Siqueira, Ivan Rosa de Rebouças, Rodrigo Bento Cunha, Lucas Hildebrand Pires da and Oliveira, Taygoara Felamingo de 2018. On the volume conservation of emulsion drops in boundary integral simulations. Journal of the Brazilian Society of Mechanical Sciences and Engineering, Vol. 40, Issue. 1,
Das, Sayan Mandal, Shubhadeep and Chakraborty, Suman 2018. Effect of temperature gradient on the cross-stream migration of a surfactant-laden droplet in Poiseuille flow. Journal of Fluid Mechanics, Vol. 835, p. 170.
Mandal, Shubhadeep Das, Sayan and Chakraborty, Suman 2017. Effect of Marangoni stress on the bulk rheology of a dilute emulsion of surfactant-laden deformable droplets in linear flows. Physical Review Fluids, Vol. 2, Issue. 11,
Mandal, Shubhadeep and Chakraborty, Suman 2017. Uniform electric-field-induced non-Newtonian rheology of a dilute suspension of deformable Newtonian drops. Physical Review Fluids, Vol. 2, Issue. 9,
Mandal, Shubhadeep Bandopadhyay, Aditya and Chakraborty, Suman 2017. The effect of surface charge convection and shape deformation on the settling velocity of drops in nonuniform electric field. Physics of Fluids, Vol. 29, Issue. 1, p. 012101.
Kree, R. Burada, P. S. and Zippelius, A. 2017. From active stresses and forces to self-propulsion of droplets. Journal of Fluid Mechanics, Vol. 821, p. 595.
Das, Sayan Mandal, Shubhadeep and Chakraborty, Suman 2017. Cross-stream migration of a surfactant-laden deformable droplet in a Poiseuille flow. Physics of Fluids, Vol. 29, Issue. 8, p. 082004.
Zinchenko, Alexander Z. and Davis, Robert H. 2017. General rheology of highly concentrated emulsions with insoluble surfactant. Journal of Fluid Mechanics, Vol. 816, p. 661.
Pal, Rajinder 2016. Fundamental Rheology of Disperse Systems Based on Single-Particle Mechanics. Fluids, Vol. 1, Issue. 4, p. 40.
Gounley, J. Boedec, G. Jaeger, M. and Leonetti, M. 2016. Influence of surface viscosity on droplets in shear flow. Journal of Fluid Mechanics, Vol. 791, p. 464.
Mandal, Shubhadeep Ghosh, Uddipta and Chakraborty, Suman 2016. Effect of surfactant on motion and deformation of compound droplets in arbitrary unbounded Stokes flows. Journal of Fluid Mechanics, Vol. 803, p. 200.
Zabarankin, Michael 2016. Analytical Solution for Spheroidal Drop under Axisymmetric Linearized Boundary Conditions. SIAM Journal on Applied Mathematics, Vol. 76, Issue. 4, p. 1606.
Mandal, Shubhadeep Bandopadhyay, Aditya and Chakraborty, Suman 2016. Dielectrophoresis of a surfactant-laden viscous drop. Physics of Fluids, Vol. 28, Issue. 6, p. 062006.
Oliveira, T. F. and Cunha, F. R. 2015. Emulsion rheology for steady and oscillatory shear flows at moderate and high viscosity ratio. Rheologica Acta, Vol. 54, Issue. 11-12, p. 951.
Zinchenko, Alexander Z. and Davis, Robert H. 2015. Extensional and shear flows, and general rheology of concentrated emulsions of deformable drops. Journal of Fluid Mechanics, Vol. 779, p. 197.
Kallendorf, Christina Fath, Anja Oberlack, Martin and Wang, Yongqi 2015. Exact solutions to the interfacial surfactant transport equation on a droplet in a Stokes flow regime. Physics of Fluids, Vol. 27, Issue. 8, p. 082104.
Avazmohammadi, Reza and Ponte Castañeda, Pedro 2015. The rheology of non-dilute dispersions of highly deformable viscoelastic particles in Newtonian fluids. Journal of Fluid Mechanics, Vol. 763, p. 386.
Mandal, Shubhadeep Bandopadhyay, Aditya and Chakraborty, Suman 2015. Effect of interfacial slip on the cross-stream migration of a drop in an unbounded Poiseuille flow. Physical Review E, Vol. 92, Issue. 2,
Schuch, Anna Leal, L. Gary and Schuchmann, Heike P. 2014. Production of W/O/W double emulsions. Part I: Visual observation of deformation and breakup of double emulsion drops and coalescence of the inner droplets. Colloids and Surfaces A: Physicochemical and Engineering Aspects, Vol. 461, p. 336.
A small-deformation perturbation analysis is developed to study the effect of surfactant on drop dynamics in viscous flows. The surfactant is assumed to be insoluble in the bulk-phase fluids; the viscosity ratio and surfactant elasticity parameters are arbitrary. Under small-deformation conditions, the drop dynamics are described by a system of ordinary differential equations; the governing equations are given explicitly for the case of axisymmetric and two-dimensional imposed flows. Analytical results accurate to third order in the flow-strength parameter (capillary number) are derived (i) for the stationary drop shape and surfactant distribution in simple shear and axisymmetric straining flows, and (ii) for the rheology of a dilute emulsion in shear flow which include a shear-thinning viscosity and non-zero normal stresses. For drops with clean interfaces, the small-deformation theory presented here improves the results of Barthès-Biesel & Acrivos (J. Fluid Mech., vol. 61, 1973, p. 1). Boundary integral simulations are used to test our theory and explore large-deformation conditions.
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