A Semi-Implicit Scheme for Modeling the Interaction Between Biological Cells and Electric Fields

A numerical method for computing the simultaneous solution to the fluid flow equations and the electrostatic field equations is described. The methodology focuses on the modeling of biological cells suspended in fluid plasma. The fluid flow is described using the Navier-Stokes equations for incompressible flows. The electric field is computed trough the Maxwell equations neglecting magnetic effects. The effect of the electric field on the fluid flow is accounted for through the Maxwell stresses. The systems are described by a set of partial differential equations where the solution requires the simultaneous computation of the velocity, pressure and electric potential fields. A semi-implicit numerical scheme is proposed. In order to decrease the computational time required, it is proposed to use a semi-implicit splitting scheme where the Navier-Stokes and Maxwell equations are solved sequentially. The method is used to reproduce the response of human leukocytes immersed in a rotating electric field. An agreement between the numerical results and the data from experiments is observed.