Abstract
Inelasticity effects on the migration of a drop and pairwise interaction of drops in a simple shear flow are studied using a finite-difference front-tracking method. The Carreau-Yasuda model is used to adjust the shear-thinning behavior of fluids. Results showed that drop deformation and migration rate of drops in an inelastic system are smaller than those in a Newtonian one. It was revealed that inelasticity has larger effects for the case in which Newtonian drops suspended in a non-Newtonian phase. The time of collision process is shorter for an inelastic system in comparison with the Newtonian one. For two Newtonian drops in an elastic matrix, the results demonstrated that the drops exhibit reversible cross-flow migration at high inelasticity.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Change history
27 May 2019
Due to an error at the publisher, Eq. (1) for authors <Emphasis Type="Italic">Sadegh Mohammadi Masiri et al</Emphasis>. was listed incorrectly. The original Eq. (1) is as follows:
References
Aggarwal, N. and K. Sarkar, 2007, Deformation and breakup of a viscoelastic drop in a Newtonian matrix under steady shear, J. Fluid Mech. 584, 1–21.
Anand, A. and K.R. Rajagopal, 2004, A shear-thinning viscoelastic fluid model for describing the flow of blood, Int. J. Cardiovasc. Med. Sci. 4, 59–68.
Ashrafizaadeh, M. and H. Bakhshaei, 2009, A comparison of non-Newtonian models for lattice Boltzmann blood flow simulations, Comput. Math. Appl. 58, 1045–1054.
Bayareh, M. and S. Mortazavi, 2009, Numerical simulation of the motion of a single drop in a shear flow at finite Reynolds numbers, Iran. J. Sci. Technol. Trans. B-Eng. 33, 441–452.
Bayareh, M. and S. Mortazavi, 2011a, Three-dimensional numerical simulation of drops suspended in simple shear flow at finite Reynolds numbers, Int. J. Multiph. Flow 37, 1315–1330.
Bayareh, M. and S. Mortazavi, 2011b, Binary collision of drops in simple shear flow at finite Reynolds numbers: Geometry and viscosity ratio effects, Adv. Eng. Softw. 42, 604–611.
Bayareh, M. and S. Mortazavi, 2011c, Effect of density ratio on the hydrodynamic interaction between two drops in simple shear flow, Iran J. Sci. Technol.-Trans. Mech. Eng. 35, 121–132.
Bayareh, M. and S. Mortazavi, 2013, Equilibrium position of a buoyant drop in Couette and Poiseuille flows at finite Reynolds numbers, J. Mech. 29, 53–58.
Bird, R., R.C. Armstrong, and O. Hassager, 1987, Dynamics of Polymer Liquids, Vol.1: Fluid Mechanics, 2nd ed., Wiley, New York.
Gan, Y.X., 2012, Continuum Mechanics: Progress in Fundamentals and Engineering Applications, InTech, Rijeka.
Guido, S. and M. Simeone, 1998, Binary collision of drops in simple shear flow by computer-assisted video optical microscopy, J. Fluid Mech. 357, 1–20.
Li, J. and Y. Renardy, 2000, Shear-induced rupturing of a viscous drop in a Bingham liquid, J. Non-Newton. Fluid Mech. 95, 235–251.
Li, X. and K. Sarkar, 2005, Negative normal stress elasticity of emulsions of viscous drops at finite inertia, Phys. Rev. Lett. 95, 256001.
Liu, J., C. Zho, T. Fu, Y. Ma, and H. Li, 2013, Numerical simulation of the interactions between three equal-interval parallel bubbles rising in non-Newtonian fluids, Chem. Eng. Sci. 93, 55–66.
Loewenberg, M. and E.J. Hinch, 1996, Numerical simulation of a concentrated emulsion in shear flow, J. Fluid Mech. 321, 395–419.
Mighri, F., P.J. Carreau, and A. Ajji, 1998, Influence of elastic properties on drop deformation and breakup in shear flow, J. Rheol. 42, 1477–1490.
Mortazavi, S. and G. Tryggvason, 2000, A numerical study of the motion of drops in Poiseuille flow. Part 1. Lateral migration of one drop, J. Fluid Mech. 411, 325–350.
Mukherjee, S. and K. Sarkar, 2009, Effects of viscosity ratio on deformation of a viscoelastic drop in a Newtonian matrix under steady shear, J. Non-Newton. Fluid Mech. 160, 104–112.
Mukherjee, S. and K. Sarkar, 2013, Effects of matrix viscoelasticity on the lateral migration of a deformable drop in a wallbounded shear, J. Fluid Mech. 727, 318–345.
Potapov, A., R. Spivak, O.M. Lavrenteva, and A. Nir, 2006, Motion and deformation of drops in Bingham fluid, Ind. Eng. Chem. Res. 45, 6985–6995.
Premlata, A.R., M.K. Tripathi, B. Karri, and K.C. Sahu, 2017, Numerical and experimental investigations of an air bubble rising in a Carreau-Yasuda shear-thinning liquid, Phys. Fluids 29, 033103.
Rallison, J.M., 1984, The deformation of small viscous drops and bubbles in shear flows, Annu. Rev. Fluid Mech. 16, 45–66.
Schlichting, H., 1968, Boundary-Layer Theory, 6th ed., McGraw-Hill, New York.
Sibillo, V., M. Simeone, and S. Guido, 2004, Break-up of a Newtonian drop in a viscoelastic matrix under simple shear flow, Rheol. Acta 43, 449–456.
Subramanian, R.S., 2002, Non-Newtonian flows, Department of Chemical and Biomolecular Engineering, Clarkson University, 1–5 (Retrieved from http://web2.clarkson.edu/projects/subramanian/ch330/notes/Non-Newtonian%20Flows.pdf).
Sun, W., C. Zhu, T. Fu, Y. Ma, and H. Li, 2019, 3D simulation of interaction and drag coefficient of bubbles continuously rising with equilateral triangle arrangement in shear-thinning fluids, Int. J. Multiph. Flow 110, 69–81.
Unverdi, S.O. and G. Tryggvason, 1992, Computations of multifluid flows, Physica D 60, 70–83.
Varanasi, P.P., M.E. Ryan, and P. Stroeve, 1994, Experimental study on the breakup of model viscoelastic drops in uniform shear flow, Ind. Eng. Chem. Res. 33, 1858–1866.
Wan, S., D. Morrison, and I.G. Bryden, 2000, The flow of Newtonian and inelastic non-Newtonian fluids in eccentric annuli with inner-cylinder rotation, Theor. Comput. Fluid Dyn. 13, 349–359.
Yue, P., J.J. Feng, C. Liu, and J. Shen, 2005, Viscoelastic effects on drop deformation in steady shear, J. Fluid Mech. 540, 427–437.
Zhang, L., C. Yang, and Z.S. Mao, 2010, Numerical simulation of a bubble rising in shear-thinning fluids, J. Non-Newton. Fluid Mech. 165, 555–567.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Masiri, S.M., Bayareh, M. & Nadooshan, A.A. Pairwise interaction of drops in shear-thinning inelastic fluids. Korea-Aust. Rheol. J. 31, 25–34 (2019). https://doi.org/10.1007/s13367-019-0003-8
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s13367-019-0003-8