Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-19T13:56:04.114Z Has data issue: false hasContentIssue false
  • English
  • Français

Electrohydrodynamics of deflated vesicles: budding, rheology and pairwise interactions

Published online by Cambridge University Press:  21 March 2019

B. Wu  and
S. Veerapaneni Open the ORCID record for S. Veerapaneni [Opens in a new window]
B. Wu
Affiliation:
Department of Mathematics, University of Michigan, 530 Church Street, Ann Arbor, MI 48109, USA
S. Veerapaneni*
Affiliation:
Department of Mathematics, University of Michigan, 530 Church Street, Ann Arbor, MI 48109, USA
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

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.

JFM classification

Biological Fluid Dynamics: Capsule/cell dynamics Biological Fluid Dynamics: Membranes Complex Fluids: Suspensions
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 867 , 25 May 2019 , pp. 334 - 347
Copyright
© 2019 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

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), B519–B542.Google Scholar
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), 2334–2380.Google Scholar
Baygents, J. C., Rivette, N. J. & Stone, H. A. 1998 Electrohydrodynamic deformation and interaction of drop pairs. J. Fluid Mech. 368, 359–375.Google Scholar
Fygenson, D. K., Marko, J. F. & Libchaber, A. 1997 Mechanics of microtubule-based membrane extension. Phys. Rev. Lett. 79 (22), 4497.Google Scholar
Hsiao, G. C. & Wendland, W. L. 2008 Boundary Integral Equations, vol. 164. Springer.Google Scholar
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, 66–81.Google Scholar
Kolahdouz, E. M. & Salac, D. 2015 Dynamics of three-dimensional vesicles in DC electric fields. Phys. Rev. E 92 (1), 012302.Google Scholar
Kress, R. 1999 Linear Integral Equations, Applied Mathematical Sciences, vol. 82. Springer.Google Scholar
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), B740–B772.Google Scholar
McConnell, L. C., Miksis, M. J. & Vlahovska, P. M. 2013 Vesicle electrohydrodynamics in DC electric fields. IMA J. Appl. Maths 78 (4), 797–817.Google Scholar
McConnell, L. C., Vlahovska, P. M. & Miksis, M. J. 2015 Vesicle dynamics in uniform electric fields: squaring and breathing. Soft Matt. 11, 4840–4846.Google Scholar
Mori, Y. & Young, Y.-N. 2018 From electrodiffusion theory to the electrohydrodynamics of leaky dielectrics through the weak electrolyte limit. J. Fluid Mech. 855, 67–130.Google Scholar
Nganguia, H. & Young, Y.-N. 2013 Equilibrium electrodeformation of a spheroidal vesicle in an AC electric field. Phys. Rev. E 88 (5), 052718.Google Scholar
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, 248–271.Google Scholar
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), 6466–6484.Google Scholar
Riske, K. A. & Dimova, R. 2005 Electro-deformation and poration of giant vesicles viewed with high temporal resolution. Biophys. J. 88 (2), 1143–1155.Google Scholar
Ristenpart, W. D., Vincent, O., Lecuyer, S. & Stone, H. A. 2010 Dynamic angular segregation of vesicles in electrohydrodynamic flows. Langmuir 26 (12), 9429–9436.Google Scholar
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.Google Scholar
Salipante, P. F. & Vlahovska, P. M. 2014 Vesicle deformation in DC electric pulses. Soft Matt. 10 (19), 3386–3393.Google Scholar
Schwalbe, J. T., Vlahovska, P. M. & Miksis, M. J. 2011 Vesicle electrohydrodynamics. Phys. Rev. E 83 (4), 046309.Google Scholar
Veerapaneni, S. 2016 Integral equation methods for vesicle electrohydrodynamics in three dimensions. J. Comput. Phys. 326, 278–289.Google Scholar
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), 2334–2353.Google Scholar
Vlahovska, P. M. 2019 Electrohydrodynamics of drops and vesicles. Annu. Rev. Fluid Mech. 51 (1), 305–330.Google Scholar
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), 4789–4803.Google Scholar
Zhang, J., Zahn, J. D., Tan, W. & Lin, H. 2013 A transient solution for vesicle electrodeformation and relaxation. Phys. Fluids 25 (7), 071903.Google Scholar