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LBM Investigation of Immiscible Displacement in a Channel with Regular Surface Roughness

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Abstract

We investigated immiscible displacement in a channel considering regular surface roughness at walls. A color-fluid LBM code is developed and validated against the Hagen–Poiseuille flow before it is employed for simulating the displacement process. The dimensionless roughness height and roughness spacing ratio are defined to characterize the surface roughness. The simulation results show that the presence of surface roughness obviously impels a finger formation in a channel. The impelling effect is more significant at larger roughness heights and medium roughness spacing ratios. The critical capillary number and viscosity ratio of a finger formation is reduced with increasing roughness height. The obvious effect of wettability on the finger development in a smooth channel is attenuated in rough channels. The attenuation magnitude increases with increasing roughness height.

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References

  • Cox, R.G.: The dynamics of the spreading of liquids on a solid surface. Part 1. Viscous flow. J. Fluid Mech. 168, 169–194 (1986)

    Article  Google Scholar 

  • den Dulk, R.C., Schmidt, K.A., Sabatté, G., Liébana, S., Prins, M.W.J.: Magneto-capillary valve for integrated purification and enrichment of nucleic acids and proteins. Lab Chip 13(1), 106–118 (2013)

    Article  Google Scholar 

  • Dong, B., Yan, Y.Y., Li, W., Song, Y.: Lattice Boltzmann simulation of viscous fingering phenomenon of immiscible fluids displacement in a channel. Comput. Fluids 39(5), 768–779 (2010)

    Article  Google Scholar 

  • Govindarajan, R., Sahu, K.C.: Instabilities in viscosity-stratified flow. Annu. Rev. Fluid Mech. 46, 331–353 (2014)

    Article  Google Scholar 

  • Guan, X., Pitchumani, R.: Viscous fingering in a hele-shaw cell with finite viscosity ratio and interfacial tension. J. Fluids Eng. 125(2), 354–364 (2003)

    Article  Google Scholar 

  • Gunstensen, A.K., Rothman, D.H., Zaleski, S., Zanetti, G.: Lattice Boltzmann model of immiscible fluids. Phys. Rev. A 43(8), 4320 (1991)

    Article  Google Scholar 

  • Halpern, D., Gaver III, D.P.: Boundary element analysis of the time-dependent motion of a semi-infinite bubble in a channel. J. Comput. Phys. 115(2), 366–375 (1994)

    Article  Google Scholar 

  • He, X., Chen, S., Zhang, R.: A lattice Boltzmann scheme for incompressible multiphase flow and its application in simulation of Rayleigh–Taylor instability. J. Comput. Phys. 152(2), 642–663 (1999)

    Article  Google Scholar 

  • Hocking, L.M.: A moving fluid interface on a rough surface. J. Fluid Mech. 76(4), 801–817 (1976)

    Article  Google Scholar 

  • Homsy, G.M.: Viscous fingering in porous media. Annu. Rev. Fluid Mech. 19(1), 271–311 (1987)

    Article  Google Scholar 

  • Huang, H., Krafczyk, M., Lu, X.: Forcing term in single-phase and Shan-Chen-type multiphase lattice Boltzmann models. Phys. Rev. E 84(4), 046710 (2011)

    Article  Google Scholar 

  • Huang, H., Huang, J.-J., Lu, X.-Y., Sukop, M.C.: On simulations of high-density ratio flows using color-gradient multiphase lattice Boltzmann models. Int. J. Mod. Phys. C 24(04), 1350021 (2013)

    Article  Google Scholar 

  • Huang, H., Huang, J.-J., Lu, X.-Y.: Study of immiscible displacements in porous media using a color-gradient-based multiphase lattice Boltzmann method. Comput. Fluids 93, 164–172 (2014)

    Article  Google Scholar 

  • Jansons, K.M.: Moving contact lines on a two-dimensional rough surface. J. Fluid Mech. 154, 1–28 (1985)

    Article  Google Scholar 

  • Jones, B.J., McHale, J.P., Garimella, S.V.: The influence of surface roughness on nucleate pool boiling heat transfer. J. Heat Transf. 131(12), 121009 (2009)

    Article  Google Scholar 

  • Kandlikar, S.G., Joshi, S., Tian, S.: Effect of surface roughness on heat transfer and fluid flow characteristics at low Reynolds numbers in small diameter tubes. Heat Transf. Eng. 24(3), 4–16 (2003)

    Article  Google Scholar 

  • Kang, Q., Zhang, D., Chen, S.: Immiscible displacement in a channel: simulations of fingering in two dimensions. Adv. Water Resour. 27(1), 13–22 (2004)

    Article  Google Scholar 

  • Koplik, J., Banavar, J.R., Willemsen, J.F.: Molecular dynamics of poiseuille flow and moving contact lines. Phys. Rev. Lett. 60(13), 1282 (1988)

    Article  Google Scholar 

  • Latva-Kokko, M., Rothman, D.H.: Diffusion properties of gradient-based lattice Boltzmann models of immiscible fluids. Phys. Rev. E 71(5), 056702 (2005)

    Article  Google Scholar 

  • Latva-Kokko, M., Rothman, D.H.: Scaling of dynamic contact angles in a lattice-Boltzmann model. Phys. Rev. Lett. 98(25), 254503 (2007)

    Article  Google Scholar 

  • Lenormand, R., Touboul, E., Zarcone, C.: Numerical models and experiments on immiscible displacements in porous media. J. Fluid Mech. 189, 165–187 (1988)

    Article  Google Scholar 

  • Li, J., Qu, Z., Kong, L.R.: The obvious influence of Jamin effect on low-permeability reservoirs. Pet. Explor. Dev. 26, 93–94 (1999)

    Google Scholar 

  • Li, S., Lowengrub, J.S., Fontana, J., Palffy-Muhoray, P.: Control of viscous fingering patterns in a radial hele-shaw cell. Phys. Rev. Lett. 102(17), 174501 (2009)

    Article  Google Scholar 

  • Liu, H., Valocchi, A.J., Kang, Q., Werth, C.: Pore-scale simulations of gas displacing liquid in a homogeneous pore network using the lattice Boltzmann method. Transp. Porous Media 99(3), 555–580 (2013)

    Article  Google Scholar 

  • Liu, H., Valocchi, A.J., Werth, C., Kang, Q., Oostrom, M.: Pore-scale simulation of liquid \(\text{ CO }_2\) displacement of water using a two-phase lattice Boltzmann model. Adv. Water Resour. 73, 144–158 (2014)

    Article  Google Scholar 

  • Liu, H., Kang, Q., Leonardi, C.R., Schmieschek, S., Narváez, A., Jones, B.D., Williams, J.R., Valocchi, A.J., Harting, J.: Multiphase lattice Boltzmann simulations for porous media applications. Comput. Geosci. 20(4), 777–805 (2016)

    Article  Google Scholar 

  • Lou, Q., Guo, Z., Shi, B.: Evaluation of outflow boundary conditions for two-phase lattice Boltzmann equation. Phys. Rev. E 87(6), 063301 (2013)

    Article  Google Scholar 

  • Løvoll, G., Méheust, Y., Toussaint, R., Schmittbuhl, J., Måløy, K.J.: Growth activity during fingering in a porous hele-shaw cell. Phys. Rev. E 70(2), 026301 (2004)

    Article  Google Scholar 

  • Papadimitriou, V.A., van den Berg, A., Eijkel, J.C.T.: 3D capillary valves for versatile capillary patterning of channel walls. In: 20th International Conference on Miniaturized Systems for Chemistry and LifeSciences, MicroTAS 2016. The Chemical and Biological Microsystems Society (2016)

  • Raeini, A.Q., Blunt, M.J., Bijeljic, B.: Modelling two-phase flow in porous media at the pore scale using the volume-of-fluid method. J. Comput. Phys. 231(17), 5653–5668 (2012)

    Article  Google Scholar 

  • Redapangu, P.R., Sahu, K.C., Vanka, S.P.: A study of pressure-driven displacement flow of two immiscible liquids using a multiphase lattice Boltzmann approach. Phys. Fluids 24(10), 102110 (2012)

    Article  Google Scholar 

  • Redapangu, P.R., Sahu, K.C., Vanka, S.P.: A lattice Boltzmann simulation of three-dimensional displacement flow of two immiscible liquids in a square duct. J. Fluids Eng. 135(12), 121202 (2013)

    Article  Google Scholar 

  • Reis, T., Phillips, T.N.: Lattice Boltzmann model for simulating immiscible two-phase flows. J. Phys. A Math. Theor. 40(14), 4033 (2007)

    Article  Google Scholar 

  • Rothman, D.H., Keller, J.M.: Immiscible cellular-automaton fluids. J. Stat. Phys. 52(3), 1119–1127 (1988)

    Article  Google Scholar 

  • Saffman, P.G.: Viscous fingering in hele-shaw cells. J. Fluid Mech. 173, 73–94 (1986)

    Article  Google Scholar 

  • Saffman, PG., Taylor, G.: The penetration of a fluid into a porous medium or hele-shaw cell containing a more viscous liquid. In: Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, vol. 245, pp. 312–329. The Royal Society (1958)

  • Sahu, K.C., Matar, O.K.: Three-dimensional linear instability in pressure-driven two-layer channel flow of a newtonian and a Herschel–Bulkley fluid. Phys. Fluids 22(11), 112103 (2010)

    Article  Google Scholar 

  • Sahu, K.C., Vanka, S.P.: A multiphase lattice Boltzmann study of buoyancy-induced mixing in a tilted channel. Comput. Fluids 50(1), 199–215 (2011)

    Article  Google Scholar 

  • Sahu, K.C., Valluri, P., Spelt, P.D.M., Matar, O.K.: Linear instability of pressure-driven channel flow of a newtonian and a Herschel–Bulkley fluid. Phys. Fluids 19(12), 122101 (2007)

    Article  Google Scholar 

  • Sahu, K.C., Ding, H., Valluri, P., Matar, O.K.: Linear stability analysis and numerical simulation of miscible two-layer channel flow. Phys. Fluids 21(4), 042104 (2009a)

    Article  Google Scholar 

  • Sahu, K.C., Ding, H., Valluri, P., Matar, O.K.: Pressure-driven miscible two-fluid channel flow with density gradients. Phys. Fluids 21(4), 043603 (2009b)

    Article  Google Scholar 

  • Shan, X., Chen, H.: Lattice Boltzmann model for simulating flows with multiple phases and components. Phys. Rev. E 47(3), 1815 (1993)

    Article  Google Scholar 

  • Shan, X., Chen, H.: Simulation of nonideal gases and liquid–gas phase transitions by the lattice Boltzmann equation. Phys. Rev. E 49(4), 2941 (1994)

    Article  Google Scholar 

  • Shan, X., Doolen, G.: Multicomponent lattice-Boltzmann model with interparticle interaction. J. Stat. Phys. 81(1), 379–393 (1995)

    Article  Google Scholar 

  • Shikhmurzaev, Y.D.: Moving contact lines in liquid/liquid/solid systems. J. Fluid Mech. 334, 211–249 (1997)

    Article  Google Scholar 

  • Smith, W.O., Crane, M.D.: The Jamin effect in cylindrical tubes. J. Am. Chem. Soc. 52(4), 1345–1349 (1930)

    Article  Google Scholar 

  • Sukop, M.C.: Lattice Boltzmann modeling: an introduction for geoscientists and engineers. AGU Fall Meeting Abstracts, December (2006)

  • Swift, M.R., Orlandini, E., Osborn, W.R., Yeomans, J.M.: Lattice Boltzmann simulations of liquid–gas and binary fluid systems. Phys. Rev. E 54(5), 5041 (1996)

    Article  Google Scholar 

  • Taghavi, S.M., Alba, K., Séon, T., Wielage-Burchard, K., Martinez, D.M., Frigaard, I.A.: Miscible displacement flows in near-horizontal ducts at low Atwood number. J. Fluid Mech. 696, 175–214 (2012)

    Article  Google Scholar 

  • Talon, L., Goyal, N., Meiburg, E.: Variable density and viscosity, miscible displacements in horizontal hele-shaw cells. Part 1. Linear stability analysis. J. Fluid Mech. 721, 268–294 (2013)

    Article  Google Scholar 

  • Tanveer, S.: Surprises in viscous fingering. J. Fluid Mech. 409, 273–308 (2000)

    Article  Google Scholar 

  • Weinstein, S.J., Dussan, E.B., Ungar, L.H.: A theoretical study of two-phase flow through a narrow gap with a moving contact line: viscous fingering in a hele-shaw cell. J. Fluid Mech. 221, 53–76 (1990)

    Article  Google Scholar 

  • Wu, H.Y., Cheng, P.: An experimental study of convective heat transfer in silicon microchannels with different surface conditions. Int. J. Heat Mass Transf. 46(14), 2547–2556 (2003)

    Article  Google Scholar 

  • Wu, R., Kharaghani, A., Tsotsas, E.: Two-phase flow with capillary valve effect in porous media. Chem. Eng. Sci. 139, 241–248 (2016)

    Article  Google Scholar 

  • Xu, Z., Liu, H., Valocchi, A.J.: Lattice Boltzmann simulation of immiscible two-phase flow with capillary valve effect in porous media. Water Resour. Res. 53(5), 3770–3790 (2017)

    Article  Google Scholar 

  • Yang, J., Boek, E.S.: A comparison study of multi-component lattice Boltzmann models for flow in porous media applications. Comput. Math. Appl. 65(6), 882–890 (2013)

    Article  Google Scholar 

  • Zhang, C., Oostrom, M., Wietsma, T.W., Grate, J.W., Warner, M.G.: Influence of viscous and capillary forces on immiscible fluid displacement: pore-scale experimental study in a water-wet micromodel demonstrating viscous and capillary fingering. Energy Fuels 25(8), 3493–3505 (2011)

    Article  Google Scholar 

  • Zou, Q., He, X.: On pressure and velocity boundary conditions for the lattice Boltzmann BGK model. Phys. Fluids 9(6), 1591–1598 (1997)

    Article  Google Scholar 

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Correspondence to Youming Xiong.

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Wang, M., Xiong, Y., Liu, L. et al. LBM Investigation of Immiscible Displacement in a Channel with Regular Surface Roughness. Transp Porous Med 123, 195–215 (2018). https://doi.org/10.1007/s11242-018-1032-3

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