Ph.D Thesis

Ph.D StudentAbu Hamed Mohammad
SubjectElectrokinetic Flows about Polarizable Surfaces
DepartmentDepartment of Applied Mathematics
Supervisor ASSOCIATE PROF. Ehud Yariv


This research consist of two main tracks. In the first track we analyze the steady-state electrokinetic flow about an uncharged ideally polarizable spherical particle for the case of a Debye thickness which is large compared with particle size. The dimensionless problem is governed by two parameters: beta, the applied field magnitude (normalized with the thermal scale), and lambda, the Debye thickness (normalized with particle size). The double limit beta<< 1 and lambda>> 1 is singular, and the resolution of the flow field requires the use of inner-outer asymptotic expansions in the spirit of  Proudman and Pearson (1957). Two asymptotic limits are identified: the `moderately-thick' limit beta*lambda<< 1, in which the outer domain is characterized by the Debye thickness, and the `super-thick' limit beta*lambda>> 1, in which the outer domain represents the emergence of electro-migration in the leading-order ionic-transport process. The singularity is stronger in the comparable two-dimensional flow about a circular cylinder, where a switchback mechanism in the moderately-thick limit modifies the familiar O(beta^2) leading-order flow to O( beta^2*ln(lambda)).

The second track is about the interaction between polarizable surfaces where we consider the special case of a zero-net-charge ideally polarizable spherical particle that is suspended within an electrolyte solution, nearly in contact with an uncharged non-polarizable wall. This system  is exposed to a uniform electric field which is applied parallel to the wall. Assuming a thin Debye thickness, the induced-charge electro-osmotic flow is investigated with the goal of obtaining an approximation for the force experienced by the particle. Singular perturbations in terms of the dimensionless gap width delta are utilized to represent the small-gap singular limit delta<< 1. The fluid is decomposed into two asymptotic regions: an inner gap region, where the electric field and strain rate are large, and an outer region, where they are moderate. The leading O(delta^(sqrt(2)-2)) contribution to the force arises from hydrodynamic stresses in the inner region, while contributions from both hydrodynamic stresses at the outer region and Maxwell stresses in both regions appear in higher-order correction terms. A straightforward observation from the last result is the case of interaction between two spherical particles where the direction of the external applied electric field is perpendicular to the axis that connects there centers. In this case the repulsion force is half of the repulsion force in the previous case.