#### Date of Award

Summer 2021

#### Document Type

Dissertation

#### Degree Name

Doctor of Philosophy (PhD)

#### Department

Mathematics & Statistics

#### Program/Concentration

Computational and Applied Mathematics

#### Committee Director

Yan Peng

#### Committee Member

Gordon Melrose

#### Committee Member

Li-Shi Luo

#### Committee Member

Xiaoyu Zhang

#### Abstract

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.

#### DOI

10.25777/natr-2181

#### ISBN

9798460436453

#### Recommended Citation

Armstrong, Charles L..
"Electrohydrodynamic Simulations of Capsule Deformation Using a Dual Time-Stepping Lattice Boltzmann Scheme"
(2021). Doctor of Philosophy (PhD), Dissertation, Mathematics & Statistics, Old Dominion University, DOI: 10.25777/natr-2181

https://digitalcommons.odu.edu/mathstat_etds/117

#### ORCID

0000-0001-5536-8257

#### Included in

Applied Mathematics Commons, Biomechanics and Biotransport Commons, Biophysics Commons, Physics Commons