Investigation of Flow in Microchannels with Superhydrophobic Surfaces Using Hybrid Direct Simulation Monte Carlo-Navier-Stokes Method with Information Preservation Approach

Document Type : Research Article

Authors

Mechanical Department, Engineering Faculty, Razi University, Kermanshah, Iran

Abstract

In recent years, superhydrophobic surfaces have received significant attention due to properties such as drag reduction and self-cleaning. A superhydrophobic surface can be made by grooving the wall. In this case, the flow of gas caught in grooves may represent the rarefied flow. Therefore, particle-based approaches such as direct simulation Monte Carlo should be employed to simulate the flow. In this paper, laminar flow in superhydrophobic microchannels with ribs and cavities aligned perpendicular to the channel axis is investigated using a hybrid direct simulation Monte Carlo-Navier[1]Stokes method. Also, information preservation technique is employed to reduce statistical fluctuations of the direct simulation Monte Carlo method. The effects of the length of the cavity on the flow parameters such as effective slip length, and velocity slip are investigated and the results are compared with the simplified method of using Navier-Stokes equations with shear-free boundary condition as the gas-liquid interface. It is shown that the differences between the hybrid method and shear-free solution increase as the shear-free fraction increases. However, the difference is less than 6% for cases studied in this work. Therefore, it is acceptable to use the shear-free approach to reduce computational costs. Especially for Fc < 0.2 where the difference is less than 3%.

Keywords

Main Subjects


[1]  K.-Y. Law, Definitions for Hydrophilicity, Hydrophobicity, and Superhydrophobicity: Getting the Basics Right, The Journal of Physical Chemistry Letters, 5(4) (2014) 686-688.
[2]  K.A. Stevens, J. Crockett, D.R. Maynes, B.D. Iverson, Two-phase flow pressure drop in superhydrophobic channels, International Journal of Heat and Mass Transfer, 110 (2017) 515-522.
[3]  D. Sebastian, C.-W. Yao, I. Lian, Mechanical durability of engineered superhydrophobic surfaces for anticorrosion, Coatings, 8(5) (2018) 162.
[4]  D.K. Sarkar, M. Farzaneh, Superhydrophobic Coatings with Reduced Ice Adhesion, Journal of Adhesion Science and Technology, 23(9) (2009) 1215-1237.
[5]  E. Lauga, H.A. Stone, Effective slip in pressure-driven Stokes flow, Journal of Fluid Mechanics, 489 (2003) 55-77.
[6]  M.B. Martell, J.B. Perot, J.P. Rothstein, Direct numerical simulations of turbulent flows over superhydrophobic surfaces, Journal of Fluid Mechanics, 620 (2009) 31-41.
[7]  C. Teo, B. Khoo, Flow past superhydrophobic surfaces containing longitudinal grooves: effects of interface curvature, Microfluidics and Nanofluidics, 9(2-3) (2010) 499-511.
[8]  C. Teo, B. Khoo, Effects of interface curvature on Poiseuille flow through microchannels and microtubes containing superhydrophobic surfaces with transverse grooves and ribs, Microfluidics and nanofluidics, 17(5) (2014) 891-905.
[9]  Y. Chen, W. Ren, X. Mu, F. Zhang, Y. Xu, Flow inside Micro-Channel Bounded by Superhydrophobic Surface with Eccentric Micro-Grooves, World Academy of Science, Engineering and Technology, International Journal of Mechanical, Aerospace, Industrial, Mechatronic and Manufacturing Engineering, 11(9) (2017) 1567-1572.
[10]  M. Kharati-Koopaee, M.R. Akhtari, Numerical study of fluid flow and heat transfer phenomenon within microchannels comprising different superhydrophobic structures, International Journal of Thermal Sciences, 124 (2018) 536-546.
[11]  A. Gaddam, A. Agrawal, S.S. Joshi, M.C. Thompson, Slippage on a particle-laden liquid-gas interface in textured microchannels, Physics of Fluids, 30(3) (2018) 032101.
[12] J. Davies, D. Maynes, B. Webb, B. Woolford, Laminar flow in a microchannel with superhydrophobic walls exhibiting transverse ribs, Physics of fluids, 18(8) (2006) 087110.
[13]  B. Woolford, D. Maynes, B. Webb, Liquid flow through microchannels with grooved walls under wetting and superhydrophobic conditions, Microfluidics and nanofluidics, 7(1) (2009) 121-135.
[14]  A. Gaddam, A. Agrawal,  S.S. Joshi,  M.Thompson, Utilization of cavity vortex to delay the wetting transition in one-dimensional structured microchannels, Langmuir, 31(49) (2015) 1337313384.
[15]  G.A. Bird, Molecular gas dynamics, NASA STI/Recon Technical Report A, 76 (1976).
[16] G. Bird, Molecular gas dynamics and the direct simulation monte carlo of gas flows, Clarendon, Oxford, 508 (1994) 128.
[17] W. Wagner, A convergence proof for Bird’s direct simulation Monte Carlo method for the Boltzmann equation, Journal of Statistical Physics, 66(3) (1992) 1011-1044.
[18] K. Nanbu, Direct simulation scheme derived from the Boltzmann equation. I. Monocomponent gases, Journal of the Physical Society of Japan, 49(5) (1980) 2042-2049.
[19] A. Amiri-Jaghargh, A. Babakhani, Investigation of shear stress on superhydrophobic surfaces considering gaseous flow in microcavities using DSMC-IP method, in:  17th Conference on Fluid Dynamics (FD2017), Shahrood University of Technology, 2017.(In Persian)
[20] D. Hash, H. Hassan, A decoupled DSMC/NavierStokes analysis of a transitional flow experiment, in:  34th aerospace sciences meeting and exhibit, 1996, pp. 353.
[21] D. Hash, H. Hassan, Assessment of schemes for coupling Monte Carlo and Navier-Stokes solution methods, Journal of Thermophysics and Heat Transfer, 10(2) (1996) 242-249.
[22]D. Hash, H. Hassan, D. Hash, H. Hassan, Twodimensional coupling issues of hybrid DSMC/NavierStokes solvers, in:  32nd thermophysics conference, 1997, pp. 2507.
[23] O. Aktas, N. Aluru, A combined continuum/DSMC technique for multiscale analysis of microfluidic filters, Journal of Computational Physics, 178(2) (2002) 342-372.
[24] M. Darbandi, E. Roohi, A hybrid DSMC/NavierStokes frame to solve mixed rarefied/nonrarefied hypersonic flows over nano-plate and micro-cylinder, Internationa Journal for Numerical Methods in Fluids, 72(9) (2013) 937-966.
[25]  S. Tiwari, A. Klar, S. Hardt, A. Donkov, Coupled solution of the Boltzmann and Navier–Stokes equations in gas–liquid two phase flow, Computers & Fluids, 71 (2013) 283-296.
[26]  J. Fan, C. Shen, Statistical simulation of low-speed unidirectional flows in transition regime, in:  International symposium on rarefied gas dynamics, 1999.
[27]J. Fan, C. Shen, Statistical simulation of low-speed rarefied gas flows, Journal of Computational Physics, 167(2) (2001) 393-412.
[28] Q. Sun, I.D. Boyd, G.V. Candler, A hybrid continuum/particle approach for modeling subsonic, rarefied gas flows, Journal of Computational Physics, 194(1) (2004) 256-277.
[29] B. Gruncell, Superhydrophobic surfaces and their potential application to hydrodynamic drag reduction, PhD thesis, University of Southampton, 2014.
[30] E. Lobaton, T. Salamon, Computation of constant mean curvature surfaces: Application to the gas–liquid interface of a pressurized fluid on a superhydrophobic surface, Journal of colloid and interface science, .891-481 )7002( )1(413
[31] C. Ybert, C. Barentin, C. Cottin-Bizonne, P. Joseph, L. Bocquet, Achieving large slip with superhydrophobic surfaces: Scaling laws for generic geometries, Physics of fluids, 19(12) (2007) 123601.
[32] A. Babakhani, Developing a DSMC code for simulation of rarefied flow in lid–driven micro/ nano cavities using IP method, Master thesis, Razi University, 2018. (In Persian)
[33] A. Amiri-Jaghargh, Numerical Investigation of Rarefied Gas Flows in Micro/Nano Geometries using Navier-Stokes Equations and DSMC Approach, PhD thesis, Ferdowsi University of Mashhad, 2014. (In Persian)
[34] A. Amiri-Jaghargh, E. Roohi, S. Stefanov, H. Nami, H. Niazmand, DSMC simulation of micro/nano flows using SBT–TAS technique, Computers & Fluids, 102 (2014) 266-276.
[35] A. Amiri-Jaghargh, E. Roohi, H. Niazmand, S. Stefanov, DSMC simulation of low knudsen micro/ nanoflows using small number of particles per cells, Journal of Heat Transfer, 135(10) (2013) 101008.
[36] Q. Sun, Information preservation methods for modeling micro-scale gas flows, PhD thesis, University of Michigan, 2003.
[37]  F.J. Alexander, A.L. Garcia, B.J. Alder, Cell size dependence of transport coefficients in stochastic particle algorithms, Physics of Fluids, 10(6) (1998) 1540-1542.
[38]  C.-H. Choi, K.J.A. Westin, K.S. Breuer, Apparent slip flows in hydrophilic and hydrophobic microchannels, Physics of fluids, 15(10) (2003) 2897-2902.
[39]  B. John, X.-J. Gu, D.R. Emerson, Investigation of heat and mass transfer in a lid-driven cavity under nonequilibrium flow conditions, Numerical Heat Transfer, Part B: Fundamentals, 58(5) (2010) 287-303.