Effect of Surface Structure on Liquid Wettability at ... - COMSOL.com

Presented at the COMSOL Conference 2009 BostonMODELING CONTACT LINE DYNAMICSIN EVAPORATING MENISCIJ. L. Plawsky, A. Chatterjee, and P. C. Wayner, Jr.Department <strong>of</strong> Chemical and Biological Engineering,Rensselaer Polytechnic Institute, Troy, NY-12180COMSOL User's Conference, Boston 1

Introduction: Phase Change Heat TransferThe efficient acquisition and rejection <strong>of</strong> heat at very high heat fluxes (kW/cm 2 )requires synergistic advances in heat transfer materials, heat transfer surfaces, andheat transfer devicesElectronics coolingPhotonics coolingSpace & AviationSolar EnergyVarious other applications include:Coating, Plating, Cooling, Separation and Reaction, Adhesion, Boiling andCondensation, Fuel Cell, Gas Sensor (porous coatings), Heat and Mass TransferOperations & Self-Assembly.COMSOL User's Conference, Boston 2

Evaporation from Transition RegionEvaporation occurs in the region which has the lowest total resistance to heattransfer.Heat FluxTransition region controls evaporation. Goal is to maximize its extent.− Accurate modeling will enable us to engineer optimal surfacesCOMSOL User's Conference, Boston 3

Experimental System - Heat PipesISS CVB ModulePhotograph <strong>of</strong> Module• Partially filled cell forms a Constrained Vapor Bubble (CVB) design.• Meniscus is present at corners where surface and the base meet• Forms the basis for a fundamental experiment in interfacial phenomena• Can be operated isothermally or driven by a temperature gradientCOMSOL User's Conference, Boston 4

Reflectivity/Interferometry TechniqueLiquid VaporInterfaceVAPORLIQUIDSOLIDAdsorbed FilmMeniscusVarying thickness <strong>of</strong> the meniscusproduces an interference patternInterference pattern analyzed to obtaingray value at each pixelG (x) =G(x) − G min (x)G max(x) − G min(x)RL(x) = G (x) ⎡⎣ RL max− RL min⎤ ⎦ + RL minRL(x) = α + β cos2φ l (δ )κ + β cos2φ l(δ )Gray Value (a. u.)230210190170150130G oG maxGG min0 20 40 60Distance (µm)COMSOL User's Conference, Boston 5

Nonisothermal State Meniscus - Octane150000.75 W0.75 W4E-7Smooth quartz60 min etched30 min etchedDeposited oxideThickness (m)3E-72E-760 min etchedDeposited oxideCurvature (m -1 )10000500030 min etchedSmooth quartz1E-72E-86E-5 7E-5 8E-5Distance (m)00E+0 5E-8 1E-7 2E-7 2E-7 3E-7 3E-7Thickness (m)Octane (8-C) used as a working fluidCOMSOL User's Conference, Boston 6

Fluid Flow Model• Lubrication approximation used to model fluid flow.• Navier slip (solid-liquid interface) and Marangonishear (liquid-vapor interface) boundary conditionsapplied• Mass balance provides the evaporating mass flux at each pixel location.• Temperature dependence <strong>of</strong> fluid properties accounts for the capillary, Marangoni and vander Waals forces.µ d2 udz = dP l2 dyz = 0,u s= β dudz z = 0z = δ( y), τ zy= dσ lvdyP l(y) = P v− ⎡⎣ σ(y)K(y) + Π(y) ⎤ ⎦Γ =δdΓ∫ ρ lu dy q ′′ = − h fgdy0COMSOL User's Conference, Boston 7

Heat Transfer at the Contact Line• Heat transfer at the contact line was modeled using a Kelvin-Clapeyron approach.dΓdy = − &m evp = C⎛⎝⎜M2π RT1 2⎞⎠⎟⎧⎪P vMh fg⎨⎩⎪ RT vT i( T i− T v )+ V P l vRT i( )P l− P v⎫⎪⎬⎭⎪13ν 1ddy⎡⎢⎣( σ o− γ ( T lv− T v ))δ 3 δ '''− γδ 3 δ " dT lvdy + 3A23γδδ '+δ 2dT lvdy⎤⎥⎦⎡⎛+ a( T lv− T v )− b σδ "− γ ( T lv− T v )δ "− A ⎞ ⎤⎢⎝⎜δ 3 ⎠⎟ ⎥ = 0⎣⎦• Since the pressure and difference can be written in terms <strong>of</strong> the film thickness, andthe temperature difference is measured or set, the final equation can be written as a4th order differential equation for the film thickness, δ.• Boundary conditions set the film thickness and curvature at both ends <strong>of</strong> the domain.– These conditions are established from experimental observations.COMSOL User's Conference, Boston 8

Simulation Results• COMSOL simulations were performedby splitting the 4 th order equation intotwo 2 nd order equations.– Splitting allowed for more controlover boundary conditions.– Limited us to steady-statesimulation.1.00.80.60.40.2Adsorbed Film Thickness (nm)41040• We were primarily interested in whetherthe model could simulate the curvaturepr<strong>of</strong>iles we observe experimentally.70.00.20.40.6Dimensionless Position0.81.0• Peak in curvature only occurs for smallvalues <strong>of</strong> the adsorbed film thicknesscorresponding to high values <strong>of</strong> thedisjoining pressure.6543Adsorbed Film Thickness (nm)410402• Steep curvature gradient required topump liquid into the transition region forevaporation.100.00.20.40.6Dimensionless Position0.81.0COMSOL User's Conference, Boston 9

Simulation Results – Octane Low Heat Input• COMSOL simulation was able toreproduce the experimental datafrom an octane meniscus.• The incorporation <strong>of</strong>hydrodynamic slip was necessaryto match both the position <strong>of</strong> thecurvature peak and the spread <strong>of</strong>the peak.65432OctaneExperimental DataCOMSOL Simulation - no slipCOMSOL Simulation - slipslip length β = 120 nmδ 0= 6 nmq = 0.17 W1• Peak height is controlled by thethickness <strong>of</strong> the adsorbed filmahead <strong>of</strong> the contact line.00.00.20.40.6Dimensionless Position0.81.0COMSOL User's Conference, Boston 10

Simulation Results - Octane & Pentane• COMSOL simulation was applied to anoctane meniscus at a higher heat fluxand a pentane meniscus.1412108OctaneExperimental DataComsol Simulationslip length β = 80 nmδ 0= 2.8 nmq = 0.75 W• Simulation was able to successfullyreproduce the curvature pr<strong>of</strong>iles for bothfluids.642• Adsorbed film thicknesses are lowerthan those measured experimentally, butthe trend reproduces experimentalobservations.– Pentane adsorbed film thicknessesare much larger than octane.00.00.20.4r<strong>of</strong>ilePosition0.60.81.0• Slip lengths are not unreasonably large,but more experimental work is neededto determine if they exist.COMSOL User's Conference, Boston 11

Conclusions• COMSOL model was successfully able to reproduce experimental observations— Model was able to match both the film thickness and curvature pr<strong>of</strong>iles for octane andpentane menisci.— Model results provided the correct trend for both the adsorbed film thickness as afunction <strong>of</strong> heat input and also the adsorbed film thickness as a function <strong>of</strong> liquidHamaker constant. Adsorbed film thicknesses were smaller than those measuredexperimentally.— Model results suggest that hydrodynamic slip is required to successfully model theevaporation <strong>of</strong> thin films.• Meniscus model improvements− Verify the requirement for a slip length.− Extend model to cover the entire meniscus, not just the field-<strong>of</strong>-view <strong>of</strong> the experiment.− Extend model to handle transient situations. Focus on recession during evaporation andmeniscus oscillation, both <strong>of</strong> which have been observed experimentally.COMSOL User's Conference, Boston 12

AcknowledgementsLift<strong>of</strong>f <strong>of</strong> Discovery with CVB Experiment8/29/2009COMSOL User's Conference, Boston 13

Hamakar constant, Lifshitz TheoryA=34⎛ ε1−ε3kT⎜⎝ ε1+ ε3⎞⎛ε2⎟⎜⎠⎝ε2−ε3+ ε3⎞⎟ +⎠3hνe8 22 2 2 2( n1− n3)( n2− n3)2 2( + ) 1 2 2 2 2( + ) 1 ⎧ 2 2 2 2 2n n n n ( n + n ) 1+ ( n + n )1323⎨⎩132312⎫⎬⎭SLW= γ(ecosθ−1)∆GLW=SLW⎛⎜d⎝ h20e2⎞⎟⎠COMSOL User's Conference, Boston 14

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