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The New Jersey Institute of Technology's
Electronic Theses & Dissertations Project

Title: A numerical method for electro-kinetic flow with deformable interfaces
Author: Ma, Manman
View Online: njit-etd2013-079
(xiii, 108 pages ~ 1.0 MB pdf)
Department: Department of Mathematical Sciences
Degree: Doctor of Philosophy
Program: Mathematical Sciences
Document Type: Dissertation
Advisory Committee: Siegel, Michael (Committee co-chair)
Booty, Michael R. (Committee co-chair)
Cummings, Linda Jane (Committee member)
Singh, Pushpendra (Committee member)
Morris, Jeffrey Franklin (Committee member)
Date: 2013-05
Keywords: Electro-kinetics
Hybrid numerical method
Moving boundary problem
Small deformation
Boundary integral method
Availability: Unrestricted

We consider two-phase flow of ionic fluids whose motion is driven by an imposed electric field. At a fluid-fluid interface, a screening cloud of ions develops and forms an electro-chemical double layer or ‘Debye layer’. The applied electric field acts on the ionic cloud it induces, resulting in a strong slip flow near the interface. This is known as ‘induced-charge electro-kinetic flow’, and is an important phenomenon in microfluidic applications and in the manipulation of biological cells. The models with two different cases including the fast or slow charging time scales are studied both analytically and numerically. We address a significant challenge in the numerical computation of such flows in the thin-double-layer limit, by using the slenderness of the layer to develop a fast and accurate ‘hybrid’ or multiscale numerical method. The method incorporates an asymptotic analysis of the electric potential and fluid dynamics in the Debye layer into a boundary integral numerical solution of the full moving boundary problem.

We present solutions for the quasi-steady state problem with ψ = O(1) and solutions for the time dependent problem with ψ « 1, where ψ is the dimensionless surface potential. Leading order problems for both electric fields and fluid fields are solved with boundary conditions and matching methods. The small deformation theories when Ca is small (Ca is the electric capillary number) for both quasi-steady state and time dependent problems are developed to check numerical simulations.

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