Electrohydrodynamic Simulations of the Deformation of Liquid-Filled Capsules

A comprehensive two- and three-dimensional framework for the electrohydrodynamic simulation of deformable capsules is provided. The role of a direct current (DC) electric field on the deformation and orientation of a liquid-filled capsule is thoroughly considered numerically. This framework is based on lattice Boltzmann method for the fluid, finite element method for the membrane structure of the capsule, fast immersed interface method for the electric field and immersed boundary method being used to consider the fluid-structure-electric interaction. Under the effect of electric field, two different types of equilibrium states, prolate or oblate are obtained. The numerical algorithm is also applied to study the interfacial tension droplet and red blood cell under shear flow. The capsules are more deformed and arrive at equilibrium status more quickly under stronger electric field. Bending stiffness will suppress the deformation and cause transition from tank-treading to tumbling for the red blood cell. However, the applied electric field will slow down the transition from tank-treading to the tumbling motion or even stay in the tank-treading motion with stronger electric field

Direct Numerical Simulations of Electrophoresis of Charged Colloids

We propose a numerical method to simulate electrohydrodynamic phenomena in charged colloidal dispersions. This method enables us to compute the time evolutions of colloidal particles, ions, and host fluids simultaneously by solving Newton, advection-diffusion, and Navier--Stokes equations so that the electrohydrodynamic couplings can be fully taken into account. The electrophoretic mobilities of charged spherical particles are calculated in several situations. The comparisons with approximation theories show quantitative agreements for dilute dispersions without any empirical parameters, however, our simulation predicts notable deviations in the case of dense dispersions.Comment: 4pages, 3figures, to appear in Phys. Rev. Let

An efficient neural-network and finite-difference hybrid method for elliptic interface problems with applications

A new and efficient neural-network and finite-difference hybrid method is developed for solving Poisson equation in a regular domain with jump discontinuities on embedded irregular interfaces. Since the solution has low regularity across the interface, when applying finite difference discretization to this problem, an additional treatment accounting for the jump discontinuities must be employed. Here, we aim to elevate such an extra effort to ease our implementation by machine learning methodology. The key idea is to decompose the solution into singular and regular parts. The neural network learning machinery incorporating the given jump conditions finds the singular solution, while the standard finite difference method is used to obtain the regular solution with associated boundary conditions. Regardless of the interface geometry, these two tasks only require supervised learning for function approximation and a fast direct solver for Poisson equation, making the hybrid method easy to implement and efficient. The two- and three-dimensional numerical results show that the present hybrid method preserves second-order accuracy for the solution and its derivatives, and it is comparable with the traditional immersed interface method in the literature. As an application, we solve the Stokes equations with singular forces to demonstrate the robustness of the present method

Electrohydrodynamic Simulations of Capsule Deformation Using a Dual Time-Stepping Lattice Boltzmann Scheme

Capsules are fluid-filled, elastic membranes that serve as a useful model for synthetic and biological membranes. One prominent application of capsules is their use in modeling the response of red blood cells to external forces. These models can be used to study the cell’s material properties and can also assist in the development of diagnostic equipment. In this work we develop a three dimensional model for numerical simulations of red blood cells under the combined influence of hydrodynamic and electrical forces. The red blood cell is modeled as a biconcave-shaped capsule suspended in an ambient fluid domain. Cell deformation occurs due to fluid motion and electrical forces that arise due to differences in the electrical properties between the internal fluid, external fluid, and cell membrane. The electrostatic equations are solved using the immersed interface method. A finite element method is used to compute the membrane’s elastic forces and the membrane’s bending resistance is described by the Helfrich bending energy functional. The membrane forces are coupled to the fluid equations through the immersed boundary method, where the elastic, bending, and electric forces appear as force densities in the Navier-Stokes equations. The fluid equations are solved using a novel dual time-stepping (DTS) lattice Boltzmann method (LBM), which decouples the fluid and capsule discretizations. The computational efficiency of the DTS scheme is studied for capsules in shear flow where it is found that the newly proposed scheme decreases computational time by a factor of 10 when compared to the standard LBM capsule model. The method is then used to study the dynamics of spherical and biconcave capsules in a combined shear flow and DC electric field. For spherical capsules the effect of field strength, shear rate, membrane capacitance, and membrane conductance are studied. For biconcave capsules the effect of the electric field on the tumbling and tank-treading modes of biconcave capsules is discussed

Electro-deformation of a moving boundary: a drop interface and a lipid bilayer membrane

This dissertation focuses on the deformation of a viscous drop and a vesicle immersed in a (leaky) dielectric fluid under an electric field. A number of mathematical tools, both analytical and numerical, are developed for these investigations. The dissertation is divided into three parts. First, a large-deformation model is developed to capture the equilibrium deformation of a viscous spheroidal drop covered with non-diffusing insoluble surfactant under a uniform direct current (DC) electric field. The large- deformation model predicts the dependence of equilibrium spheroidal drop shape on the permittivity ratio, conductivity ratio, surfactant coverage, and the elasticity number. Results from the model are carefully compared against the small-deformation (quasispherical) analysis, experimental data and numerical simulation results in the literature. Moreover, surfactant effects, such as tip stretching and surface dilution effects, are greatly amplified at large surfactant coverage and high electric capillary number. These effects are well captured by the spheroidal model, but cannot be described in the second-order small-deformation theory. The large-deformation spheroidal model is then extended to study the equilibrium deformation of a giant unilamellar vesicle (GUV) under an alternating current (AC) electric field. The vesicle membrane is modeled as a thin capacitive spheroidal shell and the equilibrium vesicle shape is computed from balancing the mechanical forces between the fluid, the membrane and the imposed electric field. Detailed comparison against both experiments and small-deformation theory shows that the spheroidal model gives better agreement with experiments in terms of the dependence on fluid conductivity ratio, electric field strength and frequency, and vesicle size. Asymptotic analysis is conducted to compute the crossover frequency where a prolate vesicle crosses over to an oblate shape, and comparisons show the spheroidal model gives better agreement with experimental observations. Finally, a numerical scheme based on immersed interface method for two-phase fluids is developed to simulate the time-dependent dynamics of an axisymmetric drop in an electric field. The second-order immersed interface method is applied to solving both the fluid velocity field and the electric field. To date this has not been done before in the literature. Detailed numerical studies on this new numerical scheme shows numerical convergence and good agreement with the large-deformation model. Dynamics of an axisymmetric viscous drop under an electric field is being simulated using this novel numerical code

Three-Dimensional Numerical Simulation of Deformation of a Single Drop under Uniform Electric Field

In this paper, deformation of a drop suspended in another immiscible fluid that is influenced by an external uniform electric field is investigated through fully 3D numerical simulations. The electric field is applied by imposing an electric potential difference in the ambient fluid. The Leaky dielectric model is used to obtain the electric field, charge distribution and eventually applied electric force at the interface. This force creates both oblate and prolate shapes, and also induces various Electrohydrodynamic flows inside and outside of the drop depending on the conductivity and permittivity ratio of the drop and the ambient fluid. A finite difference/front-tracking method is used. The results are presented for a wide range of non-dimensional parameters for predicting the drop deformation quantitatively and qualitatively. Different flow patterns are induced inside and outside of the drop. The results show a good agreement with theoretical and experimental results in the literature. For the sake of consideration of the problem in more detail, four specific cases are investigated

An enriched finite element/level-set model for two-phase electrohydrodynamic simulations

In this work, a numerical model for the simulation of two-phase electrohydrodynamic (EHD) problems is proposed. It is characterized by a physically consistent treatment of surface tension as well as a jump in the electric material properties. The formulation is based on a finite element method enriched with special shape functions, capable of accurate capturing discontinuities both in the fluid pressure and the gradient of the electric potential. Phase interface is, thus, represented as a zero-thickness boundary. The proposed methodology allows modeling the electric force as an interfacial one, strictly abiding with the physics. The approach is tested using the droplet deformation benchmarks. Moreover, application of the method to study a three-dimensional (3D) case, not characterized by symmetry of revolution, is shown. The proposed methodology defines a basis for an enriched finite element method for a wide range of EHD problems.The authors acknowledge the financial support of the Ministerio de Ciencia, Innovaci on e Universidades of Spain via the “Severo Ochoa Programme” for Centres of Excellence in R&D (Referece No. CEX2018-000797-S) given to the International Centre for Numerical Methods in Engineering (CIMNE). The work of C. Narvaez-Mu~noz was supported by the “Severo Ochoa Ph.D. Scholarship” Reference No. PRE2020-096632. Parts of this work were done in the framework of DIDRO project (Toward establishing a Digital twin for manufacturing via drop-on-demand inkjet printing. Proyectos Estrat egicos Orientados a la Transici on Ecol ogica y a la Transici on Digital. Reference No. TED2921-130471B-I00) supported by the Ministerio de Ciencia, Innovaci on e Universidades of Spain. M. Hashemi acknowledges the funding received from European Union’s Horizon 2020 Research and Innovation Programme (European High-Performance Computing Joint Undertaking Grant Agreement No. 955558) as part of EFLOWS4HPC project. P. Ryzhakov and J. Pons-Prats are Serra Hunter fellows.Peer ReviewedPostprint (published version