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Migration of a Drop in Simple Shear Flow at Finite Reynolds Numbers: Size and Viscosity Ratio Effects

Authors: M. Bayareh, S. Mortazavi

Abstract:

The migration of a deformable drop in simple shear flow at finite Reynolds numbers is investigated numerically by solving the full Navier-Stokes equations using a finite difference/front tracking method. The objectives of this study are to examine the effectiveness of the present approach to predict the migration of a drop in a shear flow and to investigate the behavior of the drop migration with different drop sizes and non-unity viscosity ratios. It is shown that the drop deformation depends strongly on the capillary number, so that; the proper non-dimensional number for the interfacial tension is the capillary number. The rate of migration increased with increasing the drop radius. In other words, the required time for drop migration to the centreline decreases. As the viscosity ratio increases, the drop rotates more slowly and the lubrication force becomes stronger. The increased lubrication force makes it easier for the drop to migrate to the centre of the channel. The migration velocity of the drop vanishes as the drop reaches the centreline under viscosity ratio of one and non-unity viscosity ratios. To validate the present calculations, some typical results are compared with available experimental and theoretical data.

Keywords: drop migration, shear flow, front-tracking method, finite difference method.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1085435

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References:


[1] Taylor, G.I., The deformation of emulsions in definable fields of flow, Proc,Ray.Soc. (London), 1934, A146, 501-523.
[2] Karnis,A. and Mason,S.G., Particle motions in sheared suspensions. XXΙΙΙ. Wall migration of fluid drops, J.Colloid and Inerface. Science, 1967, 24, 164-169.
[3] Halow,J.S., and Willis,G.B., Radial migration of spherical particles in Couette system, AICHE J., 1970, 16, 281-286.
[4] Rallison, J.M., The deformation of small viscous drops and bubbles in shear flows, Annu, Rev. Fluid Mech., 1984, 16, 45-66.
[5] Magna, M. and Stone, H.A., Buoyancy-driven interactions between two deformable viscous drops, J.Fluid Mech, 1993, 256, 647-683.
[6] Zhou, H. and Pozrikidis,C., The flow of suspensions in channels: single files of drops, Phys. Fluids, 1993, A5(2), 311-324.
[7] Feng, J., Hu, H.H., and Joseph, D.D., Direct simulation of initial value problems for the motion of solid bodies in a Newtonian fluid. Part2. Couette and Poiseuille flows, J.Fluid Mech, 1994, 277, 271-301.
[8] Li, X., Zhou H. and Pozrikidis,C., A numerical study of the shearing motion of emulsions and foams, J.Fluid Mech, 1995, 286, 374-404.
[9] Loewenberg, M. and Hinch, E., Numerical simulation of a concentrated emulsion in shear flow, J.Fluid Mech., 1996, 321, 395-419.
[10] Esmaeeli, A., and Tryggvason, G., Direct numerical simulations of bubbly flows Part1. Low Reynolds number arrays, J.Fluid Mech, 1998, 377, 313-345.
[11] Mortazavi, S.S. and Tryggvasson, G., A numerical study of the motion of drop in Poiseuille flow, part1: lateral migration of one drop, J.Fluid Mech, 1999, 411, 325-350.
[12] Esmaeeli, A., and Tryggvason, G., Direct numerical simulations of bubbly flows Part2. Low Reynolds number arrays, J.Fluid Mech, 1999, 385, 325-358.
[13] Balabel A., Binninger B., Herrmann M. and Peters N., Calculation of droplet deformation by surface tension effects using the Level Set method, J. Combustion Science and Technology, 2002, 174, 257-278.
[14]
[Crowdy D.G., Compressible bubbles in Stokes flow, J. Fluid Mech., 2003, 476, 345-356.
[15] Yoon Y., Borrell M., Park C.C., and Leal G., Viscosity ratio effects on the coalescence of two equal-sized drops in a two-dimensional linear flow, J. Fluid Mech., 2005, 525, 355-379.
[16] Norman, J.T., Nayak, H.V., and Bonnecaze T.B., Migration of buoyant particles in low-Reynolds-number pressure-driven flows, J. Fluid Mech., 2005, 523, 1-35.
[17] Yang B.H., Wang J., Hu H.H., Pan T.W., and Glowinski R., Migration of a sphere in tube flow, J. Fluid Mech., 2005, 540, 109-131.
[18] Sibillo, V., Pasquariello, G., Simeone, M., Cristini, V., and Guido, S., Drop deformation in micro confined shear flow, PhysRevLett, 2007, 97, pp. 2-4.
[19] Zhao, X., Drop break up in dilute Newtonian emulsions in simple shear flow: new drop break up mechanism. J. Rheology, 2007, 51, 367-192.
[20] Unverdi, S.O., and Tryggvason, G., Computations of multi-fluid flows, J. Physics, 1992, D60, 70-83.
[21] Ho, B. P., and Leal, L. G., Inertial migration of rigid spheres in twodimensional unidirectional flows, J. Fluid Mech., 1974, 65, 365-383.
[22] Vasseur, P., and Cox, R.G., The lateral migration of a spherical particle in two-dimensional shear flow, J. Fluid Mech., 1976, 78, 385-402.
[23] Janssen, P.J.A., and Anderson, P.D., A boundary integral model for drop deformation between two parallel plates with non-unit viscosity ratio drops, J. of Computational Physics, 2008, 227, 8807-8819.