Ph.D Student | Abu Hamed Mohammad |
---|---|

Subject | Electrokinetic Flows about Polarizable Surfaces |

Department | Department of Applied Mathematics |

Supervisor | Professor 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.