Electrohydrodynamics of Drops and Vesicles

Literature Cited

1. Anna SL 2016. Droplets and bubbles in microfluidic devices. Annu. Rev. Fluid Mech. 48:285–309
   [Google Scholar]
2. Aranda S, Riske KA, Lipowsky R, Dimova R 2008. Morphological transitions of vesicles induced by AC electric fields. Biophys. J. 95:L19–21
   [Google Scholar]
3. Bharti B, Velev OD 2015. Assembly of reconfigurable colloidal structures by multidirectional field-induced interactions. Langmuir 31:7897–908
   [Google Scholar]
4. Bricard A, Caussin JB, Desreumaux N, Dauchot O, Bartolo D 2013. Emergence of macroscopic directed motion in populations of motile colloids. Nature 503:95–98
   [Google Scholar]
5. Brochard F, Lennon JF 1975. Frequency spectrum of the flicker phenomenon in erythrocytes. J. Phys. 36:1035–47
   [Google Scholar]
6. Brosseau Q, Hickey G, Vlahovska PM 2017. Electrohydrodynamic Quincke rotation of an ellipsoid. Phys. Rev. Fluids 2:014101
   [Google Scholar]
7. Brosseau Q, Vlahovska PM 2017. Streaming from the equator of a drop in an external electric field. Phys. Rev. Lett. 119:034501
   [Google Scholar]
8. Castro-Hernandez E, Campo-Cortes F, Manuel Gordillo J 2012. Slender-body theory for the generation of micrometre-sized emulsions through tip streaming. J. Fluid Mech. 698:423–45
   [Google Scholar]
9. Cebers A, Lemaire E, Lobry L 2000. Electrohydrodynamic instabilities and orientation of dielectric ellipsoids in low-conducting fluids. Phys. Rev. E 63:016301
   [Google Scholar]
10. Collins RT, Jones JJ, Harris MT, Basaran OA 2008. Electrohydrodynamic tip streaming and emission of charged drops from liquid cones. Nat. Phys. 4:149–54
    [Google Scholar]
11. Collins RT, Sambath K, Harris MT, Basaran OA 2013. Universal scaling laws for the disintegration of electrified drops. PNAS 110:4905–10
    [Google Scholar]
12. Danov KD, Kralchevsky PA 2013. Forces acting on dielectric colloidal spheres at a water/nonpolar-fluid interface in an external electric field. 1. Uncharged particles. J. Colloid Interface Sci. 405:278–90
    [Google Scholar]
13. Das D, Saintillan D 2013. Electrohydrodynamic interaction of spherical particles under Quincke rotation. Phys. Rev. E 87:043014
    [Google Scholar]
14. Das D, Saintillan D 2017.a A nonlinear small-deformation theory for transient droplet electrohydrodynamics. J. Fluid Mech. 810:225–53
    [Google Scholar]
15. Das D, Saintillan D 2017.b Electrohydrodynamics of viscous drops in strong electric fields: numerical simulations. J. Fluid Mech. 829:127–52
    [Google Scholar]
16. de la Mora JF 2007. The fluid dynamics of Taylor cones. Annu. Rev. Fluid. Mech. 39:217–43
    [Google Scholar]
17. DeBruin KA, Krassowska W 1999. Modeling electroporation in a single cell. I. Effects of field strength and rest potential. Biophys. J. 77:1213–24
    [Google Scholar]
18. Deshmukh SD, Thaokar RM 2013. Deformation and breakup of a leaky dielectric drop in a quadrupole electric field. J. Fluid Mech. 731:713–33
    [Google Scholar]
19. Dimova R, Bezlyepkina N, Jordo MD, Knorr RL, Riske KA et al. 2009. Vesicles in electric fields: some novel aspects of membrane behavior. Soft Matter 5:3201–12
    [Google Scholar]
20. Dobnikar J, Snezhko A, Yethiraj A 2013. Emergent colloidal dynamics in electromagnetic fields. Soft Matter 9:3693–704
    [Google Scholar]
21. Doerr A, Hardt S 2015. Driven particles at fluid interfaces acting as capillary dipoles. J. Fluid Mech. 770:5–26
    [Google Scholar]
22. Dolinsky Y, Elperin T 2009. Electrorotation of a leaky dielectric spheroid immersed in a viscous fluid. Phys. Rev. E 80:066607
    [Google Scholar]
23. Dommersnes P, Rozynek Z, Mikkelsen A, Castberg R, Kjerstad K et al. 2013. Active structuring of colloidal armor on liquid drops. Nat. Commun. 4:2066
    [Google Scholar]
24. Dubash N, Mestel AJ 2007. Behaviour of a conducting drop in a highly viscous fluid subject to an electric field. J. Fluid Mech. 581:469–93
    [Google Scholar]
25. Esmaeeli A, Sharifi P 2011. Transient electrohydrodynamics of a liquid drop. Phys. Rev. E 84:036308
    [Google Scholar]
26. Evans E, Rawicz W 1990. Entropy driven tension and bending elasticity in condensed-fluid membranes. Phys. Rev. Lett. 64:2094–97
    [Google Scholar]
27. Feng JQ 1996. Dielectrophoresis of a deformable fluid particle in a non-uniform electric field. Phys. Rev. E 54:4438–41
    [Google Scholar]
28. Fernandez A 2008.a Response of an emulsion of leaky dielectric drops immersed in a simple shear flow: drops less conductive than the suspending fluid. Phys. Fluids 20:043304
    [Google Scholar]
29. Fernandez A 2008.b Response of an emulsion of leaky dielectric drops immersed in a simple shear flow: drops more conductive than the suspending fluid. Phys. Fluids 20:043303
    [Google Scholar]
30. Gañán-Calvo AM, López-Herrera JM, Herrada MA, Ramos A, Montanero JM 2018. Review on the physics of electrospray: from electrokinetics to the operating conditions of single and coaxial Taylor cone-jets, and AC electrospray. J. Aerosol Sci. 125:32–56
    [Google Scholar]
31. Gañán-Calvo AM, López-Herrera JM, Rebollo-Muñoz N, Montanero JM 2016. The onset of electrospray: the universal scaling laws of the first ejection. Sci. Rep. 6:32357
    [Google Scholar]
32. Ghazian O, Adamiak K, Castle GSP, Higashiyama Y 2014. Oscillation, pseudo-rotation and coalescence of sessile droplets in a rotating electric field. Colloids Surf. A 441:346–53
    [Google Scholar]
33. Grosse C, Schwan HP 1992. Cellular membrane potentials induced by alternating fields. Biophys. J. 63:1632–42
    [Google Scholar]
34. Ha JW, Yang SM 1995. Effects of surfactant on the deformation and stability of a drop in a viscous fluid in an electric field. J. Colloid Interface Sci. 175:369–85
    [Google Scholar]
35. Ha JW, Yang SM 1998. Effect of nonionic surfactant on the deformation and breakup of a drop in an electric field. J. Colloid Interface Sci. 206:195–204
    [Google Scholar]
36. Ha JW, Yang SM 2000.a Electrohydrodynamics and electrorotation of a drop with fluid less conductive than that of the ambient fluid. Phys. Fluids 12:764–72
    [Google Scholar]
37. Ha JW, Yang SM 2000.b Rheological responses of oil-in-oil emulsions in an electric field. J. Rheol. 44:235–56
    [Google Scholar]
38. Haluska C, Marchi-Artzner V, Brienne J, Lehn L, Lipowsky R, Dimova R 2004. Fusion of giant vesicles observed with time resolution below millisecond. Biophys. J. 86:519A
    [Google Scholar]
39. He H, Salipante PF, Vlahovska PM 2013. Electrorotation of a viscous droplet in a uniform direct current electric field. Phys. Fluids 25:032106
    [Google Scholar]
40. Huang HF, Zahn M, Lemaire E 2011. Negative electrorheological responses of micro-polar fluids in the finite spin viscosity small spin velocity limit. I. Couette flow geometries. J. Electrost. 69:442–55
    [Google Scholar]
41. Jones TB 1984. Quincke rotation of spheres. IEEE Trans. Ind. Appl. 20:845–49
    [Google Scholar]
42. Karyappa RB, Deshmukh SD, Thaokar RM 2014. Breakup of a conducting drop in a uniform electric field. J. Fluid Mech. 754:550–89
    [Google Scholar]
43. Kim S, Karrila SJ 1991. Microhydrodynamics: Principles and Selected Applications Boston: Butterworth-Heinemann
44. Knorr RL, Staykova M, Gracia RS, Dimova R 2010. Wrinkling and electroporation of giant vesicles in the gel phase. Soft Matter 6:1990–96
    [Google Scholar]
45. Kokot G, Das S, Winkler RG, Gompper G, Aranson IS, Snezhko A 2017. Active turbulence in a gas of self-assembled spinners. PNAS 114:12870–75
    [Google Scholar]
46. Kolahdouz EM, Salac D 2015.a Dynamics of three-dimensional vesicles in DC electric fields. Phys. Rev. E 92:012302
    [Google Scholar]
47. Kolahdouz EM, Salac D 2015.b Electrohydrodynamics of three-dimensional vesicles: a numerical approach. SIAM J. Sci. Comput. 37:B473–94
    [Google Scholar]
48. Lac E, Homsy GM 2007. Axisymmetric deformation and stability of a viscous drop in a steady electric field. J. Fluid. Mech. 590:239–64
    [Google Scholar]
49. Lacoste D, Lagomarsino M, Joanny J 2007. Fluctuations of a driven membrane in an electrolyte. Europhys. Lett. 77:18006
    [Google Scholar]
50. Lacoste D, Menon GI, Bazant MZ, Joanny JF 2009. Electrostatic and electrokinetic contributions to the elastic moduli of a driven membrane. Eur. Phys. J. E 28:243–64
    [Google Scholar]
51. Lanauze JA, Walker LM, Khair AS 2013. The influence of inertia and charge relaxation on electrohydrodynamic drop deformation. Phys. Fluids 25:112101
    [Google Scholar]
52. Lanauze JA, Walker LM, Khair AS 2015. Nonlinear electrohydrodynamics of slightly deformed oblate drops. J. Fluid Mech. 774:245–66
    [Google Scholar]
53. Larson RG 1999. The Structure and Rheology of Complex Fluids Oxford: Oxford Univ. Press
54. Lavrentovich OD 2016. Active colloids in liquid crystals. Curr. Opin. Colloid Interface Sci. 21:97–109
    [Google Scholar]
55. Lemaire E, Lobry L 2002. Chaotic behavior in electro-rotation. Physica A 314:663–71
    [Google Scholar]
56. Lemaire E, Lobry L, Pannacci NA 2008. Viscosity of an electro-rheological suspension with internal rotations. J. Rheology 52:769–83
    [Google Scholar]
57. Loubet B, Hansen PL, Lomholt MA 2013. Electromechanics of a membrane with spatially distributed fixed charges: flexoelectricity and elastic parameters. Phys. Rev. E 88:062715
    [Google Scholar]
58. Malkus WVR, Veronis G 1961. Surface electroconvection. Phys. Fluids 4:13–23
    [Google Scholar]
59. Mandal S, Chakraborty S 2017.a Effect of nonuniform electric field on the electrohydrodynamic motion of a drop in Poiseuille flow. Phys. Fluids 29:052006
    [Google Scholar]
60. Mandal S, Chakraborty S 2017.b Influence of interfacial viscosity on the dialectrophoresis of drops. Phys. Fluids 29:052002
    [Google Scholar]
61. Mandal S, Chakraborty S 2017.c Uniform electric-field-induced non-Newtonian rheology of a dilute suspension of deformable Newtonian drops. Phys. Rev. Fluids 2:093602
    [Google Scholar]
62. McConnell LC, Miksis MJ, Vlahovska PM 2013. Vesicle electrohydrodynamics in DC electric fields. IMA J. Appl. Math. 78:797–817
    [Google Scholar]
63. McConnell LC, Miksis MJ, Vlahovska PM 2015.a Continuum modeling of the electric-field-induced tension in deforming lipid vesicles. J. Chem. Phys. 143:243132
    [Google Scholar]
64. McConnell LC, Miksis MJ, Vlahovska PM 2015.b Vesicle dynamics in uniform electric fields: squaring and breathing. Soft Matter 11:4840–46
    [Google Scholar]
65. Melcher JR, Taylor GI 1969. Electrohydrodynamics—a review of role of interfacial shear stress. Annu. Rev. Fluid Mech. 1:111–46
    [Google Scholar]
66. Mikkelsen A, Rozynek Z, Khobaib K, Dommersnes P, Fossum JO 2017. Transient deformation dynamics of particle laden droplets in electric field. Colloids Surf. A 532:252–56
    [Google Scholar]
67. Mori Y, Young YN 2018. Electrohydrodynamics of leaky dielectrics as the weak electrolyte limit of an electrodiffusion model. arXiv:1709.02321 [physics.flu-dyn]
68. Nganguia H, Young YN, Layton AT, Hu WF, Lai MC 2015. An immersed interface method for axisymmetric electrohydrodynamic simulations in Stokes flow. Commun. Comput. Phys. 18:429–49
    [Google Scholar]
69. Nganguia H, Young YN, Vlahovska PM, Blawzdziewcz J, Zhang J, Lin H 2013. Equilibrium electro-deformation of a surfactant-laden viscous drop. Phys. Fluids 25:092106
    [Google Scholar]
70. Ouriemi M, Vlahovska PM 2014. Electrohydrodynamics of particle-covered drops. J. Fluid Mech. 751:106–20
    [Google Scholar]
71. Ouriemi M, Vlahovska PM 2015. Electrohydrodynamic deformation and rotation of a particle-coated drop. Langmuir 31:6298–305
    [Google Scholar]
72. Pairam E, Fernández-Nieves A 2009. Generation and stability of toroidal droplets in a viscous liquid. Phys. Rev. Lett. 102:234501
    [Google Scholar]
73. Pan XD, McKinley GH 1997. Characteristics of electrorheological responses in an emulsion system. J. Colloid Interface Sci. 195:101–13
    [Google Scholar]
74. Pascall AJ, Squires TM 2011. Electrokinetics at liquid/liquid interfaces. J. Fluid Mech. 684:163–91
    [Google Scholar]
75. Perrier DL, Rems L, Boukany PE 2017. Lipid vesicles in pulsed electric fields: fundamental principles of the membrane response and its biomedical applications. Adv. Colloid Interface Sci. 249:248–71
    [Google Scholar]
76. Pillai R, Berry JD, Harvie DJE, Davidson MR 2016. Electrokinetics of isolated electrified drops. Soft Matter 12:3310–25
    [Google Scholar]
77. Portet T, Dimova R 2010. A new method for measuring edge tensions and stability of lipid bilayers: effect of membrane composition. Biophys. J. 99:3264–73
    [Google Scholar]
78. Portet T, Mauroy C, Demery V, Houles T, Escoffre JM et al. 2012. Destabilizing giant vesicles with electric fields: an overview of current applications. J. Membr. Biol. 245:555–64
    [Google Scholar]
79. Riske KA, Dimova R 2005. Electro-deformation and poration of giant vesicles viewed with high temporal resolution. Biophys. J. 88:1143–55
    [Google Scholar]
80. Riske KA, Dimova R 2006. Electric pulses induce cylindrical deformations on giant vesicles in salt solutions. Biophys. J. 91:1778–86
    [Google Scholar]
81. Riske KA, Knorr RL, Dimova R 2009. Bursting of charged multicomponent vesicles subjected to electric pulses. Soft Matter 5:1983–86
    [Google Scholar]
82. Rozynek Z, Castberg R, Kalicka A, Jankowski P, Garstecki P 2015. Electric field manipulation of particles in leaky dielectric liquids. Arch. Mech. 67:385–99
    [Google Scholar]
83. Rozynek Z, Mikkelsen A, Dommersnes P, Fossum JO 2014. Electroformation of Janus and patchy capsules. Nat. Commun. 5:3945
    [Google Scholar]
84. Salipante PF, Knorr R, Dimova R, Vlahovska PM 2012. Electrodeformation method for measuring the capacitance of bilayer membranes. Soft Matter 8:3810–16
    [Google Scholar]
85. Salipante PF, Shapiro ML, Vlahovska PM 2015. Electric field induced deformations of biomimetic fluid membranes. Procedia IUTAM 16:60–69
    [Google Scholar]
86. Salipante PF, Vlahovska PM 2010. Electrohydrodynamics of drops in strong uniform DC electric fields. Phys. Fluids 22:112110
    [Google Scholar]
87. Salipante PF, Vlahovska PM 2013. Electrohydrodynamic rotations of a viscous droplet. Phys. Rev. E 88:043003
    [Google Scholar]
88. Salipante PF, Vlahovska PM 2014. Vesicle deformation in DC electric pulses. Soft Matter 10:3386–93
    [Google Scholar]
89. Sato H, Kaji N, Mochizuki T, Mori YH 2006. Behavior of oblately deformed droplets in an immiscible dielectric liquid under a steady and uniform electric field. Phys. Fluids 18:127101
    [Google Scholar]
90. Saville DA 1997. Electrohydrodynamics: the Taylor-Melcher leaky dielectric model. Annu. Rev. Fluid Mech. 29:27–64
    [Google Scholar]
91. Schnitzer O, Frankel I, Yariv E 2013.a Deformation of leaky-dielectric fluid globules under strong electric fields: boundary layers and jets at large Reynolds numbers. J. Fluid Mech. 734:R3
    [Google Scholar]
92. Schnitzer O, Frankel I, Yariv E 2013.b Electrokinetic flows about conducting drops. J. Fluid Mech. 722:394–423
    [Google Scholar]
93. Schnitzer O, Yariv E 2013. Nonlinear electrokinetic flow about a polarized conducting drop. Phys. Rev. E 87:041002. Erratum. 2013. Phys. Rev. E 87:059901
    [Google Scholar]
94. Schnitzer O, Yariv E 2015. The Taylor–Melcher leaky dialectric model as a macroscale electrokinetic description. J. Fluid Mech. 773:1–33
    [Google Scholar]
95. Schwalbe J, Vlahovska PM, Miksis MJ 2011.a Lipid membrane instability driven by capacitive charging. Phys. Fluids 23:041701
    [Google Scholar]
96. Schwalbe J, Vlahovska PM, Miksis MJ 2011.b Vesicle electrohydrodynamics. Phys. Rev. E 83:046309
    [Google Scholar]
97. Seifert U 1997. Configurations of fluid membranes and vesicles. Adv. Phys. 46:13–137
    [Google Scholar]
98. Seifert U 1999. Fluid membranes in hydrodynamic flow fields: formalism and an application to fluctuating quasispherical vesicles. Eur. Phys. J. B 8:405–15
    [Google Scholar]
99. Seifert U, Langer S 1993. Viscous modes of fluid bilayer membranes. Europhys. Lett. 23:71–76
    [Google Scholar]
100. Seiwert J, Miksis MJ, Vlahovska PM 2012. Stability of biomimetic membranes in DC electric fields. J. Fluid Mech. 706:58–70
     [Google Scholar]
101. Seiwert J, Vlahovska PM 2012. Instability of a fluctuating membrane driven by an AC electric field. Phys. Rev. E 87:022713
     [Google Scholar]
102. Sengupta R, Walker LM, Khair AS 2017. The role of surface charge convection in the electrohydrodynamics and breakup of prolate drops. J. Fluid Mech. 833:29–53
     [Google Scholar]
103. Sens P, Isambert H 2002. Undulation instability of lipid membranes under an electric field. Phys. Rev. Lett. 88:128102
     [Google Scholar]
104. Sheng P, Wen W 2012. Electrorheological fluids: mechanisms, dynamics, and microfluidics applications. Annu. Rev. Fluid Mech. 44:143–74
     [Google Scholar]
105. Sinha KP, Gadkari S, Thaokar RM 2013. Electric field induced pearling instability in cylindrical vesicles. Soft Matter 9:7274–93
     [Google Scholar]
106. Snezhko A 2016. Complex collective dynamics of active torque-driven colloids at interfaces. Curr. Opin. Colloid Interface Sci. 21:65–75
     [Google Scholar]
107. Staykova M, Lipowsky R, Dimova R 2008. Membrane flow patterns in multicomponent giant vesicles induced by alternating electric fields. Soft Matter 4:2168–71
     [Google Scholar]
108. Suryo R, Basaran OA 2006. Tip streaming from a liquid drop forming from a tube in a co-flowing outer fluid. Phys. Fluids 18:082102
     [Google Scholar]
109. Tadavani SK, Munroe JR, Yethiraj A 2016. The effect of confinement on the electrohydrodynamic behavior of droplets in a microfluidic oil-in-oil emulsion. Soft Matter 12:9246–55
     [Google Scholar]
110. Taylor GI 1932. The viscosity of a fluid containing small drops of another fluid. Proc. R. Soc. A 138:41–48
     [Google Scholar]
111. Taylor GI 1966. Studies in electrohydrodynamics. I. Circulation produced in a drop by an electric field. Proc. R. Soc. A 291:159–66
     [Google Scholar]
112. Torza S, Cox R, Mason S 1971. Electrohydrodynamic deformation and burst of liquid drops. Philos. Trans. R. Soc. A 269:295–319
     [Google Scholar]
113. Tseng YH, Prosperetti A 2015. Local interfacial stability near a zero vorticity point. J. Fluid Mech. 776:5–36
     [Google Scholar]
114. Turcu I 1987. Electric field induced rotation of spheres. J. Phys. A 20:3301–7
     [Google Scholar]
115. Tyatyushkin AN 2017. Unsteady electrorotation of a drop in a constant electric field. Phys. Fluids 29:097101
     [Google Scholar]
116. van Blaaderen A, Dijkstra M, van Roij R, Imhof A, Kamp M et al. 2013. Manipulating the self assembly of colloids in electric fields. Eur. Phys. J. Spec. Top. 222:2895–909
     [Google Scholar]
117. Varshney A, Gohil S, Sathe M, Yethiraj A 2016. Multiscale flow in an electro-hydrodynamically driven oil-in-oil emulsion. Soft Matter 12:1759–64
     [Google Scholar]
118. Veerapaneni S 2016. Integral equation methods for vesicle electrohydrodynamics in three dimensions. J. Comput. Phys. 326:278–89
     [Google Scholar]
119. Vlahovska PM 2010. Non-equilibrium dynamics of lipid membranes: deformation and stability in electric fields. Advances in Planar Lipid Bilayers and Liposomes 12 A Iglič103–46 Oxford: Academic
     [Google Scholar]
120. Vlahovska PM 2011. On the rheology of a dilute emulsion in a uniform electric field. J. Fluid Mech. 670:481–503
     [Google Scholar]
121. Vlahovska PM 2015. Voltage-morphology coupling in biomimetic membranes: dynamics of giant vesicles in applied electric fields. Soft Matter 11:7232–36
     [Google Scholar]
122. Vlahovska PM 2016.a Dynamics of membrane-bound particles: capsules and vesicles. Low-Reynolds-Number Flows: Fluid–Structure Interactions C Duprat, H Stone313–46 Cambridge, UK: R. Soc. Chem.
     [Google Scholar]
123. Vlahovska PM 2016.b Electrohydrodynamic instabilities of viscous drops. Phys. Rev. Fluids 1:060504
     [Google Scholar]
124. Vlahovska PM, Gracia RS, Aranda-Espinoza S, Dimova R 2009. Electrohydrodynamic model of vesicle deformation in alternating electric fields. Biophys. J. 96:4789–803
     [Google Scholar]
125. Weaver JC, Chizmadzhev YA 1996. Theory of electroporation: a review. Bioelectrochem. Bioenerg. 41:135–60
     [Google Scholar]
126. Yamamoto T, Aranda-Espinoza S, Dimova R, Lipowsky R 2010. Stability of spherical vesicles in electric fields. Langmuir 26:12390–407
     [Google Scholar]
127. Yariv E, Frankel I 2016. Electrohydrodynamic rotation of drops at large electric Reynolds numbers. J. Fluid Mech. 788:R2
     [Google Scholar]
128. Yariv E, Rhodes D 2013. Electrohydrodynamic drop deformation by strong electric fields: slender body analysis. SIAM J. Appl. Math. 73:2143–61
     [Google Scholar]
129. Yeo K, Lushi E, Vlahovska PM 2015. Collective dynamics in a binary mixture of hydrodynamically coupled microrotors. Phys. Rev. Lett. 114:188301
     [Google Scholar]
130. Young YN, Miksis M 2015. Electrohydrodynamic instability of a capacitive elastic membrane. Phys. Fluids 27:022102
     [Google Scholar]
131. Young YN, Veerapaneni S, Miksis M 2014. Long-wave dynamics of an inextensible planar membrane in an electric field. J. Fluid Mech. 751:406–31
     [Google Scholar]
132. Yu M, Lira RB, Riske KA, Dimova R, Lin H 2015. Ellipsoidal relaxation of deformed vesicles. Phys. Rev. Lett. 115:128303
     [Google Scholar]
133. Zabarankin M 2013. A liquid spheroidal drop in a viscous incompressible fluid under a steady electric field. SIAM J. Appl. Math. 73:677–99
     [Google Scholar]
134. Zabarankin M, Smagin I, Lavrenteva OM, Nir A 2013. Viscous drop in compressional Stokes flow. J. Fluid. Mech. 720:169–91
     [Google Scholar]
135. Zhang J, Song Y, Li D 2018. Electrokinetic motion of a spherical polystyrene particle at a liquid-fluid interface. J. Colloid Interface Sci. 509:432–39
     [Google Scholar]
136. Zhang J, Zahn JD, Lin H 2013.a Transient solution for droplet deformation under electric fields. Phys. Rev. E 87:043008
     [Google Scholar]
137. Zhang J, Zahn JD, Tan W, Lin H 2013.b A transient solution for vesicle electrodeformation and relaxation. Phys. Fluids 25:071903
     [Google Scholar]
138. Zholkovskij EK, Masilyah JH, Czarnecki J 2002. An electrokinetic model of drop deformation in an electric field. J. Fluid Mech. 472:1–27
     [Google Scholar]
139. Ziebert F, Bazant MZ, Lacoste D 2010. Effective zero-thickness model for a conductive membrane driven by an electric field. Phys. Rev. E 81:031912
     [Google Scholar]
140. Ziebert F, Lacoste D 2010. A Poisson–Boltzmann approach for a lipid membrane in an electric field. New J. Phys. 12:095002
     [Google Scholar]
141. Ziebert F, Lacoste D 2011. A planar lipid bilayer in an electric field: membrane instability, flow field and electrical impedance. Advances in Planar Lipid Bilayers and Liposomes 14 A Iglič73–95 Oxford: Academic
     [Google Scholar]