text:
\section{Introduction}

Onsager's theory for irreversible processes provides a formal framework for
non-equilibrium phenomena as diffusion, electrokinetic effects, and heat
conduction. The phenomenological equations relate thermodynamic fluxes to
forces, for example heat flow to a temperature gradient, or diffusion to a
concentration gradient. Intriguing physical properties arise from the
cross-terms, such as thermally driven electric currents. Onsager established
reciprocal laws between conjugate cross-coefficients \cite{Ons31}, thus
completing Thomson's derivation for the thermoelectric effects and showing
why the Seebeck and Peltier coefficients $\Pi $ and $S$ differ merely by a
temperature factor, $\Pi /S=T$ \cite{deG84}.

As another classical example, the Soret and Dufour effects describe the mass
transport in a temperature gradient, and heat flow due to a concentration
gradient. There is, however, a long-standing discussion whether, and
eventually under which conditions, the corresponding \ coefficients obey a
reciprocity relation. Thus it has been pointed out that the reciprocal laws
impose rather strong conditions on the choice of fluxes and forces, which
are not always easily verified \cite{Col60}.

The Soret and Dufour effects are often discussed in terms of Onsager's
phenomenological equations for the heat and particle currents with
cross-coefficients $L_{1Q}^{\prime }$ and $L_{Q1}^{\prime }$. It is then
\textit{assumed} that the measured thermal diffusion and Dufour coefficients
$D_{T}$\ and $D_{F}$ correspond to $L_{1Q}^{\prime }$ and $L_{Q1}^{\prime }$%
, such that the reciprocity relation for the latter applies equally well to
the former. This approach has been taken by various authors, when discussing
binary gases \cite{Ras66}, organic liquids \cite{Har13}, molecular isotope
mixtures \cite{Mor80}, premelting solids with colloidal inclusions \cite%
{Pep09}, and far-from-equilibrium systems \cite{Ge14}.

Available experiments do not provide clear evidence for or against this
assumption. Comparing thermal diffusion and Dufour data for gas mixtures,
suggests qualitative agreeement \cite{Ras66}. Regarding liquids, $D_{T}$\
and $D_{F}$ seem to agree well for mixtures of cyclohexane and
carbon-tetrachloride \cite{Ras70,Hor78}, yet significant discrepancies were
reported for benzene-cyclobenzene and other systems \cite{Ras70}. In recent
years the Soret effect of colloidal suspensions has been investigated in
great detail \cite{Wie04,Iac06,Seh14,Wue10}; unfortunately, there is a lack
of corresponding Dufour data. Molecular dynamics simulations show a good
agreement of the thermal diffusion and Dufour coefficients, at least for
simple model systems \cite{Mac86,Pao87,Mil13,Arm14}.

Here we discuss the validity of the reciprocity assumption for $D_{T}$\ and $%
D_{F}$ on the basis of non-equilibrium thermodynamics. We consider regular
systems where Onsager cross-coefficients are identical, e.g., $%
L_{1Q}^{\prime }=L_{Q1}^{\prime }$. Then the title of this paper reduces to
the question whether, and eventually under which conditions, thermal
diffusion is described by $L_{1Q}^{\prime }$. This is formalized in Sects. 2
and 3, where we define $D_{T}$\ and $D_{F}$, and present Onsager's
phenomenological equations. In Sect. 4 we discuss the case where the entropy
production is given by the vector fluxes, i.e., by the heat flow and
particle currents. In Sects. 5 and 6 we add chemical reactions and viscous
effects; the corresponding contributions to $D_{T}$ are evaluated for the
examples of micellar suspensions, polymers, and colloidal particles. The
final Sections\ 7 discuss and summarize our main results.

\section{Thermal diffusion and Dufour coefficients}

We consider a binary system\ with non-uniform temperature and composition.
Closely following \cite{deG84}, we present the linear equations for heat and
particle flows of a binary systems with volume fractions $\phi _{1}$ and $%
\phi _{2}=1-\phi _{1}$.

Then the currents of the two components satisfy $\mathbf{J}_{1}+\mathbf{J}%
_{2}=0$; the first one is defined as
\begin{equation}
\mathbf{J}_{1}=-D\mathbf{\nabla }\phi _{1}-\phi _{1}\phi _{2}D_{T}\mathbf{%
\nabla }T.  \label{2}
\end{equation}%
Besides gradient diffusion with the coefficient $D$, it comprises thermal
diffusion with coefficient $D_{T}$. In the steady state $\mathbf{J}_{1}=0$,
a finite temperature gradient imposes a non-uniform concentration $\mathbf{%
\nabla }\phi _{1}=-\phi _{1}\phi _{2}S_{T}\mathbf{\nabla }T$, with the Soret
coefficient $S_{T}=D_{T}/D$.

Similarly, the heat flow is driven by both temperature and concentration
gradients,
\begin{equation}
\mathbf{J}_{Q}^{\prime }=-\lambda \mathbf{\nabla }T-\phi _{1}\hat{\mu}%
_{11}^{\phi }D_{F}\mathbf{\nabla }\phi _{1},  \label{4}
\end{equation}%
where $\lambda $ is the thermal conductivity, $D_{F}$\ the Dufour
coefficient, and $\hat{\mu}_{11}^{\phi }$ the derivative of the chemical
potential \cite{deG84}. The hat indicates volume specific quantities, such
as the molecular chemical potential divided by the molecular volume, $\hat{%
\mu}_{k}=\mu _{k}/v_{k}$. The choice of volume fraction variables $\phi _{k}$
implies that $\mathbf{J}_{1}$ has the dimension of a velocity; one readily
finds that $D_{T}$ has the units m$^{2}$s$^{-1}$K$^{-1}$, whereas $D_{F}$\
has those of a diffusion coefficient, m$^{2}$s$^{-1}$.

The heat flow $\mathbf{J}_{Q}^{\prime }$ comprises two contributions,
ordinary heat diffusion with conductivity $\lambda $, and the Dufour effect
which is driven by a concentration gradient in an anisotropic medium. Note
that $\mathbf{J}_{Q}^{\prime }$ does not account for enthalpy transport due
to the particle current but is defined at $\mathbf{J}_{1}=0$. In the case of
a finite particle current, the total heat flow reads
\begin{equation}
\mathbf{J}_{Q}=\mathbf{J}_{Q}^{\prime }+\hat{h}_{1}\mathbf{J}_{1}+\hat{h}_{2}%
\mathbf{J}_{2}=\mathbf{J}_{Q}^{\prime }+(\hat{h}_{1}-\hat{h}_{2})\mathbf{J}%
_{1},  \label{5}
\end{equation}%
with the specific enthalpies $\hat{h}_{k}$ of the two components.

In many instances it is assumed that the off-diagonal coefficients $D_{T}$\
and $D_{F}$\ are related through Onsager's reciprocal laws according to
\begin{equation}
D_{T}\overset{?}{=}\frac{D_{F}}{T}.  \label{6}
\end{equation}%
The temperature factor is due to historical convention, similar to that
between the Seebeck and Peltier coefficients, $S=\Pi /T$. Kinetic theory
confirms this relation to be satisfied in ideal gas mixtures \cite{Cha60},
and there is evidence for its validity in liquid isotope mixtures \cite%
{Mor80}. Little can be said on ordinary binary liquids \cite{Ras70,Hor78}
and complex fluids.

\section{Phenomenological equations}

The above Eqs. (\ref{2}) and (\ref{4}) provide the experimental definition
of the thermal diffusion and Dufour coefficients.\ Closely following Ref.
\cite{deG84}, we summarize the corresponding theory, that is, Onsager's
linear relations for thermodynamic fluxes and forces. We do not discuss the
regression hypothesis \cite{Ell00} and suppose that the fluxes are linear
functions of the forces; note this assumption is often not justified for
chemical reactions.

\subsection{Entropy production}

Like any thermodynamic function, the entropy is constant in an equilibrium
state. Non-equilibrium phenomena are intimately related to entropy
production. For example, gradient diffusion according to Fick's law $\mathbf{%
J}_{1}=-D\mathbf{\nabla }\phi _{1}$ tends to smear out any \ composition
inhomogeneity and produces entropy at a rate $\sigma \propto D(\mathbf{%
\nabla }\phi _{1})^{2}$. By the same token, a non-uniform temperature
induces a heat flow $\mathbf{J}_{Q}=-\lambda \mathbf{\nabla }T$ from the hot
to the cold and augments the entropy as $\sigma =\lambda (\mathbf{\nabla }%
T/T)^{2}$. Similar relations arise for chemical reactions and for viscous
flow.

In the case of an initial perturbation, the system relaxes toward an
equilibrium state ($\mathbf{\nabla }\phi _{1}=0$, $\mathbf{\nabla }T=0$,...)
of constant entropy. On the other hand, if the inhomogeneity is maintained
through continuous heat or matter supply, the system reaches a stationary
non-equlibrium state and produces entropy at a constant rate.

With the mentioned dynamic variables, the rate of entropy production per
unit volume reads as

\begin{equation}
\sigma =\mathbf{J}_{Q}\cdot \mathbf{\nabla }\frac{1}{T}-\sum_{k}\mathbf{J}%
_{k}\cdot \mathbf{\nabla }\frac{\hat{\mu}_{k}}{T}-\sum_{i}\mathcal{J}%
_{i}A_{i}-\frac{\mathbf{\Pi :G}}{T}\mathbf{,}  \label{12}
\end{equation}%
where $\mathbf{J}_{Q}$ is the heat flux, $\mathbf{J}_{k}$ are the volume
currents of the molecular species, $\mathcal{J}_{i}$ are the compositon
changes due to chemical reactions, and $\mathbf{\Pi }$ is the viscous
pressure tensor. The corresponding thermodynamic forces are the gradients of
the inverse temperature and the Planck potential $\hat{\mu}_{k}/T$, the
affinities $A_{i}$, and the symmetrized rate of change of the fluid velocity
field $\mathbf{v(r)}$, with components $G_{mn}=\frac{1}{2}(\partial
_{m}v_{n}+\partial _{n}v_{m})$.\

For sufficiently weak deviations from the equilibrium state, Onsager
established linear relations between the fluxes and forces. Because of the
Curie symmetry principle, the phenomenlogical relations do not mix scalar,
vector, and tensor quantities. Thus the coefficient matrix of the
phenomenological equations is block-diagonal and decays in parts that are
characterized by their tensor properties.

\subsection{Vector currents}

The vector quantities $\mathbf{J}_{Q}$ and $\mathbf{J}_{k}$ describe heat
and mass diffusion. For a binary system ($n=2$) they\ form 3 generalized
fluxes which are, however, not linearly independent and can be reduced to 2
independent flows.\ When describing the composition in terms of volume
fractions, the particle currents cancel each other, $\mathbf{J}_{2}=-\mathbf{%
J}_{1}$; eliminating that of the second component one obtains
\begin{subequations}
\label{15}
\begin{eqnarray}
\mathbf{J}_{1} &=&L_{1Q}\mathbf{\nabla }\frac{1}{T}-L_{11}\mathbf{\nabla }%
\frac{\hat{\mu}_{1}-\hat{\mu}_{2}}{T}\mathbf{,}  \label{15a} \\
\mathbf{J}_{Q} &=&L_{QQ}\mathbf{\nabla }\frac{1}{T}-L_{Q1}\mathbf{\nabla }%
\frac{\hat{\mu}_{1}-\hat{\mu}_{2}}{T}\mathbf{.}  \label{15b}
\end{eqnarray}%
The last term of each equation gives rise to both thermal and concentration
gradients,
\end{subequations}
\begin{equation}
\mathbf{\nabla }\frac{\hat{\mu}_{k}}{T}=\hat{h}_{k}\mathbf{\nabla }\frac{1}{T%
}+\frac{\mathbf{\nabla }_{T}\hat{\mu}_{k}}{T},  \label{24}
\end{equation}%
where $\hat{h}_{i}$ is the enthalpy and $\mathbf{\nabla }_{T}$ the gradient
at constant temperature. Thus the thermodynamic force $\mathbf{\nabla }_{T}%
\hat{\mu}_{k}$ involves the derivative of the chemical potential with
respect to composition.

In many instances it turns out convenient to regroup all temperature
gradients according to
\begin{subequations}
\label{16}
\begin{eqnarray}
\mathbf{J}_{1} &=&L_{1Q}^{\prime }\mathbf{\nabla }\frac{1}{T}-L_{11}^{\prime
}\frac{\mathbf{\nabla }_{T}(\hat{\mu}_{1}-\hat{\mu}_{2})}{T}\mathbf{,}
\label{16a} \\
\mathbf{J}_{Q}^{\prime } &=&L_{QQ}^{\prime }\mathbf{\nabla }\frac{1}{T}%
-L_{Q1}^{\prime }\frac{\mathbf{\nabla }_{T}(\hat{\mu}_{1}-\hat{\mu}_{2})}{T}%
\mathbf{.}  \label{16b}
\end{eqnarray}%
Comparison with (\ref{12}) readily provides relations between unprimed and
primed coefficients, e.g. $L_{1Q}^{\prime }=L_{1Q}-L_{11}(\hat{h}_{1}-\hat{h}%
_{2})$.

The heat flow $\mathbf{J}_{Q}^{\prime }$\ is defined such that the entropy
production involves products of conjugate forces and currents; for a binary
system with $\mathbf{J}_{1}+\mathbf{J}_{2}=0$, the contribution of the
vector quantities reads
\end{subequations}
\begin{equation*}
\mathbf{J}_{Q}^{\prime }\cdot \mathbf{\nabla }\frac{1}{T}-\mathbf{J}%
_{1}\cdot \frac{\mathbf{\nabla }_{T}(\hat{\mu}_{1}-\hat{\mu}_{2})}{T}\mathbf{%
.}
\end{equation*}%
According to (\ref{5}) the primed heat flux accounts for diffusive transport
only, whereas $\mathbf{J}_{Q}$ comprises in addition the enthalpy carried by
the particle current $\mathbf{J}_{1}$. In the steady-state of a closed
system, the latter vanishes and one has $\mathbf{J}_{Q}=\mathbf{J}%
_{Q}^{\prime }$.

\subsection{Scalar and tensor quantities}

Now we turn to the remaining terms of the entropy production rate. That
involving chemical reactions is described by scalar fields,
\begin{equation}
\mathcal{J}_{i}=-\sum_{j}l_{ij}A_{j}/T,  \label{14}
\end{equation}%
where the coefficients $l_{ij}$ relate the reaction products to the
affinities $A_{i}$.

Finally, the linear relation between the viscous pressure and the velocity
gradient,
\begin{equation}
\mathbf{\Pi }=\mathbf{-\eta G,}  \label{18}
\end{equation}%
involves the fourth-rank viscosity tensor $\mathbf{\eta }$, which structure
is rather simple in isotropic liquids, yet becomes more complex in liquid
crystals \cite{Mon12}. For compressible fluids, the contraction $\mathbf{\Pi
:G}$ comprises also a scalar term, which is small for most liquids and thus
will discarded.

\subsection{Reciprocal laws}

According to Onsager's reciprocal laws, the coefficient matrices $\mathbf{l}$%
, $\mathbf{L}$, $\mathbf{L}^{\prime }$, and $\mathbf{\eta }$ are symmetric,
and in particular%
\begin{equation}
L_{1Q}^{\prime }=L_{Q1}^{\prime }.
\end{equation}%
In many works on thermal diffusion, both chemical reactions and viscous flow
are discarded from the beginning. Then the different terms in (\ref{16}) are
readily identified with those in (\ref{2}) and (\ref{4}),
\begin{equation}
\lambda \overset{?}{=}\frac{L_{QQ}^{\prime }}{T^{2}},D\overset{?}{=}\frac{%
\hat{\mu}_{11}^{\phi }L_{11}^{\prime }}{\phi _{2}T},D_{T}\overset{?}{=}\frac{%
L_{1Q}^{\prime }}{\phi _{1}\phi _{2}T^{2}},D_{F}\overset{?}{=}\frac{%
L_{Q1}^{\prime }}{\phi _{1}\phi _{2}T},  \label{20}
\end{equation}%
where $\hat{\mu}_{11}^{\phi }$ is the usual derivative with respect to
composition \cite{deG84}. Since $L_{1Q}^{\prime }$ and $L_{Q1}^{\prime }$
are reciprocal coefficients, these relations confirm (\ref{6}) for the
thermal diffusion and Dufour coefficient. \

The above decomposition of the linear relations according to their tensorial
properties does not imply, however, that the underlying physical phenomena
are decoupled. Whether each of the fluxes (\ref{16}), (\ref{14}), and (\ref%
{18}) can be treated independently from the others, cannot be determined on
formal grounds, but has to be inferred from the physical properties of the
system under consideration.

In the following we evaluate $D_{T}$ for different models and determine in
each case whether or not Eq. (\ref{20}) is satisfied.

\section{Diffusion}

Here we consider the case of a binary system where both chemical reactions
and viscous effects are absent. Then the entropy production and
phenomenological relations reduce to the vector quantities $\mathbf{J}_{Q}$,
$\mathbf{J}_{1}$, and $\mathbf{J}_{2}$, implying that $D_{T}$ and $D_{F}$
are reciprocal coefficients according to (\ref{6}). Still, the remaining
three independent coefficients have to be determined from physical
considerations. The general theory parallels Chapt.\ XI \S 8 of Ref. \cite%
{deG84}; the notation with volume fractions and examples are developped in
Ref. \cite{Wue14}.

\subsection{Vector fluxes}

It turns out instructive to eliminate the heat current $\mathbf{J}_{Q}$,
contrary to (\ref{16}) where we eliminated the current of the second
component $\mathbf{J}_{2}$. Then one obtains the particle fluxes as linear
functions of the thermodynamic forces $\mathbf{\nabla }(\hat{\mu}_{k}/T)$,
\begin{equation}
\mathbf{J}_{1}=-\phi _{1}\phi _{2}T\left( B_{1}\mathbf{\nabla }\frac{\hat{\mu%
}_{1}}{T}-B_{2}\mathbf{\nabla }\frac{\hat{\mu}_{2}}{T}\right) ,  \label{22}
\end{equation}%
where the coefficients $B_{i}$ depend on composition and on temperature. (As
compared to the notation in \cite{Wue14}, a factor $\phi _{1}\phi _{2}T$ has
been introduced for convenience.)

Note that the currents $\mathbf{J}_{k}$ have the dimension of a velocity.
Our choice of volume fraction variables $\phi _{i}$ is motivated by the
volume conservation in incompressible liquids, which results in the relation
$\mathbf{J}_{1}+\mathbf{J}_{2}=0$. For gases, where momentum is conserved,
one would prefer to take mass fractions.

Eq. (\ref{22}) implies that diffusion and thermal diffusion are given by the
gradient of the Planck potentials $\hat{\mu}_{k}/T$. Spelling out the
gradients,%
\begin{equation}
\mathbf{\nabla }\frac{\hat{\mu}_{k}}{T}=-\frac{\hat{h}_{k}}{T^{2}}\mathbf{%
\nabla }T+\frac{\hat{\mu}_{kk}^{\phi }}{T}\mathbf{\nabla }\phi _{k},
\label{19}
\end{equation}%
recollecting the terms in $\mathbf{J}_{1}$ and comparing with (\ref{2}) one
obtains the diffusion coefficient
\begin{subequations}
\label{26}
\begin{equation}
D=\left( \phi _{1}B_{1}+\phi _{2}B_{2}\right) \phi _{1}\hat{\mu}_{11}^{\phi
}.  \label{26a}
\end{equation}%
Similarly one finds for the thermal diffusion and Dufour coefficients \cite%
{deG84}
\begin{equation}
D_{T}=\frac{\hat{h}_{2}B_{2}-\hat{h}_{1}B_{1}}{T}=\frac{D_{F}}{T}.
\label{26b}
\end{equation}

Eqs. (\ref{16}) and (\ref{26}) provide formally equivalent expressions for
the particle current (\ref{2}): The former depends on two unknowns $%
L_{11}^{\prime }$ and $L_{1Q}^{\prime }$, and the latter on $B_{1}$ and $%
B_{2}$. These coefficients can not be derived from equilibrium properties;
they have to be taken from experiment or molecular dynamics simulations, or
inferred from models for the molecular mobility.

On the other hand, the equilibrium quantities appearing in (\ref{26}), that
is, the thermodynamic factor $\phi _{1}\hat{\mu}_{11}^{\phi }$ and the
specific enthalpies $\hat{h}_{i}$, can be calculated from first principles
\cite{Hel60}, or can be taken from numerical simulations \cite{Mil13} or
experiment \cite{Wue14}.

\subsection{Comparison to experiment}

Thermal diffusion is usually discussed in terms of (\ref{16a}). When
comparing to experiments, however, Eqs. (\ref{26}) turn out to be a more
promising starting point. Two mobilities $B_{k}$ appear in both $D$ and $%
D_{T}$ and thus provide a strong relation between thermal diffusion and
diffusion data. When taking the parameters $B_{k}$ as constants, they can be
determined from the tracer diffusion coefficients of the two species,
\end{subequations}
\begin{equation}
\begin{array}{ccc}
B_{2}=D(\phi _{1})/\phi _{1}\hat{\mu}_{11}^{\phi } & \text{for} & \phi
_{1}\rightarrow 0, \\
B_{1}=D(\phi _{1})/\phi _{1}\hat{\mu}_{11}^{\phi } & \text{for} & \phi
_{1}\rightarrow 1.%
\end{array}
\label{25}
\end{equation}%
A slightly different scheme has been used for Soret data of several
molecular mixtures such as benzene-cyclohexane \cite{Wue14}. Together with
measured values for the partial enthalpies $\hat{h}_{2}$, this allows
comparison with the thermal diffusion coefficient $D_{T}$.

A particularly interesting situation arises for isotope mixtures. Molecular
isotopes show similar thermodynamics, yet differ in dynamical properties
such as the attempt frequency of activated jumps. Thus any difference in the
mobilities $B_{k}$ can be related to a specific model. Such approaches have
been developped for mass effects. For mixtures such as CCl$_{4}$-CBr$_{4}$
the $B_{k}$ have been expressed through the activation free energy \cite%
{Mor80,Sax62}. The isotope effect observed upon deuteration in
benzene-cyclohexane mixtures, has been related to the molecular collision
rates \cite{Vil11}.

\begin{figure}[tbp]
\includegraphics[width=\columnwidth]{Fig1.png}
\caption{Soret data for mixtures of normal alkanes C$_{10}-$C$_{n}$, where
the number $n$ of carbon atoms of the second component varies from 5 to 20.
The experimental data are from Leahy-Dios and Firoozabaadi \protect\cite%
{Lea07} (squares) and Blanco et al. \protect\cite{Bla08} (circles). The
theoretical curve is calculated from (\protect\ref{70}) as discussed in the
main text.}
\label{fig1}
\end{figure}

\subsection{Alkane mixtures}

Thermal diffusion behavior according to (\ref{26}) is expected in mixtures
of similar molecules, such as short alkanes. Indeed, small molecules induce
weak hydrodynamic flow, which is rapidly superseded by the molecular
diffusion. Then the Soret coefficient $S_{T}=D_{T}/D$ depends on the partial
enthalpies $\hat{h}_{k}$, the chemical potentials $\hat{\mu}_{k}$, and the
molecular mobilities $B_{k}$.

Assumung that the latter are identical, independently of the molecular
weight, we thus have \cite{Wue14}
\begin{equation}
S_{T}=\frac{1}{T}\frac{\hat{h}_{2}-\hat{h}_{1}}{\phi _{1}\hat{\mu}_{11}}\ \
\ \ \ \ \ \ \ (B_{1}=B_{2}).  \label{70}
\end{equation}%
Refining early work by Haase \cite{Haa49}, similar relations have been
discussed by several authors \cite{Kem89,Shu98,Esl09}. In Fig. 1 we compare
this expression with Soret data for equimolar alkane mixtures, which are
taken from Refs. \cite{Lea07,Bla08}.

The theoretical curve has been calculated from (\ref{70}), with the
thermodynamic factor equal to unity such that $\phi _{1}\hat{\mu}%
_{11}=k_{B}T/(\phi _{1}v_{2}+\phi _{2}v_{1})$, and the specific enthalpy $%
\hat{h}_{n}=h_{n}/v_{n}$ given by
\begin{subequations}
\label{72}
\begin{eqnarray}
h_{n} &=&-(n+0.65)\times 4.64\frac{\text{kJ}}{\text{mol}},  \label{72a} \\
v_{n} &=&(n+2.02)\times 16.35\frac{\text{cm}^{3}}{\text{mol}}.  \label{72b}
\end{eqnarray}%
These simple laws perfectly fit the measured vaporization enthalpy \cite%
{Chi03} and molecular volume $v_{n}$. The theoretical curve in Fig. 1
strongly depends on the off-set parameters $0.65$ and $2.02$, as discussed
in the Appendix.

The particularly simple fit arises since the Soret coefficient $%
S_{T}=D_{T}/D $ depends on the ratio $B_{1}/B_{2}$ only (which, moreover,
has been put to unity.) A more complex situation occurs when considering
thermal diffusion and diffusion data separately.\ The many data on the
composition dependence of $D_{T}$ and $D$ \cite{Mad10,deM12} should
unambiguously determine the mobilities $B_{k}$ and verify whether the
assumption $B_{1}=B_{2}$ is justified. On the other hand, if the data for $%
D_{T}$ and $D$ turned out not to be compatible with (\ref{26}), this would
suggest that $D_{T}$ cannot be explained in terms of the vector fluxes (\ref%
{15}) but depends on other phenomena such as viscous stress.

\subsection{Comparison with heat conductivity}

So far we discussed the relation between diffusion and thermal diffusion
coefficients in terms of the quantities $B_{k}$. As shown by de Groot and
Mazur, a more general formulation of the heat and particle flows relates the
coefficients $D$ and $D_{T}$\ to the heat conductivity $\lambda $. To this
purpose, we note that the thermodynamic forces on component $k$ can be
written as $\sum_{l}a_{kl}\mathbf{\nabla (}\hat{\mu}_{l}/T)$, with a
mobility matrix that is symmetric ($a_{12}=a_{21}$) and positive definite ($%
a_{11}a_{22}\geq a_{21}^{2}$).

The $B_{k}$ appearing in (\ref{22}) depend on these mobilities through
\end{subequations}
\begin{equation}
B_{1}=\frac{\phi _{2}a_{11}-\phi _{1}a_{12}}{\phi _{1}\phi _{2}T},\ \ \ \
B_{2}=\frac{\phi _{1}a_{22}-\phi _{2}a_{21}}{\phi _{1}\phi _{2}T}.
\label{21}
\end{equation}%
Insertion in (\ref{26}) provides the diffusion and thermal diffusion
coefficients in terms of the $a_{ij}$. Similarly, the heat conductivity is
given by the mobilities according to \cite{deG84}%
\begin{equation}
\lambda =\frac{a_{11}\hat{h}_{1}^{2}+2a_{12}\hat{h}_{1}\hat{h}_{2}+a_{22}%
\hat{h}_{2}^{2}}{T^{2}}.  \label{23}
\end{equation}%
Thus the three transport coefficients $D$, $D_{T}$, and $\lambda $\ are
expressed through three paramaters $a_{11}$, $a_{22}$, and $a_{12}$. These
quantities vary with composition, such that a set of experimental data for $%
D(\phi _{1})$, $D_{T}(\phi _{1})$, and $\lambda (\phi _{1})$ determines the
mobility matrix $a_{kl}(\phi _{1})$.

Here one should remind that (\ref{26}) and (\ref{23}) rely on the assumption
that vector fluxes and forces entirely determined the heat and particle
currents. Thus in the first place, these relations provide a criterion for
the validity of this assumption. As a crude estimate, we replace the
mobilities by $a_{ij}\sim a$, neglect composition factors $\phi _{i}\sim 1$,
and thus obtain $D\sim ak_{B}/v$ and $\lambda \sim a(H/v)^{2}/T^{2}$, \
where $H$ and $v$\ are the molar enthalpy and volume. Eliminating $a$ leads
to $\lambda \sim H^{2}D/vk_{B}T^{2}$; inserting typical values of $H,D,v$,
as measured e.g. for benzene, one finds a thermal conductivity $\lambda \sim
0.03$ Wm$^{-1}$K$^{-1}$; which is about five times smaller than the
experimental value.\

This estimate suggests that it could be instructive to fit experimental or
simulation data for $D$, $D_{T}$, and $\lambda $\ with Eqs. (\ref{26}) and (%
\ref{23}). The elements of the mobility matrix $a_{kl}$ do, however, not
necessarily provide a good starting point; thus according to (\ref{21}) and (%
\ref{25}), constant diagonal elements $a_{kk}$ would result in a diverging
diffusion coefficient $D$. In view of (\ref{25}) one would rather prefer to
replace the $a_{kl}$ with well-behaved quantities; as a possible choice we
note $B_{1}$, $B_{2}$, and
\begin{equation*}
B_{3}=\frac{a_{12}}{\phi _{1}\phi _{2}T}.
\end{equation*}%
Then the expressions in (\ref{26}) are completed by the thermal conductivity
\begin{equation}
\lambda =\frac{\phi _{1}\hat{h}_{1}^{2}B_{1}+\phi _{2}\hat{h}%
_{2}^{2}B_{2}+(\phi _{1}\hat{h}_{1}+\phi _{2}\hat{h}_{2})^{2}B_{3}}{T}.
\label{27}
\end{equation}%
The positivity condition for the mobility matrix imposes
\begin{equation*}
B_{1}B_{2}+(\phi _{2}B_{1}+\phi _{1}B_{2})B_{3}\geq 0.
\end{equation*}%
We recall that the $B_{k}$ depend on composition. The relations (\ref{26})
and (\ref{27}) suggest that, in a simple model, these quantities could be
taken as constants.

\section{Chemical reactions}

Here we discuss how chemical reactions modify heat and mass flow. In
physical terms, it is clear they affect the local composition and thus
induce diffusion currents; inversely, thermal diffusion creates a
non-uniform composition which in turn perturbs the chemical equilibrium and
thus provokes reactions.

Because of the Curie principle, the phenomenological equations (\ref{16})
and (\ref{14}) do not contain cross terms between the scalar and vector
quantities, and thus do not mix the reaction kinetics and diffusion. This
does not imply, however, that scalar and vector fluxes are independent of
each other, nor that diffusion is simply determined by the matrix $\mathbf{L}
$.

\subsection{Reaction-diffusion coupling}

Consider the case of a single chemical reaction between two components. Then
the entropy production (\ref{12}) comprises the scalar fluxes $\mathcal{J}%
_{i}=\dot{\phi}_{i}$. The reaction kinetics obey the rate equations
\begin{equation}
\dot{\phi}_{1}=\gamma \phi _{2}-\Gamma \phi _{1}=-\dot{\phi}_{2},  \label{32}
\end{equation}%
where the point indicates time derivatives and the transitions $%
1\leftrightarrow 2$ occur with rates $\gamma $ and $\Gamma $. According to
the principle of detailed balanced, their ratio $\gamma /\Gamma
=e^{-G/k_{B}T}$ is determined by the free enthalpy difference $G$ of the two
states.

In addition to the reaction velocity $\dot{\phi}_{k}$, the total change of
the volume fraction with time comprises the divergence of the diffusion
current $\mathbf{J}_{k}$,%
\begin{equation}
\frac{d}{dt}\phi _{k}=\dot{\phi}_{k}+\mathbf{\nabla \cdot J}_{k},  \label{36}
\end{equation}%
where the last term corresponds to a source or sink for the considered
species. Eq. (\ref{36}) provides a coupling between the scalar and vector
fluxes $\dot{\phi}_{k}$ and $\mathbf{J}_{k}$, and thus induces a relation
between the a priori independent phenomenological equations (\ref{16}) and (%
\ref{14}).

Here we consider the steady state where $d\phi _{k}/dt=0$. The resulting
equation
\begin{equation}
\dot{\phi}_{k}+\mathbf{\nabla \cdot J}_{k}=0  \label{38}
\end{equation}%
does not imply the arrest of the reaction nor that the currents $\mathbf{J}%
_{k}$ vanish.\ It simply requires that a local creation of molecules ($\dot{%
\phi}_{1}>0$) is balanced by a net outgoing particle flow, and annihilation (%
$\dot{\phi}_{1}<0$) by an incoming flow. In general the solution of (\ref{38}%
) cannot be given in closed form, especially if the rate ratio $\gamma
/\Gamma =e^{-G/k_{B}T}$ depends on temperature.\

Thermal conductivity of a binary system with constant rates has been studied
in detail by de Groot and Mazur in Chapter XI \S 8 of Ref. \cite{deG84}. As
a main result these authors find that the diffusivities are not simply given
by the matrix $\mathbf{L}$, but depend on the reaction parameters; moreover,
the explicit result for the thermal conductivity shows an intricate spatical
variation. This leads to the conclusion that Eq. (\ref{20}) is not valid in
the presence of chemical reactions.

\begin{figure}[tbp]
\includegraphics[width=\columnwidth]{Fig2.png}
\caption{Steady-state currents resulting from the equilibrium between
micellar and molecular states in a surfactant solution. For $H>0$, micelle
formation is favored at high temperatures, and the dissolved molecular state
at lower temperatures. This temperature dependent equilibrium feeds
stationary micelle and molecular currents $J_{1}$ and $J_{2}$. For $H<0$ all
arrows point in the opposite direction. }
\end{figure}

\subsection{Micelle kinetics}

As an instructive example, we consider a solution of tensioactive molecules
that partly aggregate to micelles. The micellar and molecular states occupy
volume fractions $\phi _{1}$ and $\phi _{2}$, with $\phi _{1}+\phi _{2}\ll 1$%
. For the sake of simplicity we suppose that the cross-coefficients in the
vector fluxes are small and thus put
\begin{subequations}
\label{35}
\begin{equation}
L_{kQ}^{\prime }=0=L_{Qk}^{\prime }.
\end{equation}%
Then the particle currents take the form $\mathbf{J}_{k}=-D_{k}\mathbf{%
\nabla }\phi _{k}$, where%
\begin{equation}
D_{k}=\frac{L_{kk}^{\prime }\phi _{k}\hat{\mu}_{kk}^{\phi }}{\phi _{1}\phi
_{2}T},\ \ \ \ \ D_{T}=0
\end{equation}%
implies the absence of thermal diffusion.

Now we take the kinetics of micelle formation into account \cite{Kaa09}.\
Micellar aggregation of $N$ molecules and dissolution through the inverse
process, as described by the rate equation (\ref{32}). This
\textquotedblleft chemical reaction\textquotedblright\ occurs on a time
scale of nanoseconds, and thus is much faster than diffusion over
macroscopic lengths $L$, which occurs on a time scale $L^{2}/D$ that by far
exceeds seconds. This means that the second term in (\ref{38}) is small.

The steady-state of a homogeneous system is determined by the equilibrium of
the chemical reaction ($\dot{\phi}_{1}=0$) which reads as $\phi _{1}/\phi
_{2}=\gamma /\Gamma =e^{-G/k_{B}T}$. Yet here this ratio is not constant in
space but varies because of the non-uniform temperature $T(\mathbf{r)}$.
Expanding the rate equation (\ref{32}) to linear order in the coordinates $%
\mathbf{r}$, we have
\end{subequations}
\begin{equation}
\gamma \phi _{2}-\Gamma \phi _{1}+\mathbf{r\cdot \nabla }\left( \gamma \phi
_{2}-\Gamma \phi _{1}\right) +\mathbf{\nabla \cdot J}_{1}=0.
\end{equation}%
The first term describes the equilibrium state at $\mathbf{r}=0$. Since
diffusion is much slower than the chemical reaction, $D/L^{2}\ll \gamma $,
the last term is negligible. Evaluating the gradient of the remainder we
find
\begin{equation}
0=\Gamma \phi _{1}\frac{H}{k_{B}T^{2}}\mathbf{\nabla }T+\gamma \mathbf{%
\nabla }\phi _{2}-\Gamma \mathbf{\nabla }\phi _{1},  \label{37}
\end{equation}%
where we have inserted the Gibbs-Helmholtz relation
\begin{equation*}
\frac{d}{dT}\frac{G}{k_{B}T}=-\frac{H}{k_{B}T^{2}}
\end{equation*}%
with the enthalpy $H$.

Thus chemical equilibrium in the presence of a non-uniform temperature
gradient imposes gradients of the micellar and molecular volume fractions,
which in turn drive the diffusion currents $\mathbf{J}_{k}=-D_{k}\mathbf{%
\nabla }\phi _{k}$. Inserting $\mathbf{J}_{1}+\mathbf{J}_{2}=0$ in (\ref{37}%
) we find the steady-state composition gradients
\begin{equation}
\mathbf{\nabla }\phi _{1}^{\text{st}}=\phi _{1}\frac{D_{2}\Gamma }{%
D_{1}\gamma +D_{2}\Gamma }\frac{H}{k_{B}T^{2}}\mathbf{\nabla }T  \label{39}
\end{equation}%
and $\mathbf{\nabla }\phi _{2}^{\text{st}}=-(D_{1}/D_{2})\mathbf{\nabla }%
\phi _{1}^{\text{st}}.$ This implies a finite stationary current of micelles
\begin{equation}
\mathbf{J}_{1}^{\text{st}}=-\phi _{1}\frac{D_{1}D_{2}\Gamma }{D_{1}\gamma
+D_{2}\Gamma }\frac{H}{k_{B}T^{2}}\mathbf{\nabla }T=-\phi _{1}D_{T}\mathbf{%
\nabla }T,  \label{40}
\end{equation}%
and the opposite flow of the molecular state. The second equality defines a
thermal diffusion coefficient $D_{T}$ for the first component. Its
dependence on the rates $\gamma $\ and\ $\Gamma $, and on the micellar
enthalpy $H$, indicates that this current is driven by the chemical
reaction. The micelle and molecular currents $\mathbf{J}_{1}^{\text{st}}$
and $\mathbf{J}_{2}^{\text{st}}$ are shown in Fig. 2 and related to the
gradient of the chemical equilibrium condition (\ref{37}).

Finally we define the Soret coefficient of the solution through the gradient
of the total surfactant content $\phi ^{\text{st}}=\phi _{1}^{\text{st}%
}+\phi _{2}^{\text{st}}$,
\begin{equation*}
\mathbf{\nabla }\phi ^{\text{st}}+\phi ^{\text{st}}S_{T}\mathbf{\nabla }T=0.
\end{equation*}%
Rearranging the above expressions one finds
\begin{equation}
S_{T}=\frac{D_{1}-D_{2}}{D_{1}\gamma +D_{2}\Gamma }\frac{\gamma \Gamma }{%
\gamma +\Gamma }\frac{H}{k_{B}T^{2}}\mathbf{.}
\end{equation}%
This contribution could be relevant for thermophoresis experiments on SDS
solutions\ \cite{Vig10}.

As a summary of this Section, the non-uniform equilibrium condition (\ref{37}%
) imposes the steady-state composition gradient $\mathbf{\nabla }\phi _{1}^{%
\text{st}}$, which in turn, induces the thermally driven micellar current $%
\mathbf{J}_{1}^{\text{st}}$.\ Thus we have $D_{T}\neq 0$ in spite of $%
L_{kQ}^{\prime }=0$, which clearly invalidates Eq. (\ref{20}).

\section{Viscous effects $-$ thermophoresis}

Now we turn to the case where the entropy production (\ref{12}) comprises a
viscous term. We repeat that the phenomenological equations are
block-diagonal, and thus do not mix viscous and particle fluxes\textbf{\ }$%
\Pi $ and $\mathbf{J}_{k}$. Yet there is ample experimental evidence that
thermally driven motion in colloidal dispersions is essentially determined
by viscous effects. In physical terms the moving particle engenders in the
surrounding fluid a velocity field $\mathbf{v(r)}$, which produces entropy
according to the last term in (\ref{12}). Accordingly, most theoretical
works on colloidal thermophoresis rely on a hydrodynamic approach which
deals with the coupling of the mass flux $\mathbf{J}_{1}$ in (\ref{16}) and
the viscous pressure tensor (\ref{18}).

We consider colloidal particles dispersed in continuous solvent without
molecular structure. The chemical potential per particle $\mu =h-Ts$, or
partial free enthalpy, is given by the interaction enthalpy $h$ and the
translational entropy $s=-k_{B}\ln \phi _{1}$; the former is proportional to
the particle surface and the latter decreases with the particle content $%
\phi _{1}$. From the thermodynamic force (\ref{24}) one expects that $D$ and
$D_{T}$ arise from the volume fraction and temperature derivatives,
respectively.\

In this Section we sketch the derivation of $D$ and $D_{T}$ in terms of
Stokes' equation $\eta \mathbf{\nabla }^{2}\mathbf{v=\nabla }P$, with the
solvent viscosity $\eta $, velocity field $\mathbf{v}$, and pressure $P$.\ A
rather simple physical picture emerges for the diffusion coefficient, where
the hydrodynamic flow corresponds to the Stokes drag of a particle subject
to an entropic force $-k_{B}T\nabla \phi _{1}$. Regarding the thermophoretic
mobility $D_{T}$, the relation between the thermodynamic force and the
particle velocity is less straightforward, but relies on an argument
developped by Derjaguin and on the concept of an effective slip velocity
close to a solid surface \cite{And89}. The latter provides a hydrodynamic
boundary condition with links viscous flux with the particle motion.\

\subsection{Stokes-Einstein diffusion coefficient}

Gradient diffusion in a collodial dispersion is determined by the interplay
between thermal noise and Stokes drag; in the present notation the
coefficient reads
\begin{equation}
D=\frac{\phi _{1}\mu _{11}^{\phi }}{6\pi \eta R}=\frac{k_{B}T}{6\pi \eta R}.
\label{52}
\end{equation}%
The numerator results from the thermodynamic force $\nabla \mu $ exerted by
a concentration gradient, whereas the denominator accouts for Stokes
friction for a sphere of radius $R$. In the second equality we have used
that in a dilute suspension the thermodynamic factor simplifies according to
$\phi _{1}\mu _{11}^{\phi }=k_{B}T$ \cite{deG84}.

In the absence of viscous effects and for $\phi _{1}\rightarrow 0$, Eq. (\ref%
{26a}) gives
\begin{equation*}
D=B_{2}\phi _{1}\hat{\mu}_{11}^{\phi }=k_{B}TB_{2}/v_{1},
\end{equation*}%
with the solvent molecular mobility $B_{2}$ and the particle volume $v_{1}$
\cite{Wue14}. In the present macroscopic hydrodynamics approach (\ref{52}),
the mobility $B_{2}$ has disappeared, or rather is subsumed in the viscosity
parameter $\eta $. The dependence on the particle size $R$ is characteristic
for the solvent velocity field associated with the diffusing particle.

\subsection{Surface forces and slip velocity}

Now we turn to the thermophoretic mobility $D_{T}$, which describes
colloidal motion driven by a temperature gradient. For the case of thermal
diffusion, the coefficient (\ref{26b}) was obtained as the product of the
thermodynamic forces with the molecular mobilities. Thermophoresis is more
complex since the motion is related to a velocity field $\mathbf{v(r)}$ in
the surrounding fluid; the resulting viscous pressure $\Pi $ contributes
significantly to the entropy production.

As pointed out by Anderson \cite{And89}, the fundamental principle of
thermophoresis is similar to electrophoresis and to motion in concentration
gradients. As shown in Fig. 3, the temperature gradient induces a shear
stress within a boundary layer of thickness $\lambda $. At distances beyond $%
\lambda $, the resulting flow profile saturates at the effective slip
velocity $v_{S}$. Matching the far-field $\mathbf{v(r)}$ to the boundary
condition $v_{S}$, one finds that the particle moves at a velocity
\begin{equation}
u=-D_{T}\nabla T=-\frac{2}{3}v_{S}.  \label{54}
\end{equation}%
Thus calculating $D_{T}$\ is reduced to the hydrodynamic problem of
evaluating the flow\ around the particle.

In the phenomenological equations, there are no cross-terms between the
particle current $\mathbf{J}_{k}$ and the viscous flux $\mathbf{\Pi }$. Yet
the hydrodynamic boundary conditions couple the particle motion to the fluid
velocity field. In the following we give Derjaguin's evaluation for this
coupling.

\begin{figure}[tbp]
\includegraphics[width=\columnwidth]{Fig3.png}
\caption{a) Colloidal particle in a temperature gradient. The boundary layer
is characterized by the excess specific enthalpy $\hat{h}$ (grey-blue). b)
The case of a thin boundary layer ($\protect\lambda \ll R$) is equivalent to
a flat surface where, at distances beyond $\protect\lambda $, thermoosmosis\
leads to an effective slip velocity $v_{S}$. c). Heat and volume flows in a
capillary. The pressure gradient $\Delta P/L$ results in Poiseulle flow with
parabolic velocity profile $v(z)$. Since $\hat{h}=0$ in the core of the
capillary, the excess heat flow (\protect\ref{62}) occurs in the boundary
layers of thickness $\protect\lambda $. A temperature gradient $\Delta T/L$
results in thermal creep flow along the solid boundary; the velocity profile
in the boundary layer depends on the detail of $h(z)$.\ The constant
velocity in the core of the capillary can be determined from Onsager's
reciprocal law for the coefficients in (\protect\ref{56}). Then the
resulting slip velocity (\protect\ref{66}) applies equally well at the
surface of a colloidal particle and, finally, determines the thermophoretic
mobility according to (\protect\ref{54}). }
\end{figure}

\subsection{Onsager relation for enthalpy and volume flows}

In their 1941 paper on the thermoosmotic effect, Derjaguin and Sidorenkov
consider the conjugate heat flow instead of the thermally-driven velocity
\cite{Der41,Der87}. In a second step, the latter is obtained from a
reciprocity relation. This is achieved in the geometry shown in Fig. 3c,
where the height $D$ of the capillary is much smaller than its length $L$
and its width $w$. The thermophoretic coefficient $D_{T}$ is obtained by
mapping the boundary problem on the surface of a colloidal particle to the
capillary flow velocity, according to (\ref{54}).

The thermodynamic forcers, that is the temperature gradient $\nabla T=\Delta
T/L$ and pressure gradient $\nabla P=\Delta P/L$, are constant and oriented
along the capillary axis. The corresponding fluxes, that is the flows of
heat and volume, are linear functions of the forces,
\begin{subequations}
\label{56}
\begin{align}
J_{V}& =\frac{\dot{V}}{wD}=-L_{VQ}\frac{\nabla T}{T}-L_{VV}\nabla P, \\
J_{Q}& =\frac{\dot{Q}}{wD}=-L_{QQ}\frac{\nabla T}{T}-L_{QV}\nabla P.
\end{align}%
Here $\dot{V}$ and $\dot{Q}$ are the integrated volume and heat flows
through the capillary, whereas $J_{V}$ and $J_{Q}$ are the\ average current
densities, like $\mathbf{J}_{Q}$ in previous sections. The dimension of $%
\dot{Q}$ is energy/time, and that of $\dot{V}$ is volume/time.

The diagonal coefficients $L_{VV}$ and $L_{QQ}$ are described by the
Hagen-Poiseuille law for laminar flow and the thermal conduction of the
liquid, respectively. The off-diagonal coefficients account for the
cross-currents; $L_{QV}$ gives the pressure-driven heat flow, and $L_{VQ}$
the temperature-driven volume flow. \ According to Onsager's reciprocal
relations, these coefficients are identical,
\end{subequations}
\begin{equation}
L_{QV}=L_{VQ}.  \label{58}
\end{equation}%
The transport coefficients are calculated from Stokes' equation $\eta \nabla
^{2}v=\nabla P$ for the velocity field $v(z)$, completed with the boundary
conditions $v(0)=0=v(D)$.

First consider the flows driven by a pressure difference. In a narrow
capillary, the velocity depends on the vertical coordinate $z$ only. Then
Stokes' equation reduces to $\eta \partial _{z}^{2}v=\nabla P$; it is solved
by
\begin{equation}
v(z)=\frac{z(z-D)}{2\eta }\nabla P\ \ \ \ \ \ \ (0\leq z\leq D)  \label{60}
\end{equation}%
and results in the volume flow $\dot{V}=-(wD^{3}/12\eta )\nabla P$ and $%
L_{VV}=D^{2}/12\eta $. The heat flow consists of the excess enthalpy of the
liquid close to the upper and lower boundaries of the capillary,
\begin{equation}
\dot{Q}=w\int_{0}^{D}dz\hat{h}(z)v(z).  \label{62}
\end{equation}%
The specific enthalpy $\hat{h}$ is measured with respect to that of the bulk
liquid, $\hat{h}_{\infty }$, such that $\hat{h}\rightarrow 0$\ outside the
interaction layers. Dividing the integral by $wD$ and identifiying with $%
J_{Q}=-L_{QV}\nabla P$, we find the transport coefficient%
\begin{equation}
L_{QV}=-\frac{1}{\eta }\int_{0}^{D/2}dzz\hat{h}(z).  \label{64}
\end{equation}%
Here we have used that the lower and upper boundaries of the capillary carry
identical amounts of heat, and have inserting the velocity profile close to
the lower boundary, $v(z)=-zD\nabla P/2\eta $ for $z\ll D$.

Now we turn to the temperature-driven volume flow at constant pressure.
Except for the boundary layer, the velocity profile is constant across the
capillary; to leading order in $\lambda /D$, the volume current reads $%
J_{V}=v_{S}$. Identifying this with $J_{V}=-L_{VQ}\nabla T/T$ and using the
reciprocal relation (\ref{58}), we find
\begin{equation}
v_{S}=-\frac{\nabla T}{\eta T}\int_{0}^{\infty }dzz\hat{h}(z).  \label{66}
\end{equation}%
We have used that $\hat{h}$ is finite in the boundary layer of thickness $%
\lambda \ll D$ only and vanishes in the core of the capillary; thus we have
replaced the upper bound $D/2$ with infinity. (In passing we note that the
additional factor 2 occuring in previous work \cite{Der87,Pia04} is related
to the missing $\frac{1}{2}$ in the Poiseuille velocity profile used there.)

\subsection{Thermophoretic and Dufour coefficients}

The above cross-coefficient $L_{QV}$ applies to any surface with an excess
enthalpy $\hat{h}$ within a thin boundary layer. In particular, $v_{S}$
describes the quasislip velocity $v_{S}$ occuring close to the surface of a
colloidal particle, as illustrated in Fig. 3b. From the hydrodynamic
boundary condition (\ref{54}) one readily obtains the thermophoretic
mobility of the particle,
\begin{equation}
D_{T}=-\frac{2}{3\eta T}\int_{0}^{\infty }dzz\hat{h}(z)=\frac{2}{3}\frac{%
L_{QV}}{T}.  \label{69}
\end{equation}%
In the second equality we have used (\ref{64}) with $\lambda /D\rightarrow 0$%
. Note that $D_{T}$ does not depend on the particle radius $R$. (This is
valid as long as the particle radius is larger than the interaction length, $%
R\gg \lambda $. In the opposite case, the numerical prefactor $\frac{2}{3}$
has to be replaced with unity \cite{Wue10}.)

Thus thermophoresis stems from the volume flow $\dot{V}$ driven by
thermo-osmosis along a solid-liquid interface. The coefficient $%
L_{VQ}=L_{QV} $ has been evaluated through the conjugate phenomenon, that
is, the heat flow $\dot{Q}$ due to a Poiseuille flow. The second equality in
Eq. (\ref{69}) relies explicitly on the Onsager reciprocity law (\ref{58}).
It is clear that $D_{T}$ as defined above, has no relation with the Dufour
effect $D_{F}$. In physical terms, the above argument does not lead to heat
flow induced by a non-uniform colloidal volume fraction, and the actual
conjugate flux $\dot{Q}$ has nothing do with a non-uniform composition.

Still, in a colloidal suspension with non-uniform volume fraction $\phi $,
there may be an additional heat flux $\dot{Q}_{F}\propto L_{Q1}^{\prime
}\nabla \phi $, and the reciprocal coefficient $L_{1Q}^{\prime }$ is
expected to contribute an additional term to (\ref{69}). The many data
collected for colloidal thermophoresis suggest, however, that this extra
term is small. In particular, experiments show that $D_{T}$ is independent
of the particle size; it would be rather surprising if the heat flow $\dot{Q}%
_{F}$, and thus the thermal diffusion and Dufour coefficient $L_{Q1}^{\prime
}=L_{1Q}^{\prime }$, did not vary with the particle size.

\section{Discussion}

\subsection{Are $D_{T}$ and $D_{F}$ reciprocal coefficients?}

Reciprocicity is an undoubted property of the cross-coefficients in
Onsager's equations, such as $L_{1Q}^{\prime }$ and $L_{Q1}^{\prime }$ in (%
\ref{16}), or $L_{QV}$ and $L_{VQ}$ in (\ref{58}). This paper addressed the
question to what extent these reciprocal relations imply $D_{T}=D_{F}/T$ for
the thermal diffusion and Dufour coefficients \ in liquids, and under which
conditions the identification of Eq. (\ref{20}) is valid. In the absence of
scalar and vector fluxes, we find that the model equations (\ref{2}) are
identical to Onsager's linear relation (\ref{16}), implying $D_{T}=D_{F}/T$.

Adding a chemical reaction and coupling to the vector fluxes through (\ref%
{38}), we obtain a finite $D_{T}$ even for $L_{1Q}^{\prime }=0$. The
corresponding micelle current (\ref{40}) is driven by the equilibrium
composition of the chemical reaction. Thus we find that Eq. (\ref{20}) is
not satisfied in the presence of chemical reactions, in agreement with the
more formal study by de Groot and Mazur \cite{deG84}.

A similar result is obtained for viscous effects. Thermophoresis in
colloidal suspensions is governed by hydrodynamic flow in the vicinity of
the particle, as shown in general by Anderson \cite{And89} and worked out in
detail for electric-double layer interactions \cite{Wue10,Esl14}. The
mobility $D_{T}$ is given by the interaction enthalpy in the boundary layer.
The corresponding Onsager coefficient $L_{QV}$ is not related to Dufour
effect and its coefficient $L_{Q1}^{\prime }$.

Our analysis suggests that the mobility $D_{T}$ defined in (\ref{2}) and
measured in many experiments, comprises different contributions: thermal
diffusion, thermophoresis, spatially varying chemical reaction rates,... \
In each case, there is a conjugate effect with a reciprocal coefficient.
Above we have discussed the relation between thermal diffusion and the
Dufour effect ($L_{1Q}^{\prime }=L_{Q1}^{\prime })$, and thermophoresis and
the pressure-driven heat flow ($L_{VQ}=L_{QV}$). Similarly, the equilibrium
between the molecular and micellar states in a surfactant solution, feeds a
steady micelle current (\ref{40}) that is proportional to the temperature
gradient; the coeffiicient $D_{T}$ is determined by the reaction rates of
micelle formation.

\subsection{Thermal diffusion or thermophoresis?}

Most authors use \textquotedblleft thermal diffusion\textquotedblright\ for
molecular mixtures and \textquotedblleft thermophoresis\textquotedblright\
for colloidal suspensions, though in both cases the coefficient $D_{T}$ is
defined by (\ref{2}). The above discussion gives a more precise meaning to
this disctinction. In the case of thermal diffusion, viscous effects are
absent, and $D_{T}$ and the Dufour coefficient are related by reciprocity.
In the stationary state the particle currents vanish, $\mathbf{J}_{1}=0$,
and so does the corresponding entropy production.

Thermophoresis, on the other hand, is determined by viscous flow. Then the
mobility $D_{T}$ is given by the Onsager cross-coefficient $L_{VQ}$ which
describes volume flow due to a temperature gradient. As worked out in a
previous paper \cite{Wue13}, the entropy production related to the particle
fluxes vanishes in the steady state $\mathbf{J}_{1}=0$, the viscous flux
continues to dissipate energy. The hydrodynamic flow around each particle
maintains a finite rate of entropy production $\mathbf{\Pi :G}>0$.

\subsection{Comparison with experiment and simulations}

According to the preceding discussion, the reciprocity relation between $%
D_{T}$ and $D_{F}$ is valid for thermal diffusion only. In other words,
reciprocity requires that diffusion and thermal diffusion coefficients can
be expressed through the mobilities $B_{k}$ as in (\ref{26}). In view of the
fit of \ $S_{T}=D_{T}/D$ in Fig.\ 1, the alkane data\ are not in
contradicton with the thermal diffusion picture. In order to obtain
conclusive evidence, one would have to consider the coefficients $D_{T}$ and
$D$ separately, and this at different composition. \ On the contrary, data
on polymer solutions and particle suspensions rather agree with
thermophoresis mechanism, indicating that viscous effects prevail if the
solute is much larger than the solvent molecules \cite{Gid76,Bro81}. Yet the
break-down of the thermal diffusion picture may occur well before viscous
behavior in the sense of macroscopic hydrodynamics sets in.

In technical terms, (\ref{26}) ceases to be valid if the molecules respond
differently to the thermal and concentration gradients in the thermodynamic
force (\ref{19}). Yet nothing is known about the underlying mechanisms and
the relevant parameters. At present it is not even clear whether the thermal
diffusion picture applies to mixtures of organic molecules of similar size
and weight, such as benzene, cyclohexane, and alkanes. Whereas thermal
diffusion data are available for many systems \cite%
{Har13,Deb01,Kit04,Kit05,Har06}, there are only few studies on the Dufour
effect \cite{Ras70,Hor78}. Comparison of measured $D_{T}$ and $D$ with (\ref%
{26}) could provide valuable information.

In recent years, molecular dynamics simulations have become a powerful tool
for studying the thermal diffusion and transport properties. Besides the
dependencies on molecular enthalpy, mass, and size \cite{Mue99,Art07,Gal08},
both diagonal and off-diagonal Onsager coefficients have been evaluated \cite%
{Mac86,Pao87,Mil13,Arm14}. For the investigated Lennard-Jones systems, the
simulations confirm reciprocity of the thermal diffusion and Dufour
coefficients. So far there is no systematic numerical study of the validity
of (\ref{4}) and (\ref{26}). The above discussion suggests a break-down of
the thermal diffusion upon differentiating the two components in molecular
size or shape.

\section{Summary}

In this paper we discussed the coefficient $D_{T}$ of thermally driven
transport in three situations, where the entropy production is dominated by
diffusion, chemical reactions, or viscous flow. In the first case, $D_{T}$
is determined by the molecular enthalpy and diffusion constants $B_{i}$
according to (\ref{26}).\ The conjugate effect is the Dufour effect, and $%
D_{T}$ and $D_{F}$\ are reciprocal coefficients.

As an example of chemical reactions, the temperature-dependent equilibrium
between micellar and molecular states in a surfactant solution, imposes a
steady-state diffusion current. The resulting coefficient $D_{T}$ in (\ref%
{40}) is given by reaction rates and the micelle enthalpy $H$. As the
reciprocal effect, an externally imposed micelle current feeds a stationary
reaction flux $\mathcal{J}=\dot{\phi}_{1}$.

\begin{figure}[tbp]
\includegraphics[width=\columnwidth]{Fig4.png}
\caption{Molar volume of normal alkanes. The circles give the measured
values at room temperature, the solid line has been calculated from Eq. (%
\protect\ref{72b}). }
\end{figure}

If dissipation is dominated by viscous stress, as for colloidal suspensions
in (\ref{69}), $D_{T}$ depends on the interaction enthalpy and the solute
viscosity. The reciprocal cross-coefficient $L_{QV}$ accounts for advective
heat flow in a pressure gradient.

Thus in the presence of chemical reactions or viscous effects, $D_{T}$ is
not related to the Dufour effect. In future work, it would be interesting to
study whether and to which extent, the thermal diffusion picture (\ref{26})
is valid in binary molecular mixtures.

\textbf{Acknowledgement. }This work was supported by Agence Nationale de la
Recherche through contract ANR-13-IS04-0003.

\section{Appendix: Alkane enthalpy and volume}

The fit of alkane Soret data in Fig. 1 relies heavily on the variation of
the molecular enthalpy and volume (\ref{72}) with the number $n$ of carbon
atoms. In particular, the relative off-set values of $0.65$ and $2.02$
determine to a large extent the theoretical curve. If these numbers were
identical, the specific enthalpy $\hat{h}=h/v$ would be independent of $n$,
and $S_{T}$ would vanish for all mixtures; exchaning the off-set values
would result in a positive Soret effect for the lighter component.

An at least qualitative explanation for the off-set of $0.65\times
4.64\approx 2.9$ kJ/mol is given by a simple geometrical argument for
polymers on a 3D cubic lattice. A monomer has 6 couplings with next
nearest-neighbor molecules and a dimer has $\frac{10}{2}=5$ such couplings
per unit. For a rigid high polymer there are $4(n+2)$ couplings, that is,
about 4 per monomer, and a slightly smaller value occurs for flexible
polymers. These numbers are very close to the factor in (\ref{72a}).

The volume off-set accounts for the fact that the density of shorter alkanes
is smaller; it is related to the larger entropy of short chains. Fig. 4
shows measured values of the molecular volume $v_{n}$.\ The solid curve,
calculated from (\ref{72b}), provides a very good fit to these data.

redpajama_set_name: RedPajamaArXiv


Combination or Combi Boiler - These produce hot water on demand and are highly economical. A great solution for properties with limited space thanks to their single unit form without the need for a cylinder.
System Boiler - In homes with more than one-bathroom System Boilers are ideal because they use a cylinder to store hot water, while most of the heating takes place in the boiler itself.
Regular Boiler - These are a particularly good option for replacing old boilers without having to update the entire central heating system. They use a hot water cylinder as well as cold water and an additional storage tank which is usually found in attic space.
With our help choosing the right boiler for you, we guarantee a professional boiler installation by one of our highly competent engineers.
Just as your car needs a service on a regular basis, it's strongly recommended that your boiler is serviced annually too. In the long run it can save you money as having a service ensures that your boiler is running efficiently, but also identifies any potential problems which can be costly to repair in the future.
Servicing boilers is second nature to our professional and qualified team at Williams who make sure that it is working as effectively as possible. From multiple occupancy apartment blocks to bungalows with a small system, our knowledge of boilers of all shapes and sizes won't let you down.
Boiler emergencies can happen when you least expect them, and sometimes when you need your boiler most. It can be a distressing time but our friendly and reliable engineers in Bristol and surrounding areas such as Bath and South Gloucestershire are on hand to help. As soon as you call, we aim to be with your as soon as possible to run tests, exchange parts and fix any issues to get your hot water running again.
Williams are industry experts in mending faulty boilers, so no matter what boiler type, make or model we can fix the problem efficiently and cost effectively.


While we are unaware of a TripAdvisor Tourism page that is specific to Pentacre, there are nearby communities that are likely to provide the information that you're looking for. If you want to learn more about those communities, the following map should be of help.
Below is a list of those communities which have a TripAdvisor Tourism page and are relatively close to Pentacre - within 50 miles [80.5 km]<1>.
Unfortunately, we don't know of an official website for Pentacre. If you can help, please contact us through our Feedback Page.
<1> Our distances are not driving distances, but are calculated as a 'straight-line' distance. A straight line distance ignores obstructions like rivers, canyons, lakes, et cetera - it's truly a line from Point A (ie- Pentacre) to Point B.
Our distance measurements begin at a specific point in Pentacre. The point we use is located at these GPS coordinates - Latitude: 38.3904, Longitude: -81.4035 [Map]. In this case, the coordinates for Pentacre have been provided by the Geographic Names Information System (GNIS).


Avadhoota Datta Peetham, Sri Ganapati Sachchidananda Ashrama, Mysore, founded by Parama Pujya Sri Swamiji, is a world-renowed institution for the social, moral and spiritual welfare of mankind. Pujya Sri Swamiji's universal vision and deep compassion for the upliftment of the mankind has inspired the Datta Peetham to run a vast variety of programs, activities and projects towards enrichment of human life.
Pujya Sri Swamiji, an Avadhoota imbued with the highest spiritual attainments, is Himself ceaselessly engaged in giving direction and shape to the Peetham's diverse programs and projects. It is primarily the value placed on the intrinsic worthiness of human life and the paramount need of enhancing the same, which constitutes the underlying philosophy behind the multi - dimensional activities of the Peetham.
Sri Swamiji started the Datta Peetham more than 40 years ago, built about 30 Datta temples all over the world and established nearly 60 Gnana Bodha Sabhas and several Datta Yoga Centers in India and other countries. Sri Swamiji has established Jayalakshmi Mata Nitya Annadaana Trust which provides free food three times a day, every day - in fact it feeds nearly 20,000 people on certain occasions. Sri Swamiji is famous for His Music for Meditation and Healing Concerts all over the globe. He has composed more than 5,000 songs in several languages and produced a number of music albums, the profit of which goes towards these social projects. He has conducted more than 200 Healing and Meditation concerts all over the world. Sri Swamiji sings highly devotional songs with His divine voice.
Ammavodi, a home for destitute aged women is a shelter to aged women who have no one to care.
Educational aid to poor students in the vicinity of the ashram.
Eye camp clinic at Chennai, India.
Donation of 20 lakhs for flood relief fund.
Distribution of Educational aids to Poor students.
1) Repair of the damaged bore well and construction of a water tank.
2) Free Multi-Speciality Medical Camp.


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How to tell if you're an invasive species
By the time you're in the supermarket and you see a large, green slug on the shelf, you might have guessed that the creature is an invasive aquatic species.
The problem is, there is no way to tell for sure.
But it's important to know that many species are so incredibly invasive that there's no easy way to determine whether they're native or introduced.
And some species are just so huge, so large that it's almost impossible to know if you are native or foreign to the area.
And even if you can identify them, you don't know what the species is going to do to your environment, since many species will move on without you.
So the first step to identifying an invasive organism is to know what it is, and what it does.
An invasive species is any plant or animal that has an unintended effect on your environment.
To determine if a species is invasive, you have to look at its genetic make-up, its host range, and how it is reproducing.
It's also important to look for signs of its impacts, such as disease and disease transmission.
The more invasive a species, the more invasive it is.
To identify an invasive plant, you need to know its host, the plant it's native to, and the geographical area it's from.
So a common method of identification is to look through a plant's photosynthetic pathway, the part of the plant that converts photosynthesis to chemical reactions.
Plants that produce light have an endosymbiotic relationship with microbes.
Plants with photosynthesizing bacteria and algae produce chlorophyll.
Plants where the plants have anaerobic bacteria and plants where the bacteria live symbiotically have symbiotic relationships with algae.
These relationships can help you identify plants that are native to specific geographic areas, and help you determine the type of plants that can survive in certain environments.
The most important aspect of invasive plants is the host range.
That's the area of land where a plant is native.
The plants that live in the host ranges of different species have different host ranges, but they're all related to the same species.
So for example, a plant that lives in the Atlantic, the same plants that have been found in the Caribbean and South America, and in the Pacific, and all over the world are all the same plant, although the Atlantic is actually much more diverse.
This type of information can be used to identify invasive species.
For example, if you look at the genetic make up of the Atlantic Bluefin tuna, you can be pretty certain that it was an introduced species from the Atlantic.
But if you do the same thing for the Atlantic salmon, you will be able to tell that it came from the Pacific.
The species that live on the Indian Ocean have a very different host range than those that live at the Indian, which is why they are sometimes called "the Pacific island species."
You can also use genetic information to help identify invasive plants.
In most cases, invasive plants have a genetic makeup that is similar to the host plants they are native in.
This means that they can survive if they are introduced in a certain area, and it can help them spread quickly.
And invasive species can have an unusual host range too, because they can move to different areas in different parts of the world, which can make them harder to identify.
It can be hard to get a complete picture of an invasive, but you can look at where you can see them.
You can start with a list of the plants you can find native to your area.
For instance, you could look at all the invasive plants that you can't find native in your area, such a the giant brown slugs in your backyard.
You might also consider the number of native plants in your local area.
In many cases, you may be able the species to be native or not native to that area, but for some plants, it can be more important to determine the exact native plant species.
You want to know where the invasive species resides.
You can use this information to identify the plants that need protection, which means that you want to try to reduce your exposure to the invasive plant and limit its spread.
You could start by planting native species.
Plants in your own yard can help reduce the spread of invasive species and may help protect them from being eaten by predators, parasites, or diseases.
Plants may also help reduce your risk of disease outbreaks by keeping the plant population under control, preventing the plant from becoming invasive.
And if you want your plants to grow, you should plant them in a way that promotes their growth and helps reduce their risks.
If you have a list and can identify the invasive organisms, you are more likely to be able stop the spread and prevent disease.
This is particularly important when you are dealing with an invasive predator.
In the Atlantic bluefin tuna case, the Atlantic can eat and eat and consume.
But even though it eats, it doesn't die
define fisheriesdixon fisheriesfisheries biologistinland fisheries
What's next for blue crab?
How to make a seafood farm in the woods

redpajama_set_name: RedPajamaCommonCrawl


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do angler fish eat humans
These individuals were a few centimetres in size and almost all of them had what appeared to be parasites attached to them. The male ceratioids are significantly smaller than a female anglerfish, and may have trouble finding food in the deep sea. Some people also … In times of hardship for the humans, dependent on weather and availability of food, numbers of humans for the angler fish to catch reduces dramatically. March 23, 2018—A mated pair of deep-sea anglerfish has been filmed in the wild for the first time. [citation needed], A mitochondrial genome phylogenetic study suggested the anglerfishes diversified in a short period of the early to mid-Cretaceous, between 130 and 100 million years ago. The Japanese, as well as various European and African nations, also prepare several types of anglerfish … While the deep seas are cold and seemingly empty of food, many species manage to survive in … Reductions in amino acid synthesis pathways and abilities to utilize diverse sugars are found. [15], It is known that genetic makeup of the symbiont bacteria has undergone changes since they became associated with their host. In Korea and Japan monkfishliver is considered a delicacy. The angler fish is perhaps the most famous deep-sea fish. In most anglerfish species, the longest filament is the first. The anglerfish has huge jaws, so she can eat fish larger than she is. Its long, flowing spines help it sense the prey that it lures in. However, it appears that each species uses its own particular species of bacteria, and these bacteria have never been found in seawater. [14], Some evidence shows that some anglerfish acquired their bioluminescent symbionts from the local environment. Angler fish are not picky eaters. [4], All anglerfish are carnivorous and are thus adapted for the capture of prey. [13][14], The light gland is always open to the exterior, so it is possible that the fish acquires the bacteria from the seawater. In Europe and North America, the tail meat of fish of the genus Lophius, known as monkfish or goosefish (North America), is widely used in cooking, and is often compared to lobster tail in taste and texture. These are at the top of the food chain and are often predators rather than prey. As it stands, maybe a giant squid would give a free swimming human a go. They live and remain reproductively functional as long as the female lives, and can take part in multiple spawnings. This is how humans impact the angler fish. Thus, males never mature without attaching to a female, and die if they cannot find one. By the time the prey realizes the lure isn't something they themselves can eat, they've become the Angler's meal. Women have a section of spine that comes over their mouths that has a tip on the edge to catch their prey. [30] The eggs in this sheet are in a single layer, each in its own cavity. What is the conflict of the story sinigang by marby villaceran? Enjoy the videos and music you love, upload original content, and share it all with friends, family, and the world on YouTube. Their teeth make it so that their prey cannot escape their mouths. Especially in the deep sea, the occasional bycatch is not uncommon, but they are mostly not targeted. [17] The anglerfish is able to distend both its jaw and its stomach, since its bones are thin and flexible, to enormous size, allowing it to swallow prey up to twice as large as its entire body. The teeth can be depressed so as to offer no impediment to an object gliding towards the stomach, but prevent its escape from the mouth. Certain ceratioids rely on parabiotic reproduction. The larger anglerfish is the female. Megalosaurus ... What does a Angler eat? Their tissues fuse. Where Do Angler Fish Live? However, anglerfish in the lophiidae family are targeted as a commercial fishery. [4] At birth, male ceratioids are already equipped with extremely well-developed olfactory organs[26] that detect scents in the water. Anglerfish are also known as goose fish and monkeyfish. After fusing, males increase in volume and become much larger relative to free-living males of the species. [16], In most species, a wide mouth extends all around the anterior circumference of the head, and bands of inwardly inclined teeth line both jaws. 6 minutes per 1 gel - secondly use is a light source underwater
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April 20/16: Special Board Budget Meeting / Parent Education Fund
School Boards must present a balanced budget to the Ministry of Education by June 30 (School Act, division 2, Section 113). SD61 finalizes next school year's budget to avoid staffing upheavals over the summer, and at the school level in September, as much as possible.
This was the 4th and final budget meeting of 4 meetings dedicated to the topic, at which Trustees asked questions, discussed options, and had discussions with members of the public. Partner group input had been sought before the meetings.
One member of the public attended for part of this final budget meeting. The agenda was approved with an addition of a motion from the floor from Whiteaker: That the Board create a Parent Education Fund as part of the 2016-17 budget . No public presentations to the Board. Full agenda with financial statements and schedules here.
C. 1 2016/17 Annual Budget Debate
a) Recommended Motions [recommended by Secretary-Treasurer]
i) That the Board approve carrying forward $5,910,764 to the 2016/17 school year to be applied against the projected deficit./ Carried. Unanimous.
ii) That the Board approve not spending up to $800,000 on capital assets from the local capital reserve in 2015/16. / Whiteaker: Motion to postpone indefinitely. / Carried. Unanimous.
The motion was believed by Trustees to unnecessary as the original motion allowed spending "up to", which would include spending nothing; as well, negatively worded motions are discouraged by Robert's Rules 11th Edition p 105: "It is preferable to avoid a motion containing a negative statement…". "Postpone indefinitely" demonstrates intention by the meeting to not deal with the motion.
iii) That the Board approve carrying forward $1,800,000 to the 2017/18 school year to be applied against the projected deficit. / Carried. Unanimous.
b) New Business:
i) Whiteaker: That the Board create a Parent Education Fund as part of the 2016-17 budget item : PAC Grant of $6000, which will be administered under the guidelines for the Parent Education Fund. / Tabled to June Board meeting. Motion to table: For: Ferris, Leonard, Loring-Kuhanga, Nohr, Orcherton, Paynter, Whiteaker Against: McNally, Watters
Whiteaker:Last year this fund held $7000, and was successful. The SD61 Strategic Plan emphasizes building community and this fund does that, as schools collaborate to pool resources for parent education and events. With 48 school sites = 48 PACs, at $260 per school, the fund = $6,000. Suggest run this one more year and look at data then to see how it's working. In year 2 there will probably be more involvement as PACs increasingly utilize the fund.
Paynter: Is this $6000 in the budget?
Secretary-Treasurer: The $6000 would come from the item "PAC funding" . District PACS / DPACs [like VCPAC] get 24 cents per student FTE plus $165 per school, plus in SD61, $4000 annually to help support the Vancouver Island Parent Conference which the SD61 DPAC has organized.[Additionally, DPACs get gaming grants which they apply for. Some Districts allot $0 to the local DPAC. Whiteaker's presentation on DPAC funding from May 2015 here.] Last year the Fund re-allocation was $7000 ($4000 from the Conference District grant plus another $3000). DPAC (VCPAC) would still get $10,000. Over past number of years SD61 has budgeted $10,000 but this didn't reflect the formula the District agreed to use over the years, so the budget was adjusted. The Board has been giving $16,000 to VCPAC on an annual basis. [VCPAC has a significant contingency fund, around $20,000.]
Orcherton: We have been spending $16,000 a year on VCPAC, so this motion is to take $6,000 from that for PACS, leaving $10,000 for VCPAC?
Secretary-Treasurer: Yes.
Orcherton: Won't support this. VCPAC should have the money they've had in the past. VCPAC / DPAC can find ways to educate more parents with less money. Feel strongly that this is disrespecting VCPAC. VCPAC feels not respected by this Board.
Ferris: Scope and quality of conference VCPAC puts on is exeptional. $16,000 is a small amount of money. Could create a fund outside of it. Not necessarily against a separate fund. Taking fro VCPAC / DPAC is not right.
McNally: The new SD61 Strategic Plan emphasizes community and the Parent Education fund strengthens collaboration and community amongst schools as they combine resources to benefit their parent community. Don't understand claims that this fund is not supporting parents. It's direct support of parents at the parent-controlled school PAC level.Some Districts give no money to the DPAC.
Secretary-Treasurer: The $7,000 last year had a 1 year term associated with it, and was not a permanent reallocation.
Leonard: Against this last year and against it now. DPAC should administer all the money.
Paynter: Was a pilot project. Expectation was that information would come back as a basis to make a decision going forward. Don't have that. Motion to table to June Board meeting. / Motion to table carried. For: Ferris, Leonard, Nohr, Orcherton, Paynter, Whiteaker Against motion to table: Loring-Kuhanga, McNally, Watters
C.2 2016/17 Annual Budget Bylaw
a) Recommended motion (recommended by Secretary-Treasurer)
i) That the Board agree to give all 3 readings of the 2016/17 Annual Budget Bylaw at the meeting of April 20, 2016. (Motion to be carried unanimously.) / Carried. Unanimous.
ii) That the Board 2016/17 Annual Budget Bylaw in the amount of $211,963,918 be read a 1st, 2nd and 3d time, and passed and adopted on this 20th day of April 2016, and that the Secretary-Treasurer and Board Chair be authorized to sign , seal and execute this bylaw on behalf of the Board. / Carried. For: Ferris, Leonard, Loring-Kuhanga, McNally, Orcherton, Paynter, Watters, Whiteaker Against: Nohr
Nohr: Support all the work that has gone into this budget, but not the motion. Letter on p. 26 of this agenda describes the unmet needs in SD61 . There is a lack of direct instruction for vulnerable students. Its unacceptable that underfunding continues. This is a moral issue. [Summary of Nohr's longer speech.]
Ferris: Support the general feelings of Nohr. Support the Board and employees as well, and the consensus is that this is the best we can do at this time.
The Board will approach the partners named as potential signatories to this letter in hopes that all will agree to sign on. VCPAC has declined to be a signatory.
I voted against the SD61 budget in my first term, hoping that many Boards would follow the example of the Cowichan Board in 2012, when a majority of Trustees voted to submit only a budget that reflected true needs of the District. The Board was fired, and a Provincial Trustee appointed. It was interesting to see one person only making motions and one person only voting on them. Very efficient. None of that messy debate and democracy.
No other Board voted in majority to submit a needs budget only.
SD61 has submitted a parallel "needs budget" in the past, and this year is submitting the document on p.26 (above) of the agenda which specifies needs identified by stakeholders that can't be met with the funding we get from the Province.
I voted in favour of this budget because I believe that handing over the Board of SD61 Greater Victoria to a provincial government appointed Trustee would create greater problems for the District and students at this time, but next year, if major cuts are required, that assessment may not hold.
The Greater Victoria school board has passed a 2016-17 budget without major problems, but a tougher time is expected in 2017."We're in a better position than most school boards are," said chairwoman Edith Loring-Kuhanga."A lot of the school boards across the province are having to make some serious cuts. We will face that next year." Projections indicate there could be a deficit of $7 million to $8 million, she said. The Board has approved a 2016-17 operating budget of about $182 million and an overall budget of $212 million that includes capital funds and other items.
April 18/16: Board Meeting: Annual Facilities Grant / Pride Parade
May 2/16: Ed Policy & Directions: Aboriginal Student Achievement Review / Student Assessment Update


HomeEditorialOld, young – does it matter?
Not so long ago, research protocols excluded older cancer patients based on chronologic age. Now they exclude patients with comorbidities, and as most older patients suffer additional ailments, they do not fit the protocols. But these people are looking for our help.
Reconciling real-world medicine with artificial barriers that might limit treatment of any patient without good reason is one of the tasks of geriatric oncology. We have to develop strategies that enable us to evaluate the risks and benefits of curative treatments in all our patients, not only in the 'Olympic champions' who are fit enough to enter a standard research protocol.
Progress is slow but it will certainly accelerate as awareness grows of the huge unmet need. We have to find answers based on adequate evidence, as more and more older patients are seen in hospitals and doctors' offices, not only in the aging societies of Europe but all over the world. The time-bomb of the aging population is ticking, and governments need guidance to allocate the necessary resources for this growing segment of the population. If the cancer community does not provide that guidance, older patients could end up without access to key cancer services, just as happened with kidney dialysis services two decades ago.
We need to learn from our colleagues in other areas of medicine, and especially from the real experts – the geriatricians. But in many countries they are few and far between, and in heavy demand, so true collaboration remains a challenge. The International Society of Geriatric Oncology (SIOG), a member of the European Cancer Organisation (ECCO), plays an important role here by providing guidance, developed by multidisciplinary taskforces, to the nurses and physicians who treat the growing number of cancer patients with complex health issues.
But the taskforces themselves often lack top level evidence, so their recommendations, which are published in major journals including SIOG's Journal of Geriatric Oncology, need to be periodically revisited as new evidence emerges. With the help of the European School of Oncology, SIOG now also organises advanced courses, attended by physicians from all over the world, to train geriatricians in basic aspects of oncology, and oncologists in the fundamentals of geriatrics.
These courses will hopefully lead to many innovative clinical research projects, to be conducted in collaboration with national groups and others like the European Organisation for Research and Treatment of Cancer. The findings should help answer the many unresolved questions about how to prevent and treat cancer in older people, and how best to care for patients and support their families and friends. They will also demonstrate that age, frailty and comorbidities do matter, and that only research that includes this growing group of patients can provide the evidence we need to provide truly personalised care, respecting the patient's goals, and recognising the risks and benefits of the suggested treatment.
1 Comment on Old, young – does it matter?
Very good points! Let's make sure research includes the populations most needing medical solutions! And please INCLUDE patients in the research agenda setting, prioritization, protocol design and evaluations!!


A holiday villa can make for a sensible investment, particularly for anyone who plans to divide their time between two countries. While far more expensive than mainland Spain, Mallorca enjoys stable growth in property value and, with more and more people emigrating from their native lands, some might predict a healthy property rise from purchasing on the island, providing that their investment is sound and fully researched.
Demand for Mallorca holiday villas in the most popular resorts for both holiday and longer lets is rarely met, and during the high season prices can treble those charged during the cooler months. Even if you're planning to live in your property for much of the year, it's still possible to repay your annual mortgage costs with what is earned during the summer.
You will need to decide whether to let your property independently or through an agent. If you choose the latter, be selective and seek a recommendation; standards differ wildly and commission can be steep.
If your Mallorca holiday villa needs staffing you should account for spending almost double an employee's annual wage after social charges' contributions plus the two months' bonus salary given each year. Corporation tax on small to medium sized businesses rests at 30%, and the assets deductible system is not as generous as in some overseas countries.
Location beachfront properties are always in high demand, as are those located in beautiful surrounds and the more popular towns.
Many villas offer pools, so if yours does not have one then it may get passed over in favour of the competition.
Good transport links it might be beautiful, but if it takes three hours to get to the nearest town then the customer may not be happy.
Weather remember that the southern and western parts of the island enjoy year round sunshine and good amenities. In the north and east winters are far colder, and thus these areas tend to operate on a six month year.
Growth potential is its nearest town enjoying a programme of redevelopment, are more high end restaurants and shops opening up? Or are there plans to open a rubbish dump next door and a pylon right in the middle of that lovely sea view?


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It seems as though China can't get enough of glass. On May 1, the world's largest glass-bottomed observation platform opened 1,300 feet above the Jingdong Stone Forest Gorge in the Pinggu District near Beijing. The platform is nearly 4,500 feet square and hangs 107 feet beyond the edge of a cliff in the gorge.
The Jingdong Stone Forest Gorge is already a popular tourist attraction and offers scenic views of colossal natural stone formations. The viewing platform is made primarily from glass and titanium. According to the curators of the site, this is the first time that lightweight titanium – typically used in the manufacturing of aircraft – has been used in the construction of a building.
The platform can also claim to be the "longest" glass observation deck in the world. Although it is circular in shape, the platform extends 107 feet beyond the wall of the cliff – a full 37 feet longer than the glass observation deck in use at the Grand Canyon.
Panels of glass that are about 5 feet high surround the open-air Jingdong platform, and visitors have been seen walking, exercising, sitting and lying down on the glass. While some tourists enjoy the daredevil nature of navigating the attraction, others find it virtually impossible to walk so high above the gorge.
Last year, tourists at the Yuntai Mountain Scenic Park were horrified to see a crack emerge in the 1,300 foot long glass walkway there. That walkway is 3,500 feet off the ground, and was closed immediately after the incident for repairs. One of the glass panels in the walkway was damaged when a sharp object fell on the panel and damaged it. No one was injured in the incident.
Other glass platforms and observation decks have been damaged similarly, including the one at the Willis Tower (formerly the Sears Tower) in Chicago. In 2014, the Willis Tower observation deck, which is an open-air surface suspended 103 stories above ground and offers a 360° view of the city, cracked while tourists were standing on it. The visitors were never in any danger; the Willis Tower observation deck is built to withstand 10,000 pounds of pressure without buckling.
In the next post, we'll look at China's newest glass suspension bridge, which is expected to open in July. In the mean time, if you're looking for some glass inspiration, please check out the rest of our site. If you'd like to purchase Glassprimer™ glass paint, please visit our online store .


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Halloween Fun!
You won't be able to escape Ballistic Pig this Hallowe'en! We're playing Official's in Ucluelet on October 26th for their party and Jack's in Tofino on October 31st! So get dressed up and come to one (or both) night for some scary rock and roll fun!
If you're looking for some slightly mellower fun Geoff's got another solo gig coming up on October 24th at The Wickaninnish Inn's Driftwood Lounge and of course Jam Night is every Monday at Jack's hosted by your favourite rockin' pigs.
Hope to see you out in the coming weeks. I'm going to leave you with a few tunes to get you in the Hallowe'en mood
Geoff Solo Thursday at Black Rock in Ucluelet
This Thursday, October 17th Geoff will be grabbing his trusty duo of Canadian made acoustic guitars as playing some cover tunes at The Black Rock Resort's Float Lounge in Ucluelet. He's played the room a couple times and it's always been fun. He may be joined on a tune or 2 by our new full-time vocalist Tara so stop in, have some sushi and a martini or whatever and enjoy some tunes.
Music will start around 7pm through to last call at 10ish
Speaking of Geoff's solo set, here's a little bit of heresy to get you in the mood
Coming up in October on the Ballistic Pig calendar: Every Monday is jam nights at Jack's in Tofino (of course). Geoff solo at The Wickaninnish Inn's Driftwood Lounge on October 24th and the (new) full band on October 26th at Official's in Ucluelet's Halloween party!
Hope we see you out there at one of these shows. -Geoff
The Show Goes On!
As I mentioned in the last post we're entering into a new Ballistic Pig Chapter (or BPC). We're turning into a 4 piece with full time female lead vocals and our set will change a bit as well. We're still playing a lot of classic rock but are planning to venture into the 80's and 90's a little more and dabble in more pop and dance type arrangements. We'll still be screaming Led Zeppelin and such (as well as Motorhead and Iron Maiden) but you'll also hear more things like P!nk, Billie Idol, Roxette and the like. We're also hoping to deepen our repertoire of CCR and 50s/ early 60s rock to get everyone dancing and singing along.
Some of the transition is happening pretty quickly and Ucluelet will get its first taste of the new Ballistic Pig experience at Official's for their Halloween party on October 26th. We've also got a show in Port Alberni at The Blue Marlin Inn (formerly The Arlington) on November 15th. I suspect we'll have a weekend at Jack's in Tofno sometime soon too. If you're booking a holiday party or other event you need entertainment for let us know as we've got a couple other tentative bookings and we wouldn't want you to be disappointed. We're also planning to play weddings in the coming year so keep that in mind.
Finally, New Ballistic Pig (minus Tara because she's out of town) will be hosting the Monday night jam at Jack's in Tofino just like usual. See you there! -Geoff
Ballistic Pig has a long history and history has chapters. This Monday we'll turn the page on a chapter of Ballistic Pig's tale as we say goodbye to Chester Hamm. Chester and Geoff formed Tofino's first taste of Ballistic Pig a few years ago playing a few gigs with Sebastian Simard. That band crumbled and Ballistic Pig was reborn in August 2012 when Chester and Geoff were asked to cover some cancellations and Jack's Pub in Tofino.
After playing together steadily for more than a year Chester has decided to head across Vancouver Island and set up in the Comox Valley. In order to keep the rock going Ballistic Pig has already began retooling. Geoff will be playing guitar again, leaving the bass to the newest Pig, Jamie Pigkard. Also, Tara 'Hamila' Halil will be joining us full-time on lead vocals. So the squealing will go on.
A huge thank you to Chester for his role in the creation of this generation of Ballistic Pig. It has been a fun year and we're all fortunate to have found group of like minded musicians in the village of Tofino. Good luck ahead and feel free to crash our gigs with your Strat any time.
Left to Right: Geoff, Nick and Chester after a gig during the "Chester Era"
Join Ballistic Pig in saying goodbye the The Old Hamm this Monday for jam night at Jack's. It's going to be Chester's last official posting as a Ballistic Pig so let's make it a good one!


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Q: "with submission"
Hamilton quickly focused on the last part of his opponent's argument as support for his attempt to
  introduce evidence of the truthfulness of his client's publications. Hamilton offered the following
  brilliantly ironic response:

Well, suppose it were so, and let us agree for once that truth is a greater sin than falsehood:
    Yet as the offenses are not equal, and as the punishment is arbitrary, that is, according as the
    judges in their discretion shall direct to be inflicted; is it not absolutely necessary that they
    should know whether the libel is true or false, that they may by that means be able to proportion
    the punishment? For would it not be a sad case if the judges, for want of a due information,
    should chance to give as severe a judgment against a man for writing or publishing a lie as for
    writing or publishing a truth? And yet this (with  submission), as monstrous and ridiculous as it
    may seem to be, is the natural consequence of Mr. Attorney's doctrine that truth makes a worse
    libel than falsehood, and must follow from his not proving our papers to be false, or not
    suffering us to prove them to be true.

Woudl someone please explain and elucidate with  submission? I guess its meaning to be the following, yet I still don't apprehend it:
2.2. [count noun] [Law]  A proposition or argument presented by counsel to a judge or jury.
Source: P38, America on Trial by Alan Dershowitz

A: More in the sense of humility. Today one would likely say "with all due respect" or "with respect to my learned opponent."

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With Wake County voters set to vote this fall on a half-cent sales tax increase that would help pay for mass transit projects, those responsible for planning and implementing projects are getting a closer look at how areas similar to the Triangle handle mass transit.
A group from the Regional Transportation Alliance traveled this week to northern Virginia to see how Arlington handles moving hundreds of thousands of people around each day.
"When a market is growing, your transportation system has to grow right along with it," Regional Transportation Alliance Executive Director Joe Milazzo said.
Milazzo said business leaders and elected officials chose to study Arlington's systems because it's similar to the Triangle.
"They're growing, high-tech areas – a lot of similarities with what we have here in Wake County, in the Triangle," Milazzo said.
The Arlington area offers many different transit options, including subway, commuter rail and a bike-sharing program similar to the one Raleigh approved this year.
Communities there also have access to something else Wake County officials want to implement: bus rapid transit.
"A lot of our buses don't come that often, and when they don't come that often, it's hard to look at that as a way you might want to get around," Milazzo said.
The Wake County transit plan calls for 20 miles of bus rapid transit corridors running along Western Boulevard, Capital Boulevard, New Bern Avenue and Wilmington Street.
Dedicated bus lanes and priority treatment at traffic signals would provide faster, more frequent service.
"Particularly in Arlington, those buses come as fast as the metro rail system, so you can count on it," Milazzo said.
Milazzo said several elements will be required to take Raleigh and the Triangle to the next level in terms of transit options.
If the referendum passes in November, Wake County would be responsible for paying half the cost of the $2.3 billion transit plan. State and federal dollars would account for the rest. Officials said a transit tax would raise an estimated $78 million a year.