Skip to main content Accessibility help

Electrohydrodynamics of deflated vesicles: budding, rheology and pairwise interactions

  • B. Wu (a1) and S. Veerapaneni (a1)


We develop a new boundary integral method for solving the coupled electro- and hydrodynamics of vesicle suspensions in Stokes flow. This relies on a well-conditioned boundary integral equation formulation for the leaky-dielectric model describing the electric response of the vesicles and an efficient numerical solver capable of handling highly deflated vesicles. Our method is applied to explore vesicle electrohydrodynamics in three cases. First, we study the classical prolate–oblate–prolate transition dynamics observed upon application of a uniform DC electric field. We discover that, in contrast to the squaring previously found with nearly spherical vesicles, highly deflated vesicles tend to form buds. Second, we illustrate the capabilities of the method by quantifying the electrorheology of a dilute vesicle suspension. Finally, we investigate the pairwise interactions of vesicles and find three different responses when the key parameters are varied: (i) chain formation, where they self-assemble to form a chain that is aligned along the field direction; (ii) circulatory motion, where they rotate about each other; (iii) oscillatory motion, where they form a chain but oscillate about each other. The last two are unique to vesicles and are not observed in the case of other soft particle suspensions such as drops.


Corresponding author

Email address for correspondence:


Hide All
Barnett, A., Wu, B. & Veerapaneni, S. 2015 Spectrally accurate quadratures for evaluation of layer potentials close to the boundary for the 2D Stokes and Laplace equations. SIAM J. Sci. Comput. 37 (4), B519B542.
Barnett, A. H., Marple, G. R., Veerapaneni, S. & Zhao, L. 2018 A unified integral equation scheme for doubly periodic Laplace and Stokes boundary value problems in two dimensions. Commun. Pure Appl. Maths 71 (11), 23342380.
Baygents, J. C., Rivette, N. J. & Stone, H. A. 1998 Electrohydrodynamic deformation and interaction of drop pairs. J. Fluid Mech. 368, 359375.
Fygenson, D. K., Marko, J. F. & Libchaber, A. 1997 Mechanics of microtubule-based membrane extension. Phys. Rev. Lett. 79 (22), 4497.
Hsiao, G. C. & Wendland, W. L. 2008 Boundary Integral Equations, vol. 164. Springer.
Hu, W.-F., Lai, M.-C., Seol, Y. & Young, Y.-N. 2016 Vesicle electrohydrodynamic simulations by coupling immersed boundary and immersed interface method. J. Comput. Phys. 317, 6681.
Kolahdouz, E. M. & Salac, D. 2015 Dynamics of three-dimensional vesicles in DC electric fields. Phys. Rev. E 92 (1), 012302.
Kress, R. 1999 Linear Integral Equations, Applied Mathematical Sciences, vol. 82. Springer.
Marple, G. R., Barnett, A., Gillman, A. & Veerapaneni, S. 2016 A fast algorithm for simulating multiphase flows through periodic geometries of arbitrary shape. SIAM J. Sci. Comput. 38 (5), B740B772.
McConnell, L. C., Miksis, M. J. & Vlahovska, P. M. 2013 Vesicle electrohydrodynamics in DC electric fields. IMA J. Appl. Maths 78 (4), 797817.
McConnell, L. C., Vlahovska, P. M. & Miksis, M. J. 2015 Vesicle dynamics in uniform electric fields: squaring and breathing. Soft Matt. 11, 48404846.
Mori, Y. & Young, Y.-N. 2018 From electrodiffusion theory to the electrohydrodynamics of leaky dielectrics through the weak electrolyte limit. J. Fluid Mech. 855, 67130.
Nganguia, H. & Young, Y.-N. 2013 Equilibrium electrodeformation of a spheroidal vesicle in an AC electric field. Phys. Rev. E 88 (5), 052718.
Perrier, D. L., Rems, L. & Boukany, P. E. 2017 Lipid vesicles in pulsed electric fields: fundamental principles of the membrane response and its biomedical applications. Adv. Colloid Interface Sci 249, 248271.
Rahimian, A., Veerapaneni, S. K. & Biros, G. 2010 Dynamic simulation of locally inextensible vesicles suspended in an arbitrary two-dimensional domain, a boundary integral method. J. Comput. Phys. 229 (18), 64666484.
Riske, K. A. & Dimova, R. 2005 Electro-deformation and poration of giant vesicles viewed with high temporal resolution. Biophys. J. 88 (2), 11431155.
Ristenpart, W. D., Vincent, O., Lecuyer, S. & Stone, H. A. 2010 Dynamic angular segregation of vesicles in electrohydrodynamic flows. Langmuir 26 (12), 94299436.
Sadik, M., Li, J., Shan, J., Shreiber, D. & Lin, H. 2011 Vesicle deformation and poration under strong dc electric fields. Phys. Rev. E 83 (6), 066316.
Salipante, P. F. & Vlahovska, P. M. 2014 Vesicle deformation in DC electric pulses. Soft Matt. 10 (19), 33863393.
Schwalbe, J. T., Vlahovska, P. M. & Miksis, M. J. 2011 Vesicle electrohydrodynamics. Phys. Rev. E 83 (4), 046309.
Veerapaneni, S. 2016 Integral equation methods for vesicle electrohydrodynamics in three dimensions. J. Comput. Phys. 326, 278289.
Veerapaneni, S. K., Gueyffier, D., Zorin, D. & Biros, G. 2009 A boundary integral method for simulating the dynamics of inextensible vesicles suspended in a viscous fluid in 2D. J. Comput. Phys. 228 (7), 23342353.
Vlahovska, P. M. 2019 Electrohydrodynamics of drops and vesicles. Annu. Rev. Fluid Mech. 51 (1), 305330.
Vlahovska, P. M., Gracia, R. S., Aranda-Espinoza, S. & Dimova, R. 2009 Electrohydrodynamic model of vesicle deformation in alternating electric fields. Biophys. J. 96 (12), 47894803.
Zhang, J., Zahn, J. D., Tan, W. & Lin, H. 2013 A transient solution for vesicle electrodeformation and relaxation. Phys. Fluids 25 (7), 071903.
MathJax is a JavaScript display engine for mathematics. For more information see

JFM classification

Electrohydrodynamics of deflated vesicles: budding, rheology and pairwise interactions

  • B. Wu (a1) and S. Veerapaneni (a1)


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed