Simulation of effective slip and drag in pressure-driven flow on superhydrophobic surfaces

The flow on superhydrophobic surfaces was investigated using finite element modeling (FEM). Surfaces with different textures like grooves, square pillars, and cylinders immersed in liquid forming Cassie state were modeled. Nonslip boundary condition was assumed at solid-liquid interface while slip boundary condition was supposed at gas-liquid interface. It was found that the flow rate can be affected by the shape of the texture, the fraction of the gas-liquid area, the height of the channel, and the driving pressure gradient. By extracting the effective boundary slip from the flow rate based on a model, it was found that the shape of the textures and the fraction of the gas-liquid area affect the effective slip significantly while the height of the channel and the driving pressure gradient have no obvious effect on effective slip.

[1]  J. Rothstein.  Slip on Superhydrophobic Surfaces , 2010 .

[2]  Michael I. Newton,et al.  Immersed superhydrophobic surfaces: Gas exchange, slip and drag reduction properties , 2010 .

[3]  B. Bhushan,et al.  Electroviscous effect on fluid drag in a microchannel with large zeta potential , 2015, Beilstein journal of nanotechnology.

[4]  M. Bazant,et al.  Tensorial hydrodynamic slip , 2008, Journal of Fluid Mechanics.

[5]  S. Quake,et al.  Microfluidics: Fluid physics at the nanoliter scale , 2005 .

[6]  B. Bhushan,et al.  The coupling of surface charge and boundary slip at the solid-liquid interface and their combined effect on fluid drag: A review. , 2015, Journal of colloid and interface science.

[7]  Howard A. Stone,et al.  ENGINEERING FLOWS IN SMALL DEVICES , 2004 .

[8]  R. C. Weast.  CRC Handbook of Chemistry and Physics , 1973 .

[9]  R. C. Weast.  HANDBOOK OF CHEMISTRY AND PHYSICS, 49th ed , 1969 .

[10]  David Qu,et al.  Wetting and Roughness , 2008 .

[11]  B. Ninham,et al.  Submicrocavity Structure of Water between Hydrophobic and Hydrophilic Walls as Revealed by Optical Cavitation , 1995 .

[12]  S. Joshi,et al.  Modeling of liquid–gas meniscus for textured surfaces: effects of curvature and local slip length , 2015 .

[13]  Chang-Hwan Choi,et al.  Structured surfaces for a giant liquid slip. , 2008, Physical review letters.

[14]  Dominik Horinek,et al.  Interfacial water at hydrophobic and hydrophilic surfaces: slip, viscosity, and diffusion. , 2009, Langmuir : the ACS journal of surfaces and colloids.

[15]  A. Dubov,et al.  Elastic instability and contact angles on hydrophobic surfaces with periodic textures , 2012 .

[16]  Howard A. Stone,et al.  Microfluidics: The no-slip boundary condition , 2005, cond-mat/0501557.

[17]  J. Rothstein,et al.  Direct velocity measurements of the flow past drag-reducing ultrahydrophobic surfaces , 2005 .

[18]  D. Quéré.  Wetting and Roughness , 2008 .

[19]  A. V. Belyaev,et al.  Tensorial slip of superhydrophobic channels. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[20]  B. Bhushan,et al.  Hydrodynamic drag-force measurement and slip length on microstructured surfaces. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[21]  Lydéric Bocquet,et al.  Flow boundary conditions from nano- to micro-scales. , 2006, Soft matter.

[22]  J. R. Philip.  Flows satisfying mixed no-slip and no-shear conditions , 1972 .

[23]  O. Vinogradova.  Slippage of water over hydrophobic surfaces , 1999 .

[24]  E. Lauga,et al.  Geometric transition in friction for flow over a bubble mattress , 2008, 0812.2004.

[25]  Tatiana V. Nizkaya,et al.  Flow in channels with superhydrophobic trapezoidal textures , 2013, 1307.2333.

[26]  Olga I. Vinogradova,et al.  Wetting, roughness and flow boundary conditions , 2010, Journal of physics. Condensed matter : an Institute of Physics journal.

[27]  S. Troian,et al.  A general boundary condition for liquid flow at solid surfaces , 1997, Nature.

[28]  Weijie Wang,et al.  Atomic Force Microscopy Measurement of Slip on Smooth Hydrophobic Surfaces and Possible Artifacts , 2015 .

[29]  Cécile Cottin-Bizonne,et al.  High friction on a bubble mattress. , 2007, Nature materials.

[30]  Olga I. Vinogradova,et al.  Drainage of a Thin Liquid Film Confined between Hydrophobic Surfaces , 1995 .

[31]  Christophe Ybert,et al.  Achieving large slip with superhydrophobic surfaces: Scaling laws for generic geometries , 2007 .

[32]  Chih-Ming Ho,et al.  Effective slip and friction reduction in nanograted superhydrophobic microchannels , 2006 .

[33]  E. Charlaix,et al.  Boundary slip on smooth hydrophobic surfaces: intrinsic effects and possible artifacts. , 2005, Physical review letters.

[34]  P Tabeling,et al.  Slippage of water past superhydrophobic carbon nanotube forests in microchannels. , 2006, Physical review letters.

[35]  Olga I. Vinogradova,et al.  Dynamic effects on force measurements. 2. Lubrication and the atomic force microscope , 2003 .

[36]  H. Ban,et al.  Effect of electrical double layer on electric conductivity and pressure drop in a pressure-driven microchannel flow. , 2010, Biomicrofluidics.

[37]  Xuezeng Zhao,et al.  The study of surface wetting, nanobubbles and boundary slip with an applied voltage: A review , 2014, Beilstein journal of nanotechnology.

[38]  K. Koynov,et al.  Direct measurements of hydrophobic slippage using double-focus fluorescence cross-correlation. , 2008, Physical review letters.

[39]  Lydéric Bocquet,et al.  Low-friction flows of liquid at nanopatterned interfaces , 2003, Nature materials.

[40]  François Feuillebois,et al.  Effective slip over superhydrophobic surfaces in thin channels. , 2008, Physical review letters.