Travelling-Wave Electrophoresis, Electro-Hydrodynamics, Electro-Rotation, and Symmetry-Breaking of a Polarizable Dimer in Non-Uniform Fields

Abstract

A theoretical framework is presented for calculating the polarization, electro-rotation, travelling-wave dielectrophoresis, electro-hydrodynamics and induced-charge electroosmotic flow fields around a freely suspended conducting dimer (two touching spheres) exposed to non-uniform direct current (DC) or alternating current (AC) electric fields. The analysis is based on employing the classical (linearized) Poisson–Nernst–Planck (PNP) formulation under the standard linearized ‘weak-field’ assumption and using the tangent-sphere coordinate system. Explicit expressions are first derived for the axisymmetric AC electric potential governed by the Robin (mixed) boundary condition applied on the dimer surface depending on the resistance–capacitance circuit (RC) forcing frequency. Dimer electro-rotation due to two orthogonal (out-of-phase) uniform AC fields and the corresponding mobility problem of a polarizable dimer exposed to a travelling-wave electric excitation are also analyzed. We present an explicit solution for the non-linear induced-charge electroosmotic (ICEO) flow problem of a free polarized dimer in terms of the corresponding Stokes stream function determined by the Helmholtz–Smoluchowski velocity slip. Next, we demonstrate how the same framework can be used to obtain an exact solution for the electro-hydrodynamic (EHD) problem of a polarizable sphere lying next to a conducting planar electrode. Finally, we present a new solution for the induced-charge mobility of a Janus dimer composed of two fused spherical colloids, one perfectly conducting and one dielectrically coated. So far, most of the available electrokinetic theoretical studies involving polarizable nano/micro shapes dealt with convex configurations (e.g., spheres, spheroids, ellipsoids) and as such the newly obtained electrostatic AC solution for a dimer provides a useful extension for similar concave colloids and engineered particles.

Self-Diffusiophoresis and Symmetry-Breaking of a Janus Dimer: Analytic Solution

“…Taking advantage of the axisymmetric nature of the physical problem with respect to the line of centres (z axis), it is convenient to employ here a semi-separable tangential-sphere system (µ, υ), which is related to a cylindrical system (r, z) by the following transformation [31,32]:…”

“…Bearing in mind that the solute concentration C(µ, υ) is a harmonic function satisfying C → 1 at infinity, one can write [32]:…”

“…Recalling again [40] that µ/ 1 + µ 2 3/2 = ∞ 0 se −s J 1 (sµ)ds and substituting Equation (32) in Equation ( 36) renders:…”

“…A special Janus dimer (JD) configuration is that of two identical touching spheres possessing distinct chemical surface activities, which is again amenable to analysis using a separable 3D orthogonal tangent-sphere coordinate system [31]. In contrast to the bi-spherical (BS) system, the tangent-sphere (TS) curvilinear system admits a more direct and compact integral formulation (as compared to infinite summation in BS) and was found useful in obtaining explicit solutions for some related electrostatic problems [32].…”

“…The structure of the paper is as follows: The problem formulation is presented in the Materials and Methods under Section 2.1 for a general free catalytic Janus dimer in the limit of a small Péclet number and a thin interaction layer [8], by employing the integral tangent-sphere formulation [32]. The solute concentration is shown to be governed by the Laplace Equation and by a mixed (Robin-type) boundary condition applied on the dimer's surface.…”