Electro-osmosis of superimposed fluids in the presence of modulated charged surfaces in narrow confinements

Abstract

In the present study, we attempt to analyse the electro-osmotic flow of two superimposed fluids through narrow confinements in the presence of axially modulated surface charges. We attempt to solve for the flow structure as well as the interface deformation by both analytical and numerical techniques. Approximate analytical solutions are obtained through asymptotic analysis for low deformations, whereas numerical solutions are obtained by applying the phase field formalism; the numerical solutions are obtained for small as well as large interfacial deformations. The analytical solutions are derived only for the transient deformation of the interface, neglecting the transience in the flow, i.e. the flow is assumed to be quasisteady. The numerical solutions, however, are derived including the effects of inertia and transients in the flow. We attempt to compare our analytical and numerical results and explore the effects of several physico-chemical parameters on the deformation of the interface as well as the nature of the flow. Our analysis reveals that parameters such as the modulation wavelength, surface tension (described through the capillary number), viscosity ratio, permittivity ratio and extent of asymmetry in the potential on the two walls are the major contributors to the deformation and the resulting flow features.

Electroosmotic transport of immiscible binary system with a layer of non‐conducting fluid under interfacial slip: The role applied pressure gradient

“…Contrarily, an apparent interfacial slip may be inherent to the microfluidic or nanofluidic transport, as attributable to the formation of nanobubble layer arising due to complex hydrophobic interactions [22][23][24][25][26]. However, till date, electroosmotic effects have primarily been considered for analyzing the underlying transport of immiscible binary system either having conducting fluid pair [27][28][29][30][31][32] or configured with conducting and nonconducting fluid pair over interfacial scales [1,3,18]. On the contrary, employment of combined effects of electroosmosis and applied pressure gradient for modulating two fluid layers transport in a narrow fluidic pathways having one nonconducting fluid could be an interesting proposition, largely attributed to the intriguing interplay of various forces involved, as well as to its huge practical relevance [1,15].…”

Electrohydrodynamic interaction between droplet pairs in a confined shear flow

“…In the present analysis, we have used phase field formalism (Jacqmin, 1999;Badalassi, Ceniceros and Banerjee, 2003;Mandal, Ghosh and Bandopadhyay, 2017) for assessing the essential dynamics of two fluid system. Several researchers (Wang, Qian and Sheng, 2008;Chaudhury, Mandal and Chakraborty, 2016;Mandal, Ghosh and Bandopadhyay, 2017) have reported this formalism in their studies and mentioned that it is fit for handling the diffuse interface of a binary fluid system with good accuracy. This approach involves a phase field variable φ for determining the distribution of the constituting fluid element, which varies from -1 in one phase to 1 in the other phase.…”

Electroosmotic Pumping Between Two Immiscible Electrical Conducting Fluids Controlled by Interfacial Phenomena

“…In this context, the very small pressure difference that arose from surface tension and curvature was ignored (Middleman 1995). This is a restrictive assumption, however, we assume that the interface remains stable because the capillary number, is very small, i.e., Ca = εE0ψc/γT << 1 (Mandal et al 2015); for instance, typical values of the physical parameters used in this study take the following values: the dielectric permittivity is ε ∼ 7 × 10 -10 C V -1 m -1 , the external electric field E0 ∼ 10 4 V m−1, the thermal voltage or characteristic electric potential in the EDL, defined latter, ψc ≤ 25 m V, and the surface tension between both fluids γT ∼ 10 -3 N m -1 . With these values, the capillary number is estimated as Ca ∼ 10 -4 .…”