wettability of a solid 
 surface is one of the most important properties 
 for microfluidic systems .
application of controlled surface wettability 
 for delivery of small amounts of fluid to the desired route in micromixers , 
 pumps , and lab on a chip systems has unlimited potential
. it may be 
 the only desired mechanism for certain applications when the input 
 of electrical power is unavailable or can change the properties of 
 the analyte fluid .
wenzel and cassie proposed and explained wetting regimes of the 
 surfaces with controlled roughness .
developed models 
 and explained the mechanisms for controlled surface wettability with 
 surface roughness , design of self - cleaning surfaces , and droplet transport 
 on micropatterned surfaces with force and energy balance . using these mechanisms , zhu et al .
tuned 
 wettability of the surface by controlling its roughness with well - designed 
 microstructures .
similarly , yang et al . explained droplet 
 manipulation on hydrophobic surface with roughened patterns with conversion 
 of gibbs energy into kinetic energy .
wier , dorrer , and narhe explained the mechanism for droplets nucleation and transition 
 from wenzel ( lower energetic state ) to cassie wetting mode ( higher 
 energetic state ) in condensation on surfaces roughened with microtopography . 

rykaczewski explained the three - dimensional 
 aspects of droplet coalescence during dropwise condensation on superhydrophobic 
 surfaces and its contribution to the heat transfer process . although 
 these topics are understood individually , the combination of two phenomena 
 ( wettability gradient for fluid delivery and fluid phase change through 
 condensation ) on one surface still represents significant challenges . 

the small and randomly distributed size of condensate droplets requires 
 a special mechanism for wettability gradient distribution over the 
 sufficiently large area of the condenser surface .
the nucleation and 
 growth of droplets on the micropatterned surface decrease their mobility ; 
 an effective mechanism is required to transfer them from the immobile 
  pinned  to the moving state .
few works have considered 
 the combination of these phenomena for enhancement of continuous condensation 
 cycle on a hydrophobic surface .
however , it is the combination of these phenomena into a single 
 model that has the potential implications for passively enhanced heat 
 transfer in heat exchangers . also , the self - cleaning condenser surface is useful for collection 
 of biological ( chemical , environmental ) aerosol samples .
first , the 
 conversion to a liquid ( denser ) phase can facilitate sample manipulation 
 and its chemical analysis when the concentrations are extremely low . 

second , this surface can deliver the sample from the collection unit 
 into an interfaced analytical or storage unit with no external power 
 input required .
the surface is installed in the flow chamber and 
 cooled with thermoelectric element under it .
the vapor in the exhaled 
 breath is condensed on it as exhaled breath gas passes over it .
the 
 exhaled breath condensate droplets are self - delivered into the interfaced 
 analysis sensor . in this work ,
we present the design of a self - cleaning 
 hydrophobic 
 condenser surface and a simple two - step technique to fabricate it . 

our design approach combines two physical phenomena : a capillary pressure 
 gradient and a wettability gradient .
the key feature of this design 
 is the shape , size , and distribution of the microfeatures and trapezoidally 
 shaped grooves and ridges .
this geometry and its distribution enhance 
 droplets transfer from the wenzel to the cassie state and directional 
 transport over long distances ( 6 mm ) .
the trapezoidal geometry of 
 the micropatterned grooves and ridges creates a capillary pressure 
 gradient which enables droplet transfer , right after nucleation , from 
 the  pinned  state , inside the groove , to the upper 
 surface of the ridge .
this geometry also 
 enhances the wettability gradient distribution on the surface ; not 
 only between radial regions but also along the radial length ( 1 mm ) 
 of each region . upon dropwise
condensation , droplets with various 
 sizes , smaller than the micropatterns dimension , follow a designed 
 wettability gradient created with micropatterns from the most hydrophobic 
 to the least hydrophobic end of the surface .
the distribution of the 
 wettability gradient was estimated with the contact angle values predicted 
 with the wenzel and cassie models based on the designed micropatterns 
 dimensions . upon fabrication , the force balance was evaluated based 
 on the measured contact angle values and dimensions of the fabricated 
 micropatterns .
this hydrophobic micropatterned condenser surface 
 promotes continuous 
 dropwise condensation cycle and has higher condensation efficiency , 
 due to its directional self - cleaning property , than a plain hydrophobic 
 surface .
removal of condensate droplets from the surface contributes 
 to the heat transfer process by allowing nucleation of multiple droplets 
 on the same site .
dropwise condensation is 
 usually preferred to a filmwise condensation regime due to its higher 
 rate of heat transfer .
a liquid film significantly reduces 
 heat transfer across the surface and lowers condensation efficiency . 
 in dropwise regime ,
heat transfer between the surface and the humid 
 air is only affected where droplets are present .
large patch - like droplets on the surface are undesirable , too , because 
 they hinder the condensation process .
therefore , continuous droplet 
 removal from the condenser surface , before they form a liquid film , 
 maintains dropwise condensation regime with low thermal resistance 
 across the surface and increases condensation efficiency .
maintaining 
 dropwise condensation regime is challenging because droplets tend 
 to coalesce into a liquid film .
see video s1 in the supporting information for more details on maintaining 
 continuous dropwise condensation cycle .
the outer diameter of the condenser surface is 20 mm and consists 
 of six concentric micropatterned circular regions with an 8 mm wide 
 collection point in the center .
both the chemical composition and 
 physical roughness of the condenser surface contribute to its performance . 

the wettability gradient is obtained by gradually varying the roughness 
 of the surface with micropatterns created by contact photolithography 
 and deep reactive ion etching .
the whole 
 condenser surface is then made hydrophobic with a plasma fluorinated 
 polybutadiene film , proposed by woodward .
fabrication of the condenser surface starts with 
 a double - side 
 polished 100 silicon wafer that is baked at 110 c 
 for 12.5 min to evaporate any moisture .
the wafer is spin - coated with 
 a layer of hmds primer and then with megaposit spr 220 - 7 photoresist , 
 12 m thick .
the micropattern geometries are transferred to the photoresist with 
 contact photolithography . after a 3 h delay to degas any nitrogen 
 trapped in the photoresist
the micropatterns are etched into silicon 
 substrate with deep reactive ion etching ( model : alcatel 601e ) .
the 
 wafer is cleaned with acetone , dried with nitrogen , and cleaned further 
 using oxygen plasma for 5 min at 200 w. microfabrication process 
 flow of mems based self - cleaning condenser 
 surface .
( e ) the wafer 
 is cleaned with acetone , dried with nitrogen , and cleaned further 
 using oxygen plasma for 5 min at 200 w. ( f ) spin - coat the wafer with 
 polybutadiene , followed by vacuum annealing , plasma treatment , and 
 postbaking .
the micropatterned surface 
 is coated with a plasma fluorinated 
 polybutadiene film to make the surface hydrophobic . 

polybutadiene ( aldrich , mw = 420  000 , 36% cis 1,4 addition , 
 55% trans 1,4 addition , 9% 1,2 addition ) is dissolved in toluene ( bdh , 
 + 99.5% purity ) at concentration of 5% ( w / w ) .
the wafer is spin - coated with the prepared solution at 2000 rpm 
 for 60 s. the thin film is annealed in a vacuum oven for 1 h at 90 
 c to remove entrapped solvent .
prior to the plasma treatment the chamber 
 is scrubbed with isopropanol followed by further cleaning using oxygen 
 plasma at 200 w for 15 min .
once the chamber reaches its base pressure 
 of 25 mtorr , cf4 gas is allowed into the chamber and the 
 electrical discharge ignited .
the plasma fluorination is carried out 
 at 150 mtorr , 60 w , and 3.0 sccm cf4 flow rate . to cure 
 the plasma fluorinated polybutadiene film ,
the wafer is postbaked 
 in a vacuum oven for 1 h at 90 c .
specific geometry and distribution 
 of the micropatterns ( grooves and ridges ) create a wettability gradient 
 toward the center of the condenser surface .
roughness of the surface 
 is controlled with the width of the grooves while the geometry of 
 the ridges is kept the same in all six regions .
only four outermost 
 circular regions are shown due to the limited window of view of the 
 microscope .
specific geometry and distribution of the micropatterns 
 create a wettability gradient in the direction toward the center of 
 the surface ( as indicated with a white arrow ) . upon fabrication ,
the self - cleaning property of the surface 
 was 
 verified with droplet self - actuated movement on dry surface and in 
 condensation .
we want to emphasize an important difference between 
 a self - cleaning surface and a self - cleaning condenser surface because 
 some surfaces lose their ability to actuate droplet movement once 
 they are wetted in condensation .
actuation of droplet motion on a 
 dry surface is one of the initial requirements for a self - cleaning 
 condenser surface .
the surface is defined dry if it is not cooled 
 and no condensation occurs on it .
the self - cleaning property of the 
 dry surface is characterized by measuring contact angle ( ca ) at each 
 micropatterned region of the surface .
a droplet of deionized water 
 with a volume of 12 l is deposited on each micropatterned 
 circular region , and its contact angle is measured with a goniometer 
 ( ram - hart model 250 ) .
droplet mobility on the dry surface is measured by placing a droplet 
 of deionized water with a volume of 3 l at the outer , most 
 hydrophobic , region of the surface and letting it flow along the wettability 
 gradient , toward the collection point .
the droplet movement is captured 
 with a video camera , 29 frames / s , coupled with the goniometer .
droplet 
 movement , velocity , and dynamic contact angle ( figure 6 ) are obtained from the images ( frames ) extracted from the 
 video files .
the droplet displacement is evaluated from the distance 
 between a set point and the droplet as time progresses from frame 
 to frame .
image frames are extracted from the video files with matlab . 
 droplet displacement and dynamic contact angles were measured from 
 each frame with gimp 2 and imagej analysis 
 software package with the drop shape analysis plugin .
reported values are averages of three measurements . after observing effective self - actuated droplet motion on the dry 
 surface , we verified droplets mobility on wet surface and estimated 
 condensation efficiency .
the surface is defined wet when it is cooled 
 below the ambient temperature and vapor condensation occurs on the 
 surface .
the condenser surface is cooled with a thermoelectric element 
 ( custom thermoelectric , part number : 12711 - 5l30 - 25cq ) .
the thermoelectric 
 cooler is fixed with thermal grease to an aluminum block ( 143  
 102  23 mm ) , which serves as a heat sink to dissipate heat from 
 the opposite side of the thermoelectric element .
the condenser surface 
 temperature is measured with a thermocouple attached to it and equals 
 14 c .
relative humidity is estimated to 51% at measured dry 
 ( 24 c ) and wet ( 17.4 c ) bulb temperatures .
an lc plus 
 reusable nebulizer ( part number : 022f81 ) is used to imitate the saturated 
 air conditions .
the condenser 
 surface is placed in proximity to the nebulizer outlet nozzle but 
 is not contained in an enclosure with the nebulizer .
the saturated 
 air flow is positioned tangentially to the condenser surface to reduce 
 effect of direct droplet deposition .
we performed two sets of experiments 
 to verify the self - cleaning property of the wet surface .
the condensation 
 efficiency of the self - cleaning surface is evaluated by mass and volume 
 per area distribution as follows .
the total amount of collected 
 condensate is found by subtracting 
 the measured weight of the dry surface before the experiment from 
 the weight of the wet surface at the end of the experiment .
the effect 
 of the self - cleaning property on condensation efficiency is analyzed 
 by performing condensation tests in similar conditions with self - cleaning 
 and plain hydrophobic surfaces .
the volumetric condensate distribution 
 was obtained from optical 
 images of the condenser surface taken at the end of the condensation 
 tests .
droplets areas are estimated based on their border profiles , 
 as seen from above .
the volume of each droplet is estimated as that 
 of a hemisphere with the corresponding diameter .
condensation patterns on four types of surfaces are compared ( figure 3 ) under controlled conditions ( temperature , humidity , 
 and pressure ) , demonstrating a progression toward a self - cleaning 
 condenser surface .
the left - hand column images show the surfaces , 
 and the right - hand column images show condensation on the corresponding 
 surfaces .
patch - like condensation ( figure 3b ) is observed on a bare silicon surface ( figure 3a ) ; the droplets have large base diameters , 35 mm , 
 and are flattened , 1 mm high .
these droplets have low contact angle 
 and are precursors of the formation of a liquid film that will cover 
 the surface , once they coalesce .
the condensation mode changes from 
 filmwise to dropwise ( figure 3d ) when the flat 
 silicon surface is made hydrophobic by plasma fluorination of polybutadiene 
 ( figure 3c ) . from the side 
 view ,
droplet profiles are spherical with diameters of 0.52.0 
 mm and have contact angles greater than 90. because of the high 
 contact angle ( 122.2 ) and low hysteresis , these droplets are 
 unstable on the condenser surface ( figure 3d ) and move erratically once the surface is disturbed from a horizontal 
 position .
this hydrophobic surface ( figure 3c ) enhances dropwise condensation and droplet mobility but lacks 
 directionality .
micropatterning the surface with specifically 
 designed and distributed 
 microfeatures alters the surface energy and creates a wettability gradient .
figures 3e , f show the micropatterned silicon surface , which 
 is not chemically treated , and condensation on it .
the condensation 
 regime is dropwise on the micropatterned region of the surface but 
 patch - like on the unpatterned regions of the surface ( center and beyond 
 the outer edge of the patterned surface ) .
the three stretched droplets 
 sitting at the outer edge of the micropatterned area are in contact 
 with the roughened region and spread along the wettability gradient 
 along the two outer circular stages .
different condensation regimes 
 and droplets propagation ( extension ) along the wettability gradient 
 on hydrophobic surface suggest that roughening the surface with spatially 
 oriented geometrical micropatterns distributed in a specific way increases 
 surface hydrophobicity and creates a directional wettability gradient .
comparison 
 of condensation on four types of surfaces : step - by - step 
 progress toward successful design of self - cleaning microcondenser 
 surface .
the droplets are 
 patch - like , wide at the base and low at height ; they will form a liquid 
 film once their border lines meet .
( f ) the presence of wettability gradient is demonstrated with droplets 
 spreading along the micropatterns ( shown with white arrow ) . (
condensate droplets are self - collected 
 at the inner edge of the micropatterned area .
condensation on the micropatterned and chemically treated 
 surface 
 ( figure 3g , h ) demonstrates both dropwise condensation 
 and directional droplet movement .
the effect of the 
 wettability gradient is demonstrated by the fact that the microdroplets 
 self - collect at the inner edge of the micropatterned area .
these droplets 
 nucleate and grow throughout the surface and then move in the radial 
 direction due to the imbalance of surface forces acting on the opposite 
 sides of the contact line .
video s2 , in the supporting 
 information , demonstrates that capillary forces can resist 
 a flow of compressed air running at 4 m / s .
the droplets are driven 
 in the inward direction of the surface by capillary forces and resist 
 an airflow directed in the , opposite , outward direction .
some droplets 
 severely oscillate back and forth before they are blown off the surface .
high contact angle and low hysteresis are the key 
 criteria but so is the distribution of the wettability gradient and 
 the micropatterns geometry .
the micropatterns 
 dimensions must be small enough to affect the movement of small condensate 
 droplets .
the critical diameter is defined as a minimum droplet base 
 diameter , for a given length of a micropatterned region , below which 
 capillary forces will not be able to actuate droplet movement .
usually , 
 it is equal to twice the length of the surface topography features ; 
 i.e. , a droplet will move only if its base contact line covers at 
 least two regions with different wettability .
the fluid and dimensions 
 of the micropatterns determine the critical diameter of the droplet 
 that will be affected by capillary forces .
a researcher has to overcome 
 the following difficulties when designing a self - cleaning condenser 
 surface : creating an effective wettability gradient , optimizing the 
 shape , dimensions , and packing of the microtopography features to 
 provide a mechanism for condensate droplets to transfer from wenzel 
 to cassie wetting regime . increasing the condenser size
is desired 
 for providing sufficient 
 surface area for condensation , but it increases the distance that 
 a droplet has to travel toward the collection point which presents 
 the challenge of defining an effective wettability distribution over 
 a greater length . simply increasing the radial length of each micropatterned 
 region
does not solve this problem because for a droplet to move its 
 contact line must extend over at least two regions with different 
 wettability .
this will reduce 
 the overall heat transfer because droplets in each region will stay 
 immobile on the surface longer until they grow to the critical diameter . 

this will increase thermal resistance and reduce condensation efficiency . increasing the number of micropatterned regions
reduces the radial 
 length of each region and thus decreases the critical diameter of 
 the droplets .
but the difference in roughness between neighboring 
 regions decreases , too , reducing the driving force to move a droplet 
 from one region to the next .
hence , an optimal characteristic length 
 must be determined such that it is small enough for the transport 
 of droplets of various sizes and large enough to provide sufficient 
 area for condensation .
the distributed size of condensate droplets , 
 with volumes ranging 
 from less than 1 l to 4 l , complicates the droplet transport 
 problem as well .
a mechanism is needed to induce the movement 
 of droplets smaller than the length of the region in which they are 
 located . to address this ,
condensation on micropatterned hydrophobic 
 surfaces significantly 
 increases contact angle hysteresis ( cah ) which greatly affects droplet 
 mobility , creating an 
 additional challenge in the design of a self - cleaning condenser surface . 

droplets nucleate and grow in between and on top of micropatterns 
 and must transit from a wenzel state ( droplet 
 fills the micropatterns ) to a cassie 
baxter state ( droplet sits on top of the micropatterns ) upon condensation . in the cassie 
some surfaces completely lose their self - cleaning 
 property upon condensation , and others 
 partly , because droplets get pinned in 
 between microstructures .
the trapezoidal grooves and ridges of the 
 surface , described here , allow droplets transition from a wenzel to 
 a cassie  baxter state and enhance droplets 
 coalescence .
zimmerman et al . described 
 the force balance due to the capillary pressures in the contracting 
 microchannel .
capillary forces increase as the groove gets narrower 
 in the inward radial direction which causes the droplets to move in 
 the same direction toward a location 
 where the geometry is more favorable for the transition to a cassie 
droplets sitting on the top of the ridge 
 move in the inward radial direction because of the increasing width 
 ( contact area increase ) of the ridge toward the center of the surface . 

thus , we design the combination of two physical phenomena : capillary 
 pressure gradient and wettability gradient with trapezoidal geometry 
 of the micropatterns .
this geometry of the micropatterns is favorable 
 even for droplets with base diameter much smaller than the critical 
 diameter defined with the radial length of the micropatterns .
the novelty of this surface is that it provides a mechanism for 
 droplet transition from  pinned  immobile to mobile 
 state and promotes the transport of small condensed droplets over 
 large distances .
the insets in figure 4a show 
 micropatterns and droplet profiles for each circular region .
each 
 region consists of a periodic arrangement of radially oriented ridges 
 and grooves with the density of micropatterns increasing toward the 
 center of the surface .
the density of the micropatterns modulates 
 surface wettability and is changed radially to establish the wettability 
 gradient in the radial direction .
the wettability gradient 
 is distributed between the most hydrophobic end of the surface ( region 
 six ) and the least hydrophobic end ( region one ) .
both ridges and grooves 
 have trapezoidal profiles when observed from above ; the ridges get 
 wider and the grooves get narrower in the inward radial direction . 

this design creates a wettability gradient not only between the regions 
 but also along the radial length of each micropatterned region , which 
 enhances the movement of droplets with a base diameter smaller than 
 the region length and improves the self - cleaning property of the surface . to control the wettability ,
the dimensions of the ridges are kept 
 constant for all six regions and the average width of the grooves 
 is adjusted from region to region .
the width of the grooves measured 
 at the outer end of each region decreases from 110 m in region 
 six to 4 m in region one .
each region is 1 mm wide in the radial direction ; thus , 
 the maximum distance that a droplet can travel from the outer edge 
 of region six to the inner edge of region one is 6 mm .
the measured 
 contact angles decrease gradually from 157.0 to 126.7 
 toward the center of the condenser surface . the measured base diameter 
 of the moving droplet increases from 0.6 to 1.1 mm as the droplet 
 propagates from outward , most hydrophobic region , to the inward , least 
 hydrophobic region .
see video s3 in the supporting 
 information for more details on surface design and dimensions .
figure 4b compares a designed , effective , 
 contact angle distribution to a linear , ineffective , distribution . 
 reported static contact angle values are averages of four measurements 
 taken at each circular micropatterned region ; the error bars span 
 three standard deviations .
contact angle distribution1where fs is the 
 ratio of the area that contacts the droplet to the projected area 
 and e is intrinsic contact angle , i.e. , measured 
 contact angle at the unpatterned surface with similar properties ( 122.2 ) . 
 as the dimensions of micropatterns and surface hydrophobicity decrease , 
 the ability of a droplet to be affected by a change in wettability 
 decreases due to the increasing resistive forces
therefore , 
 the effective wettability gradient distribution should not be linear but increase in the inward radial direction for 
 effective directional droplet movement .
droplets deposited at the 
 outer edge of the micropatterned region stop at the third region where 
 the wettability distribution is linear . measured static contact angle 
 values ( figure 4b ) are lower than predicted 
 by approximately 10 , but the shape of their distribution closely 
 follows the designed one .
the observed decrease in contact angle difference 
 between the inner edge and region one as well as the linearity of 
 the distribution in regions one and two are explained by our technical 
 limitation to fabricate microfeatures less than 2 m at this 
 high aspect ratio .
we also note that while micropatterns in adjacent 
 regions six through two are interleaved with each other , regions one 
 and two are connected with no overlap .
measured static contact 
 angles show agreement with the values of 
 the contact angles predicted with the cassie  baxter model . 

the contact angle values predicted with the wenzel model ( not shown 
 here ) deviate significantly from the measured data .
this can be explained 
 if the droplets on the surface of the sampler are lifted by the microasperities 
 and have a liquid  vapor interface with the surface ; i.e. , the 
 wetting mechanism is in the cassie
the self - cleaning 
 property of the wet surface was tested during 
 condensation .
measurement of condensate mass , as described in the methods section , shows that the self - cleaning property 
 increases the amount of condensate by 5% in comparison to a plain 
 hydrophobic surface .
greater condensate mass proves that there is 
 a higher heat transfer rate between the moist air and the condenser 
 surface .
figure 4c shows 
 the volumetric distribution of condensate on the self - cleaning surface . 

droplets collected at the inner edge of the micropatterned 
 area ( figure 4c , inset ) .
the total estimated 
 volume , from the image analysis , shows agreement with the measured 
 condensate mass .
the volumetric distribution of condensate on the 
 surface demonstrates the superior performance of the self - cleaning 
 condenser versus plain hydrophobic surface .
first , the self - cleaning 
 surface routes condensate droplets in the predetermined direction . 

second , the total condensate volume estimation , area under the curve , 
 shows that self - cleaning surface collects 5% more condensate than 
 a plane hydrophobic surface with similar dimensions .
droplet movement 
 is postponed where the microfeatures size is large because 
 the droplets take longer to grow to the critical size .
the data 
 point at radius 3.5 mm corresponds to the volume per area distribution 
 at the central flat region .
surface topography , effective wettability gradient 
 distribution , 
 and self - cleaning property upon condensation .
( b ) effective contact angles 
 distribution , modeled with cassie  baxter model .
linear distribution 
 is not effective , droplets stop at the third region . measured distribution 
 is effective , droplets flow from region six to region one .
inset shows droplets distribution on 
 the surface at the end of the condensation test .
the volume per area 
 at the central flat region corresponds to radius 3.5 mm .
the lines 
 connecting the data points in ( b ) and ( c ) are interpolating curves 
 to guide the eye .
it is known that condensation 
 efficiency depends on the wettability 
 of the surface ; i.e. , less hydrophobic surfaces 
 have lower nucleation energy barrier than more hydrophobic surfaces . 

we should admit that the effect of hydrophobicity gradient in the 
 shape of volume / area distribution , in figure 4c , has not been completely elucidated in this experiment .
we did 
 not study what part of the variation in condensate volume distribution 
 is due to the effect of hydrophobicity on the condensation rate itself . 
 however , we note that the slight increase in condensation efficiency 
 is in comparison to the plain hydrophobic surface with similar dimensions 
 and chemical coating ( figure 3c , d ) .
the plain 
 ( not micropatterned ) surface ( figure 3c ) is 
 less hydrophobic ( ca = 122.2 ) than its micropatterned counterpart 
 ( figure 3 g ) because roughening the surface 
 increases its hydrophobicity , with ca ranging from 122.2 to 
 157.0. consequently the plain hydrophobic surface would be expected 
 to exhibit a higher condensation rate if the rate depended only on 
 the level of surface hydrophobicity .
our experiments show the opposite 
 trend , which is consistent with a predominance of the self - cleaning 
 property .
thus , it is very likely that the increase in condensation 
 efficiency is solely due to the self - cleaning property of the surface 
 rather than its hydrophobic gradient . in order to obtain a better 
 understanding of the droplet transition 
 mechanism from the immobile nucleation to the moving state , we observed 
 the condensation cycle under the optical microscope .
the time - lapse 
 images , shown in figure 5 , illustrate a continuous condensation cycle at microscale .
this 
 condensation experiment is conducted under similar temperature and 
 humidity conditions as the previous experiment .
see video s4 in the supporting information to observe continuous 
 condensation cycle captured under optical microscope .
local spreading 
 occurs when two or more stationary growing droplets merge with neighboring 
 droplets .
the droplet starts moving along the wettability gradient 
 toward the collection point if its diameter equals or exceeds the 
 critical droplet diameter . otherwise , it remains stationary , grows , 
 or undergoes another series of local coalescences with its neighboring 
 droplets until its contact line spreads over critical length and capillary 
 forces actuate its movement .
radial spreading occurs when a droplet 
 moving along the wettability gradient toward the collection point 
 absorbs other droplets on its path .
the volume of such droplet grows 
 rapidly , which lets its contact line spread over regions with different 
 wettability .
such droplet accelerates rapidly toward the collection 
 point and clears multiple droplets from the condenser surface .
figure 5 demonstrates mechanism for continuous condensation 
 cycle on hydrophobic self - cleaning surface .
the first time frame shows 
 dry condenser surface at the beginning of the experiment .
consecutive 
 time frames demonstrate droplet nucleation and growth , local , and 
 radial spreading .
a group of droplets that undergo a series of local 
 spreading events ( frames 02:30 to 05:00 ) unite into one droplet and 
 move in the radial direction ( frame 05:30 ) .
new droplets start nucleation 
 on previously occupied cite ( frame 06:00 ) , thus enhancing continuous 
 condensation cycle .
droplet radial spreading is hard to capture under 
 optical microscope since the area of view is limited .
such droplets swipe the surface 
 in the radial direction ; one can see a cleared path behind the droplet 
 in the table of contents image .
continuous condensation cycle mechanism 
 on self - cleaning condenser 
 surface : droplet nucleation and growth ( 00:30 , 02:30 ) , local spreading 
 ( 02:30 , 03:00 ) , and radial spreading ( 05:00 , 05:30 ) to clear new sites 
 for nucleation ; new condensation cycle starts at previously occupied 
 surface ( 06:00 ) .
droplets clear the surface in the radial direction , 
 which is toward bottom right corner .
number labels indicate the droplets 
 that underwent transition . we should give interpretation of the irregular shape of some 
 droplets 
 as observed from above under optical microscope , in figure 5 and video s4 .
we believe 
 that they are not necessarily the consequence of contact angle hysteresis . 

we provided an evaluation of the contact angle hysteresis for droplets 
 at the macro scale in figure 4b .
each data 
 point represents an average contact angle at each micropatterned circular 
 region .
these measurements show that it is negligible ( 35 ) . 
 the droplets that appear irregular at microscale are small ( 10300 
 m ) , early in their growth , right after nucleation .
they transit to the cassie state as they grow , which is confirmed 
 by their near circular profiles afterward , and flow along the desired 
 direction ( videos s2 and s4 , at 5:24 and 
 6:07 ) .
video s4 clearly demonstrates the 
 effect of the capillary pressure gradient created with specific micropatterns 
 geometry described earlier .
in fact , we believe that this ability 
 of the surface to promote transition from the wenzel to cassie state 
 is the most important characteristic without which the self - cleaning 
 property would not be possible . the self - cleaning mechanism 
 on condenser surface is more complicated 
 than that on a dry surface on which a droplet is introduced and made 
 to flow due to the presence of energy gradient on that surface .
the condensate droplets have very small and distributed diameters , 
 ranging from 10 to 1000 m .
two mechanisms are required : one 
 to transfer nucleated droplets from a pinned to a mobile state , i.e. , 
 to aggregate a group of small neighboring droplets into one that is 
 large enough to be affected by the wettability gradient and another 
 to move those droplets along the wettability gradient .
we described 
 the mechanism for local coalescence , the aggregation of a group of 
 droplets into one larger droplet , during the condensation cycle .
once 
 these droplets undergo a series of local coalescences and the resulting 
 droplet achieves the critical diameter , it will undergo radial coalescence . 

it starts moving toward the center of the surface , absorbing very 
 small droplets on its path , along the wettability gradient .
the critical 
 droplet diameter is determined by the radial length of the micropatterns ; 
 in this design it is 1 mm .
thus , a droplet with a base diameter greater 
 than 1 mm will flow due to the surface tension forces imbalance on 
 its opposite sides .
dynamic contact 
 angle values , obtained from image frames extracted from the video 
 files , as described in the methods section , 
 are commensurate with static contact angle measurements but different , 
 as expected .
this surface maintained reliable performance over multiple 
 tests before its self - cleaning property degraded , mainly due to mechanical 
 damage to the surface from handling .
droplet transport characterization on 
 dry surface : contact angle , 
 position , and velocity .
the droplet is deposited on the outer region 
 and is self - propulsed toward the center . to have an effective wettability gradient path that promotes 

the 
 motion of deposited droplets is one of the initial requirements to 
 a self - cleaning condenser surface .
there are several approaches to evaluate the capillary forces acting on the droplet 
 in the presence of energy gradient . in this analysis
, we assume that 
 a droplet with a known volume is placed on dry micropatterned surface . 

the actuating and resistive forces acting on the moving droplet have 
 to satisfy the second newton s law of motion.2 distribution 
 of actuating , resistive , and net force acting on the 
 droplet over the six regions of the micropatterned surface .
the magnitudes 
 of forces are evaluated based on measured contact angles and dimensions 
 of the micropatterns .
estimated the 
 actuation 
 force with the gradient of the surface free energy of adhesion of 
 the droplet with the surface ( g = rlv(1 + cos r))3 a stable droplet has to overcome the 
 static friction caused by 
 interfacial contact before moving and 
 the reaction of viscous force during droplet motion .
the resistance 
 force comes from two sources : contact angle hysteresis , a droplet 
 has to overcome the moving barrier before it begins to move , and viscous 
 force during droplet motion .
furmidge evaluated the hysteresis force as4where 
 r and a are dynamic receding and 
 advancing contact angles at the 
 instant at which a droplet begins to move .
the hysteresis force is 
 related to the gradient of the total energy barrier defined in eqs 35 .
suda and yamada evaluated the resistive 
 force resulting from the viscous effects.5where  is the fluid viscosity , v is the velocity of the moving droplet , and xmax and xmin are 
 the characteristic lengths of a liquid .
xmax is on the order of droplet radius ( 1 mm ) , and xmin is on the order of molecular dimension ( 0.1 
 nm ) .
the net force acting on the droplet is defined as the sum of 
 the three forces .
we must note that surface condensation significantly 
 complicates such analysis due to the changes in droplets volume , droplets 
 coalescence , and greatly affected contact angle .
figure 7 shows the distribution of the actuating , 
 resistive , and net force over the surface with wettability gradient . 

this estimation is made based on the average of the four measurements 
 of micropatterns dimensions ( as fabricated ) and measured contact angles . 

an average of the measured values is used because the dimensions of 
 the fabricated topography features differ from the design values .
the forces distribution for experimental case has a similar trend 
 as measured ca s distribution , shown in figure 3b .
the lack of interlocked connection of micropatterns between 
 regions two and one significantly increases the resistive forces which 
 affect the net driving force . in experiments
, we observe that a deposited 
 droplet accelerates rapidly and then slows down as it flows down the 
 wettability gradient path .
the droplet overcomes the resistive barrier 
 at the interstage region because it acquired enough kinetic energy 
 in the previous regions .
this behavior is confirmed with figure 6 ; it shows that a droplet accelerates initially 
 and slows down at the end of the path .
we want to emphasize 
 the importance of microtopography continuity 
 when modeling the wettability gradient .
the interface between two 
 consecutive micropatterned regions has important effects on droplet 
 transport .
the regions must not be separated but have the geometry 
 and dimensions that facilitate droplet motion from one region to the 
 next .
the packing density of micropatterns on these inter - region areas 
 must not significantly vary from that of the two neighbor regions 
 but be as close to their average as possible . such distribution and 
 agreement of microtopography features over
the condenser surface will 
 result in smoothly varying wettability gradient and effective droplet 
 transport .
the goal of this work is the creation of 
 a hydrophobic self - cleaning 
 condenser surface with a directional self - cleaning property that can 
 be used for collection of biological ( chemical , environmental ) samples 
 or for condensation enhancement .
the goal is not , at this time , to 
 demonstrate a significant increase in condensation efficiency . in 
 this initial device
, we achieve optimal performance with the simplest 
 microfabrication process to ensure robustness and reliability .
our 
 work offers insights into the design of a self - cleaning microcondenser 
 surface , the effective wettability gradient distribution , and the 
 micropatterns geometry .
the self - cleaning property is demonstrated 
 with droplet manipulation on the dry and wet , upon dropwise condensation , 
 surfaces .
easy fabrication process and surface reliability may make 
 this surface a good candidate for applications in biology and microfluidics . 

future work may include maximizing the condensation rate and performance 
 of microanalysis on the chip .
 combination of two physical phenomena , 
 capillary pressure gradient 
 and wettability gradient , allows a simple two - step fabrication process 
 that yields a reliable hydrophobic self - cleaning condenser surface . 
 
 the surface is fabricated with specific microscopic topography and 
 further treatment with a chemically inert low - surface - energy material . 
 
 this process does not require growth of nanofeatures ( nanotubes ) or 
 hydrophilic  hydrophobic patterning of the surface . 
 trapezoidal 
 geometry of the microfeatures facilitates droplet transfer from the 
 wenzel to the cassie state and reduces droplet critical diameter . 
 
 the geometry of the micropatterns enhances local coalescence and directional 
 movement for droplets with diameter much smaller than the radial length 
 of the micropatterns . 
 the hydrophobic self - cleaning micropatterned 
 condenser surface prevents liquid film formation and promotes continuous 
 dropwise condensation cycle . upon dropwise condensation , 
 droplets 
 follow a designed wettability gradient created with micropatterns 
 from the most hydrophobic to the least hydrophobic end of the surface . 
 
 the surface has higher condensation efficiency , due to its directional 
 self - cleaning property , than a plain hydrophobic surface . 
 we explain 
 the self - actuated droplet collection mechanism on the condenser surface 
 and demonstrate experimentally the creation of an effective wettability 
 gradient over a 6 mm radial distance . in spite of its fabrication 
 simplicity 
 , the fabricated surface demonstrates self - cleaning property , 
 enhanced condensation performance , and reliability over time . 
 our 
 work enables creation of a hydrophobic condenser surface with the 
 directional self - cleaning property that can be used for collection 
 of biological ( chemical , environmental ) aerosol samples or for condensation 
 enhancement . 
Introduction
Methods
Results and Discussion
Conclusions