Electroosmosis over non-uniformly charged surfaces: modified Smoluchowski slip velocity for second-order fluids

Abstract

In the present paper we focus on deriving the modified Smoluchowski slip velocity of second-order fluids, for electroosmotic flows over plane surfaces with arbitrary non-uniform surface potential in the presence of thin electric double layers (EDLs). We employ matched asymptotic expansion to stretch the electric double layer and subsequently apply regular asymptotic expansions taking the Deborah number ($De$) as the gauge function. Modified slip velocities correct up to $O(De^{2})$ are presented. Two sample cases are considered to demonstrate the effects of viscoelasticity on slip velocity: (i) an axially periodic patterned potential and (ii) a step-change-like variation in the surface potential. The central result of our analysis is that, unlike Newtonian fluids, the electroosmotic slip velocity for second-order fluids does not, in general, align with the direction of the applied external electric field. Proceeding further forward, we show that the slip velocity in a given direction may, in fact, depend on the applied electric field strength in a mutually orthogonal direction, considering three dimensionality of the flow structure. In addition, we demonstrate that the modified slip velocity is not proportional to the zeta potential, as in the cases of Newtonian fluids; rather it depends strongly on the gradients of the interfacial potential as well. Our results are likely to have potential implications so far as the design of charge modulated microfluidic devices transporting rheologically complex fluids is concerned, such as for mixing and bio-reactive system analysis in lab-on-a-chip-based micro-total-analysis systems handling bio-fluids.

Electrokinetically enhanced cross-stream particle migration in viscoelastic flows

“…For low zeta potentials (ζ * p ∼ 25 mV), the slip at the particle surface can be represented by Smoluchowski's relation (Keh & Anderson 1985;Anderson 1989). Recently, Ghosh, Chaudhury & Chakraborty (2016) showed that the surface slip in the SOF does not get modified for a surface with constant zeta potential. Hence we employ the Smoluchowski slip in this work.…”

Electrophoretic motion of a non-uniformly charged particle in a viscoelastic medium in thin electrical double layer limit

“…The transport processes are governed by the Poisson–Nernst–Planck–Cauchy momentum equations (Saville 1977; Ghosh et al. 2016), along with the continuity equation for conservation of mass and the Oldroyd-B constitutive equations. Since these equations are well established, we directly start with their dimensionless forms, wherein the non-dimensional version of the any variable is expressed as .…”

“…In many instances, electrophoretic motion occurs in complex media (Ramautar, Demirci & de Jong 2006), such as bio-fluids (Babnigg & Giometti 2004; Kremser, Blaas & Kenndler 2004), polymeric solutions (Li & Koch 2020; Barron, Sunada & Blanch 1995) etc., whose constitutive behaviours show strong deviations from the Newtonian paradigm. These facets have been progressively becoming important in recent times (Berli 2010; Bandopadhyay & Chakraborty 2012 b ; Bandopadhyay, Ghosh & Chakraborty 2013; Zhao & Yang 2013; Ghosh & Chakraborty 2015; Ghosh, Chaudhury & Chakraborty 2016), because of their key roles in medical diagnostics (Madou et al. 2001; Groisman, Enzelberger & Quake 2003), particle focusing (Lu et al.…”

“…1987; Ghosh et al. 2016). On the other hand, viscoelastic constitutive models, such as the retarded motion relations (Chan & Leal 1979) as well as the differential constitutive relations (Bird et al.…”

Temperature-gradient-induced massive augmentation of solute dispersion in viscoelastic micro-flows

“…Some recent studies have demonstrated that the constitutive behaviour of these biological fluids has close resemblance to the rheology of viscoelastic fluids, and therefore the inclusion of fluid rheology and viscoelasticity in dispersion characteristics has attracted significant attention lately (Brust et al 2013;Arcos et al 2018;Hoshyargar et al 2018;Mukherjee et al 2019). While considering the thermally induced electrokinetic flow of viscoelastic fluids, an additional source of nonlinearity crops up as mediated by the constitutive behaviour of the fluid (Afonso, Alves & Pinho 2009;Coelho, Alves & Pinho 2012;Afonso, Alves & Pinho 2013;Ferrás et al 2016;Ghosh, Chaudhury & Chakraborty 2016;Mukherjee et al 2017a,b). Moreover, the degree of viscoelasticity, which is determined using physical properties like fluid viscosity and relaxation time, is a strong function of the prevalent thermal gradient, augmenting the complexity of the problem to a large extent (Bautista et al 2013;Mukherjee et al 2019).…”