Shear-induced droplet deformation: Effects of confined geometry and viscoelasticity

Taylor, 1932, The viscosity of a fluid containing small drops of another fluid, Proc Roy Soc A, 138, 41, 10.1098/rspa.1932.0169 Taylor, 1934, The formation of emulsions in definable fields of flow, Proc Roy Soc A, 146, 501, 10.1098/rspa.1934.0169 Rallison, 1984, The deformation of small viscous drops and bubbles in shear flows, Annu Rev Fluid Mech, 16, 45, 10.1146/annurev.fl.16.010184.000401 Fischer, 2007, Emulsion drops in external flow fields—the role of liquid interfaces, Curr Opin Colloid Interface Sci, 12, 196, 10.1016/j.cocis.2007.07.014 Guido, 2004, Dynamics of a liquid drop in a flowing immiscible liquid, 99, 99 Tucker, 2002, Microstructural evolution in polymer blends, Annu Rev Fluid Mech, 34, 177, 10.1146/annurev.fluid.34.082301.144051 Stone, 1994, Dynamics of drop deformation and breakup in viscous fluids, Annu Rev Fluid Mech, 26, 65, 10.1146/annurev.fl.26.010194.000433 Windhab, 2005, Emulsion processing-from single-drop deformation to design of complex processes and products, Chem Eng Sci, 60, 2101, 10.1016/j.ces.2004.12.003 Jansen, 2001, Droplet breakup in concentrated emulsions, J Rheol, 45, 227, 10.1122/1.1333001 Caserta, 2007, Drop deformation in sheared polymer blends, J Rheol, 51, 761, 10.1122/1.2723148 Barthès-Biesel, 1973, Deformation and burst of a liquid droplet freely suspended in a linear shear field, J Fluid Mech, 61, 1, 10.1017/S0022112073000534 Rallison, 1980, Note on the time-dependent deformation of a viscous drop which is almost spherical, J Fluid Mech, 98, 625, 10.1017/S0022112080000316 Chaffey, 1967, A second-order theory for shear deformation of drops, J Colloid Interface Sci, 24, 258, 10.1016/0021-9797(67)90229-9 Greco, 2002, Second-order theory for the deformation of a Newtonian drop in a stationary flow field, Phys Fluids, 14, 946, 10.1063/1.1445182 Simeone, 2004, Phase diagram, rheology and interfacial tension of aqueous mixtures of Na-caseinate and Na-alginate, Food Hydrocolloids, 18, 463, 10.1016/j.foodhyd.2003.08.004 Frith, 2010, Mixed biopolymer aqueous solutions—phase behavior and rheology, Adv Colloid Interface Sci, 161, 48, 10.1016/j.cis.2009.08.001 Luciani, 1997, Interfacial tension coefficient from the retraction of ellipsoidal drops, J Polym Sci B Polym Phys, 35, 1393, 10.1002/(SICI)1099-0488(19970715)35:9<1393::AID-POLB9>3.0.CO;2-N Guido, 1999, Measurement of interfacial tension by drop retraction analysis, J Colloid Interface Sci, 209, 247, 10.1006/jcis.1998.5818 Guido, 1998, Three-dimensional shape of a drop under simple shear flow, J Rheol, 42, 395, 10.1122/1.550942 Maffettone, 1998, Equation of change for ellipsoidal drops in viscous flow, J NonNewton Fluid Mech, 78, 227, 10.1016/S0377-0257(98)00065-2 Minale, 2010, Models for the deformation of a single ellipsoidal drop: a review, Rheol Acta, 49, 789, 10.1007/s00397-010-0442-0 Kennedy, 1994, Motion and deformation of liquid drops, and the rheology of dilute emulsions in simple shear flow, Comput Fluids, 23, 251, 10.1016/0045-7930(94)90040-X Li, 2000, Numerical simulation of breakup of a viscous drop in simple shear flow through a volume-of-fluid method, Phys Fluids, 12, 269, 10.1063/1.870305 Cristini, 2001, An adaptive mesh algorithm for evolving surfaces: simulations of drop breakup and coalescence, J Comput Phys, 168, 445, 10.1006/jcph.2001.6713 Cristini, 2003, Drop breakup and fragment size distribution in shear flow, J Rheol, 47, 1283, 10.1122/1.1603240 Chan, 1981, An experimental study of drop migration in shear flow between concentric cylinders, Int J Multiph Flow, 7, 83, 10.1016/0301-9322(81)90016-1 Uijttewaal, 1993, Droplet migration, deformation, and orientation in the presence of a plane wall: a numerical study compared with analytical theories, Phys Fluids, 5, 819, 10.1063/1.858629 Van Puyvelde, 2008, Review on morphology development of immiscible blends in confined shear flow, Polymer, 49, 5363, 10.1016/j.polymer.2008.08.055 Günther, 2006, Multiphase microfluidics: from flow characteristics to chemical and materials synthesis, Lab Chip, 6, 1487, 10.1039/B609851G Stone, 2004, Engineering flows in small devices, Annu Rev Fluid Mech, 36, 381, 10.1146/annurev.fluid.36.050802.122124 Olbricht, 1996, Pore-scale prototypes of multiphase flow in porous media, Annu Rev Fluid Mech, 28, 187, 10.1146/annurev.fl.28.010196.001155 Shapira, 1990, Low Reynolds-number motion of a droplet in shear flow including wall effects, Int J Multiph Flow, 16, 305, 10.1016/0301-9322(90)90061-M Chan, 1979, The motion of a deformable drop in a second-order fluid, J Fluid Mech, 92, 131, 10.1017/S0022112079000562 Sibillo, 2006, Drop deformation in microconfined shear flow, Phys Rev Lett, 97, 054502, 10.1103/PhysRevLett.97.054502 Vananroye, 2006, Effect of confinement on droplet breakup in sheared emulsions, Langmuir, 22, 3972, 10.1021/la060442+ Minale, 2008, A phenomenological model for wall effects on the deformation of an ellipsoidal drop in viscous flow, Rheol Acta, 47, 667, 10.1007/s00397-007-0237-0 Vananroye, 2007, Effect of confinement on the steady-state behavior of single droplets during shear flow, J Rheol, 51, 139, 10.1122/1.2399089 Vananroye, 2008, Effect of confinement and viscosity ratio on the dynamics of single droplets during transient shear flow, J Rheol, 52, 1459, 10.1122/1.2978956 Janssen, 2007, Boundary-integral method for drop deformation between parallel plates, Phys Fluids, 19, 043602, 10.1063/1.2715621 Janssen, 2008, A boundary-integral model for drop deformation between two parallel plates with non-unit viscosity ratio drops, J Comput Phys, 227, 8807, 10.1016/j.jcp.2008.06.027 Vananroye, 2008, Microconfined equiviscous droplet deformation: comparison of experimental and numerical results, Phys Fluids, 20, 013101, 10.1063/1.2835312 Renardy, 2007, The effects of confinement and inertia on the production of droplets, Rheol Acta, 46, 521, 10.1007/s00397-006-0150-y Boger, 1977, Separation of elastic and shear thinning effects in the capillary rheometer, J Rheol, 21, 515, 10.1122/1.549451 Greco, 2002, Drop deformation for non-Newtonian fluids in slow flows, J NonNewton Fluid Mech, 107, 111, 10.1016/S0377-0257(02)00144-1 Maffettone, 2004, Ellipsoidal drop model for single drop dynamics with non-Newtonian fluids, J Rheol, 48, 83, 10.1122/1.1626675 Minale, 2004, Deformation of a non-Newtonian ellipsoidal drop in a non-Newtonian matrix: extension of Maffettone–Minale model, J NonNewton Fluid Mech, 123, 151, 10.1016/j.jnnfm.2004.07.017 Guido, 2003, Effects of matrix viscoelasticity on drop deformation in dilute polymer blends under slow shear flow, Polymer, 44, 467, 10.1016/S0032-3861(02)00763-2 Guido, 2003, Deformation of a Newtonian drop in a viscoelastic matrix under steady shear flow—experimental validation of slow flow theory, J NonNewton Fluid Mech, 114, 65, 10.1016/S0377-0257(03)00118-6 Mighri, 1998, Influence of elastic properties on drop deformation and breakup in shear flow, J Rheol, 42, 1477, 10.1122/1.550897 Elmendorp, 1985, A study on polymer blending microrheology: part 1, Polym Eng Sci, 25, 1041, 10.1002/pen.760251608 Sibillo, 2004, Break-up of a Newtonian drop in a viscoelastic matrix under simple shear flow, Rheol Acta, 43, 449, 10.1007/s00397-004-0374-7 Flumerfelt, 1972, Drop breakup in simple shear fields of viscoelastic fluids, Ind Eng Chem Fund, 11, 312, 10.1021/i160043a005 Sibillo, 2005, Single drop dynamics under shearing flow in systems with a viscoelastic phase, Macromol Symp, 228, 31, 10.1002/masy.200551003 Lerdwijitjarud, 2003, Influence of weak elasticity of dispersed phase on droplet behavior in sheared polybutadiene/poly(dimethyl siloxane) blends, J Rheol, 47, 37, 10.1122/1.1530623 Lerdwijitjarud, 2004, Influence of dispersed-phase elasticity on steady-state deformation and breakup of droplets in simple shearing flow of immiscible polymer blends, J Rheol, 48, 843, 10.1122/1.1753275 Yue, 2005, Viscoelastic effects on drop deformation in steady shear, J Fluid Mech, 540, 427, 10.1017/S0022112005006166 Aggarwal, 2008, Effects of matrix viscoelasticity on viscous and viscoelastic drop deformation in a shear flow, J Fluid Mech, 601, 63, 10.1017/S0022112008000451 Aggarwal, 2007, Deformation and breakup of a viscoelastic drop in a Newtonian matrix under steady shear, J Fluid Mech, 584, 1, 10.1017/S0022112007006210 Verhulst, 2007, Drop shape dynamics of a Newtonian drop in a non-Newtonian matrix during transient and steady shear flow, J Rheol, 51, 261, 10.1122/1.2426973 Greco, 2002, Drop deformation for non-Newtonian fluids in slow flows, J NonNewt Fluid Mech, 107, 111, 10.1016/S0377-0257(02)00144-1 Verhulst, 2009, Influence of viscoelasticity on drop deformation and orientation in shear flow part 1. Stationary states, J Non-Newt Fluid Mech, 156, 29, 10.1016/j.jnnfm.2008.06.007 Verhulst, 2009, Influence of viscoelasticity on drop deformation and orientation in shear flow. Part 2: dynamics, J NonNewt Fluid Mech, 156, 44, 10.1016/j.jnnfm.2008.10.003 Mukherjee, 2009, Effects of viscosity ratio on deformation of a viscoelastic drop in a Newtonian matrix under steady shear, J NonNewt Fluid Mech, 160, 104, 10.1016/j.jnnfm.2009.03.007 Maffettone, 2005, Analysis of start-up dynamics of a single drop through an ellipsoidal drop model for non-Newtonian fluids, J NonNewt Fluid Mech, 126, 145, 10.1016/j.jnnfm.2004.11.004 Sibillo, 2006, Start-up and retraction dynamics of a Newtonian drop in a viscoelastic matrix under simple shear flow, J NonNewt Fluid Mech, 134, 27, 10.1016/j.jnnfm.2005.10.011 Mukherjee, 2010, Effects of viscoelasticity on the retraction of a sheared drop, J NonNewt Fluid Mech, 165, 340, 10.1016/j.jnnfm.2010.01.008 Yue, 2005, Diffuse-interface simulations of drop coalescence and retraction in viscoelastic fluids, J NonNewt Fluid Mech, 129, 163, 10.1016/j.jnnfm.2005.07.002 Migler, 2000, Droplet vorticity alignment in model polymer blends, J Rheol, 44, 277, 10.1122/1.551086 Mighri, 2001, Dispersion visualization of model fluids in a transparent Couette flow cell, J Rheol, 45, 783, 10.1122/1.1357823 Li, 2010, Experimental investigation of viscoelastic drop deformation in Newtonian matrix at high capillary number under simple shear flow, J NonNewt Fluid Mech, 165, 1219, 10.1016/j.jnnfm.2010.06.006 Li, 2008, Does drop size affect the mechanism of viscoelastic drop breakup?, Phys Fluids, 20, 053101, 10.1063/1.2917535 Cardinaels, 2009, Influence of confinement on the steady state behavior of single droplets in shear flow for immiscible blends with one viscoelastic component, J Rheol, 53, 1403, 10.1122/1.3236837 Minale, 2010, Microconfined shear deformation of a droplet in an equiviscous non-Newtonian immiscible fluid: experiments and modeling, Langmuir, 26, 126, 10.1021/la902187a Cardinaels, 2010, Droplet relaxation in blends with one viscoelastic component: bulk and confined conditions, Rheol Acta, 49, 941, 10.1007/s00397-010-0460-y Baroud, 2010, Dynamics of microfluidic droplets, Lab Chip, 10, 2032, 10.1039/c001191f Migler, 2001, String formation in sheared polymer blends: coalescence, breakup, and finite size effects, Phys Rev Lett, 86, 1023, 10.1103/PhysRevLett.86.1023 Pathak, 2002, Layered droplet microstructures in sheared emulsions: finite-size effects, J Colloid Interface Sci, 255, 391, 10.1006/jcis.2002.8608 Tufano, 2008, Confined flow of polymer blends, Langmuir, 24, 4494, 10.1021/la7036636 Vananroye, 2006, Structure development in confined polymer blends: steady-state shear Flow and relaxation, Langmuir, 22, 2273, 10.1021/la0527893 Caserta, 2008, Shear banding in biphasic liquid–liquid systems, Phys Rev Lett, 100, 137801, 10.1103/PhysRevLett.100.137801 Janssen, 2010, Generalized behavior of the breakup of viscous drops in confinements, J. Rheol., 54, 1047, 10.1122/1.3473924 Boufarguine, 2010, Droplet deformation of a strongly shear thinning dense suspension of polymeric micelles, Rheol Acta, 49, 647, 10.1007/s00397-009-0424-2 Capron, 2001, Water in water emulsions: phase separation and rheology of biopolymer solutions, Rheol Acta, 40, 441, 10.1007/s003970100161 Simeone, 2005, Effect of sol–gel transition on shear-induced drop deformation in aqueous mixtures of gellan and [kappa]-carrageenan, J Colloid Interface Sci, 281, 488, 10.1016/j.jcis.2004.08.095 Antonov, 2004, Interfacial tension of aqueous biopolymer mixtures close to the critical point, Int J Biol Macromol, 34, 29, 10.1016/j.ijbiomac.2004.01.001 Wolf, 2001, Influence of gelation on particle shape in sheared biopolymer blends, J Rheol, 45, 1141, 10.1122/1.1389312