Frequency response in surface-potential driven electro-hydrodynamics

TL;DR

This paper provides a Fourier-based solution for calculating slip velocity in electro-hydrodynamics with surface potential modulation, revealing resonance behavior and frequency-dependent power laws influenced by surface potential symmetry.

Contribution

It introduces a general Fourier approach to analyze frequency response in surface-potential driven electro-hydrodynamics, highlighting resonance phenomena and asymptotic power laws.

Findings

Resonance occurs at the inverse RC time of the system.

Surface potential symmetry affects the power law exponent below resonance.

Different potential shapes exhibit similar slip velocities but differ in asymptotic frequency response.

Abstract

Using a Fourier approach we offer a general solution to calculations of slip velocity within the circuit description of the electro-hydrodynamics in a binary electrolyte confined by a plane surface with a modulated surface potential. We consider the case with a spatially constant intrinsic surface capacitance where the net flow rate is in general zero while harmonic rolls as well as time-averaged vortex-like components may exist depending on the spatial symmetry and extension of the surface potential. In general the system displays a resonance behavior at a frequency corresponding to the inverse RC time of the system. Different surface potentials share the common feature that the resonance frequency is inversely proportional to the characteristic length scale of the surface potential. For the asymptotic frequency dependence above resonance we find a 1/omega^2 power law for surface potentials with either an even or an odd symmetry. Below resonance we also find a power law omega^alpha with alpha being positive and dependent of the properties of the surface potential. Comparing a tanh potential and a sech potential we qualitatively find the same slip velocity, but for the below-resonance frequency response the two potentials display different power law asymptotics with alpha=1 and alpha~2, respectively.