Vesicle electrohydrodynamic simulations by coupling immersed boundary and immersed interface method

Abstract

In this paper, we develop a coupled immersed boundary (IB) and immersed interface method (IIM) to simulate the electrodeformation and electrohydrodynamics of a vesicle in Navier-Stokes leaky dielectric fluids under a DC electric field. The vesicle membrane is modeled as an inextensible elastic interface with an electric capacitance and an electric conductance. Within the leaky dielectric framework and the piecewise constant electric properties in each fluid, the electric stress can be treated as an interfacial force so that both the membrane electric and mechanical forces can be formulated in a unified immersed boundary method. The electric potential and transmembrane potential are solved simultaneously via an efficient immersed interface method. The fluid variables in Navier-Stokes equations are solved using a projection method on a staggered MAC grid while the electric potential is solved at the cell center. A series of numerical tests have been carefully conducted to illustrate the accuracy and applicability of the present method to simulate vesicle electrohydrodynamics. In particular, we investigate the prolate-oblate-prolate (POP) transition and the effect of electric field and shear flow on vesicle electrohydrodynamics. Our numerical results are in good agreement with those obtained in previous work using different numerical algorithms.

Integral equation methods for vesicle electrohydrodynamics in three dimensions

“…The tangential derivatives of the scalar function V m on the surface can simply be computed from its surface gradient (defined in (19)), for example,…”

“…Numerical methods for solving the coupled electric, elastic and hydrodynamic governing equations for the vesicle EHD have been developed only recently [19][20][21][27][28][29]. While the works of [20] and [21] use the immersed interface method (IIM) to solve the electric potential problem and level sets to track the moving interface, the recent work of [19] employs a hybrid approach and uses immersed boundary method for fluid flow and IIM to evolve the electric variables. On the other hand, the works of [27] and [29] are based on boundary integral equation (BIE) methods, which are particularly well-suited for the vesicle EHD problem since the governing equations for the fluid motion as well as the electric potential are linear.…”

Electrohydrodynamics of deflated vesicles: budding, rheology and pairwise interactions

“…Theoretical investigation of vesicle EHD has been done via small deformation theory [21,18] and semi-analytic studies using spheroidal models [22,11]. Numerical solution of the coupled electric, elastic and hydrodynamic governing equations were computed using the boundary integral equation (BIE) methods [8,17,20] and immersed interface or immersed boundary methods [6,5]. Advantages of BIE methods are well-known-exact satisfaction of far-field boundary conditions eliminating the need for artificial boundary conditions, reduction in dimensionality leading to reduced problem sizes, and well-conditioned linear systems through carefully chosen integral representations.…”

Large deformation electrohydrodynamics of a Skalak elastic capsule in AC electric field

“…Also, the phase diagrams are constructed for deformation of a spherical elastic capsule in low (using both the boundary integral calculation and analytical theory) and high (using boundary integral method) capillary numbers in AC electric field and attempts are made to understand the underlying physics. The capacitor model is used for modeling the electrostatics [22,26,27,[34][35][36]54] while the capsule is modeled as a strain hardening Skalak membrane [49]. The deformation of an object in AC field has time-averaged and time-periodic parts, and their dependence on frequency could be significantly different.…”