigenes aufs Spiel setzt. Nun begreift sie, was sie tief in ihrem Herzen für Arjun empfindet. Auch Bunty fällt Shobha entschuldigend in die Arme.

Musik

Weblinks

Filmtitel 1999
Indischer Film
Liebesfilm

redpajama_set_name: RedPajamaWikipedia


Updated for bosh-release v183 (1.3010.0).
BOSH provides the Cloud Check CLI command (a.k.a cck) to repair IaaS resources used by a specific deployment. It is not commonly used during normal operations; however, it becomes essential when some IaaS operations fail and the Director cannot resolve problems without a human decision or when the Resurrector is not enabled.
The Resurrector will only try to recover any VMs that are missing from the IaaS or that have non-responsive agents. The cck tool is similar to the Resurrector in that it also looks for those two conditions; however, instead of automatically trying to resolve these problems, it provides several options to the operator.
In addition to looking for those two types of problems, cck also checks correct attachment and presence of persistent disks for each deployment job instance.
Problem 1 of 1: VM with cloud ID `i-914c046a' missing.
1. VM with cloud ID `i-914c046a' missing.
Note on current behaviour: cck will not wait for all release job processes to start.
Delete VM reference: the Director will not create new VM in its place. If cck is run again, it will not report that VM is missing since it's not expected to exist. Running bosh deploy after cck will backfill missing VMs.
In the above example options 3 was picked and VM reference was deleted.
Problem 1 of 1: dummy/0 (i-914c046a) is not responding.
1. dummy/0 (i-914c046a) is not responding.
Delete VM reference: the Director will not create new VM in its place. If cck is run again, it will not report that VM is unresponsive since it does not exist. Running bosh deploy after cck will backfill missing VMs.
In the above example options 4 was picked and VM reference was deleted.
Consider using cck interactively because the selected resolution will be applied to all problems that are found. Specifying --recover can be risky if new, unexpected problems occur while you run the command and selected resolution may no longer be appropriate.
Assuming there was a deployment with a VM, somehow persistent disk got detached.
Record shows that disk 'vol-549f071f' should be mounted on i-4fcd99b4.
Not mounted in any VM.
Reattach disk to instance: the Director will reattach persistent disk to the VM and mount it at its usual location /var/vcap/store.
Note on current behaviour: Release job processes will not be restarted when persistent disk is remounted.
Reattach disk and reboot instance: the Director will reattach persistent disk to the VM and reboot it so that Agent can safely mount persistent disk before starting any release job processes.
Note on current behaviour: cck will not wait until VM reboots and restarts all release job processes.
Assuming there was a deployment with a VM, somehow persistent disk got deleted.
Note: Not all CPIs implement needed functionality to determine if disk is missing. Those CPIs will report missing disk as Persistent Disk is not attached problem; however, both reattaching resolutions will fail since persistent disk would not be found.


Earache Records has announced the signing of British guitar virtuoso Ol Drake to a multi-album, worldwide recording deal.
Ol Drake is currently working on his debut solo album, which is due to be released in 2014 under the project name of OLD RAKE and is set to include a number of guest musicians.
Ol Drake comments: "Very excited to announce signing a solo deal with Earache Records.
"I established a great friendship with the guys at Earache over the years while I was with EVILE and I was happy to hear they wanted to work with me in a solo capacity.
"This will be a studio project entitled 'OLD RAKE.' I won't be touring, and I'm thankful to Earache for being understanding of this and for giving me this opportunity; I wouldn't rule out doing a few clinics here and there though.
"I've always been inspired by Steve Vai, and I've always wanted to do something in a similar approach orientated around metal with injections of other styles and ideas which interest me.
"After recently seeing the film 'Not Dead Yet' about the amazing and inspiring genius Jason Becker, it really kicked me into gear to do something with my playing; music is all I can really do, so I'm thankful for the opportunity and ability to still create music for people to hear.
"Looking forward to getting the music out there!"
Ol Drake made his name as lead guitarist for Huddersfield thrashers EVILE, during which time the band released four critically-acclaimed albums, scored a Top 10 album in the U.K. Rock charts, toured around the world with such high-profile bands as MEGADETH, and won numerous accolades, including a prestigious Metal Hammer Golden Gods award.
In 2010, Ol Drake was asked to join Australian comedian/musician Tim Minchin on stage at the U.K.'s Sonisphere festival to help perform his track "Rock N Roll Nerd", and in 2012 was nominated in the "Dimebag Darrell Shredder" award at the Metal Hammer Golden Gods, alongside the likes of Devin Townsend and FEAR FACTORY's Dino Cazares.


Why Bootstrap My Life Will Help You Launch a Life That Matters.
Do you ever worry that your life won't amount to much?
But they don't have to be your reality, *if you're willing to address them head on.* You can use those fears to drive you to launch a life that matters.
A rich life. One where you love your work and are well-known for the massive value that you create for others.
Sign up for email updates and get step-by-step training on how to launch your life that matters.
Just enter your email and click "Bootstrap Me!" below.
I'm Ryan Ferrier, the founder of Bootstrap My Life. I help young people invest in themselves professionally so that they can get paid more, do work that they love, and create value for others. Before starting Bootstrap My Life, I was a cofounder or early team member at 3 successful startup companies. My companies have been acquired by Microsoft and Zynga. As a startup operator and executive, I have hired literally hundreds of people as employees and contractors. I also currently serve as an advisor to some of Silicon Valley's top startups on their business operations and hiring strategies. **But before all of that, I was broke, unemployed, and not sure what I was going to do with my life.** Within four years, I went from unemployed to an internet executive. And here's the crazy thing (actually 3 crazy things): – I do NOT have an MBA – I was a Studio Art Major.
- I do NOT have technical chops – I am an IT guy's worst nightmare.
- I was NEVER a part of the HighQ club – no witty comment needed here. I started BML because I am convinced that radical professional (and personal) transformation is possible. I've seen it in my own life. BML teaches the exact strategies that I used to bootstrap my professional life. As well, it provides inside information on what employers and potential clients look for when making hiring decisions. Learn these strategies to bootstrap your own professional life.


Mittermeier claims the public should never have taken the video literally. However, it's apparent people took it literally because it was presented as a simple message: Blame climate change for this bear's suffering.
The post The Real Story Behind The Starving Polar-Bear Video Reveals More Manipulation appeared first on The Global Warming Policy Forum (GWPF).


for your consideration Eugenio Escudero 1950's set of 6 Manta Ray style Dinning chairs in Black lacquer wood with original upholstery Change of upholstery can be done at no extra charge. Customer to provide the upholstery.
Good. Wood restored. Original upholstery can be replaced upon request..


Framo has personnel and equipment in strategic locations all over the world and can mobilize at very short notice. We have been in charge of operations that were only possible to complete with our systems and expertise, and we have recovered cargos written off as lost by customers. We have drained tanks on vessels listing and vessels about to break apart or sink, and we have recovered cargos congealed in the tank and impossible for standard pumps to handle.
In 2005, the Thunderhorse platform was abandoned due to an approaching hurricane while still under commissioning. Meanwhile, a leakage flooded one side of the platform, causing it to list heavily. This was observed once the hurricane cleared, and Framo Houston provided 15 pump sets and a team of experts to stop the listing which would have eventually caused the platform to capsize and sink.


and deb targets to Makefile.in generated by automake.
Now autopack subproject is started therefore I aborted my "pm".
The idea is "Don't write a parser, don't write perl scripts".
You can get the infomation in Makefile.am without parser.
Put "GNUMakefile" into project root directory.
I've put "GNUMakefile" at the end of this file.
You'll get header file paths referred from the project.
"/usr/X11R6/include" :subdir gtk  ".." "/usr/include/glib-1.2"
Of course, you can change lisp style to XML.
### Use this program under the term of GNU GPL.