Ph.D Thesis

Ph.D StudentSchnitzer Ory
SubjectNonlinear Electrokinetic Phenomena in the Thin-Double-Layer
DepartmentDepartment of Applied Mathematics
Supervisor ASSOCIATE PROF. Ehud Yariv


Electrical double layers spontaneously form at solid-electrolyte interfaces. In these layers, electro-neutrality is locally violated: the solids acquire a bound surface charge, while counter-ions dissolved in the liquid accumulate in a thin diffuse layer attenuating exponentially on the Debye length scale (typically not more than a few tens of nanometers). The term “electrokinetics” collectively refers to various non-equilibrium effects in which the mobile diffuse-layer ions are forced (say, by an externally applied electric field) to drift with respect to the bound surface charge. Although originating on the nanometric Debye scale, electrokinetic effects are characteristically manifested on much larger (micrometer) scales e.g. in the form of “electro-osmotic” flow fields, or “electrophoretic” particle motion. Electrokinetic techniques are essential in colloid science, and play an increasing role in microfluidic and Lab-On-A-Chip devices.

This thesis is comprised of studies of various nonlinear electrokinetic effects, including electrophoresis of solid particles and liquid-metal drops, and “induced-charged” electrostatic flows over electrode surfaces. Towards this end, we exploit the smallness of the Debye length relative to representative system dimensions through the systematic use of singular perturbation methods. In this thin-double-layer limit, the fluid domain is conceptually decomposed into an electro-neutral bulk and a diffuse (Debye) boundary layer. The asymptotic procedure results in a coarse-grained model governing the bulk, while the Debye-layer physics are encapsulated in a set of effective boundary conditions and algebraic constraints.

In contrast to the traditional linearized analyses in the literature, our macroscale models are not limited to weak fields or weakly charged surfaces. While nonlinear, they are typically amenable to various perturbation schemes and numerical computations; in particular, they do not suffer from the infamous scale disparity associated with the thin-double-layer limit. The solutions such obtained substantially extend the understanding of nonlinear electrokinetic phenomena. Incidentally, the analyses also resolve long-standing discrepancies in the literature having to do with the order in which double asymptotic limits are taken.