Streaming-potential phenomena in the thin-Debye-layer limit. Part 3. Shear-induced electroviscous repulsion

Abstract

We employ the moderate-Péclet-number macroscale model developed in part 2 of this sequence (Schnitzer, Frankel & Yariv, J. Fluid Mech., vol. 704, 2012, pp. 109-136) towards the calculation of electroviscous forces on charged solid particles, engendered by an imposed relative motion between these particles and the electrolyte solution in which they are suspended. In particular, we are interested in the kinematic irreversibility of these forces, stemming from the diffusio-osmotic slip which accompanies the salt-concentration polarisation induced by that imposed motion. We illustrate the electroviscous irreversibility using two prototypic problems, one involving side-by-side sedimentation of two spherical particles, and the other involving a force-free spherical particle suspended in the vicinity of a planar wall and exposed to a simple shear flow. We focus upon the pertinent limit of near-contact configurations, where use of lubrication approximations provides closedform expressions for the leading-order lateral repulsion. In this approximation scheme the need to solve the advection-diffusion equation governing the salt-concentration polarisation is circumvented.

Inertial migration of an electrophoretic rigid sphere in a two-dimensional Poiseuille flow

“…However, in the aforementioned regime, the streaming potential may generate when the particle is very near the walls. This modifies the electrokinetic slip, and the associated Newtonian stresses result in a lateral 'electro-viscous force' (Bike & Prieve 1995;Schnitzer & Yariv 2016). In this work, we neglect the electro-viscous force and focus on the migration in the bulk of the channel.…”

Hybridization-based DNA biosensing with a limit of detection of 4 fM in 30 s using an electrohydrodynamic concentration module fabricated by grayscale lithography

“…In ref. 43 , we suggested an extrapolation for the force profile, considering that additional repulsive forces, including electrostatic and/or shear-induced electroviscous forces 44 and/or lubrication 45 forces, balance the viscoelastic transverse force. The resulting effective force vanishes toward the wall, and may be approximated by a linear drop, following the expression:…”

Electrokinetic oscillatory flow and energy conversion of viscoelastic fluids in microchannels: a linear analysis

“…Since it is difficult to analytically solve the full set of electrokinetic equations, three main approximation methodologies have been developed over the years, which are appropriate for low surface electric potential, weak field or flow and thin double layers, respectively. For example, the thin-double-layer limit was employed by Yariv, Schnitzer & Frankel (2011), Schnitzer, Frankel & Yariv (2012) and Schnitzer & Yariv (2016) to investigate streaming potential phenomena. However, this approximation cannot be applied to nanochannels where the EDL thickness is comparable to the size of the channel.…”