Interfacial Electric Effects on a Non-Isothermal Electroosmotic Flow in a Microcapillary Tube Filled by Two Immiscible Fluids

Abstract

In this work, a non-isothermal electroosmotic flow of two immiscible fluids within a uniform microcapillary is theoretically studied. It is considered that there is an annular layer of a non-Newtonian liquid, whose behavior follows the power-law model, adjacent to the inside wall of the capillary, which in turn surrounds an inner flow of a second conducting liquid that is driven by electroosmosis. The inner fluid flow exerts an interfacial force, dragging the annular fluid due to shear and Maxwell stresses at the interface between the two fluids. Because the Joule heating effect may be present in electroosmotic flow (EOF), temperature gradients can appear along the microcapillary, making the viscosity coefficients of both fluids and the electrical conductivity of the inner fluid temperature dependent. The above makes the variables of the flow field in both fluids, velocity, pressure, temperature and electric fields, coupled. An additional complexity of the mathematical model that describes the electroosmotic flow is the nonlinear character due to the rheological behavior of the surrounding fluid. Therefore, based on the lubrication theory approximation, the governing equations are nondimensionalized and simplified, and an asymptotic solution is determined using a regular perturbation technique by considering that the perturbation parameter is associated with changes in the viscosity by temperature effects. The principal results showed that the parameters that notably influence the flow field are the power-law index, an electrokinetic parameter (the ratio between the radius of the microchannel and the Debye length) and the competition between the consistency index of the non-Newtonian fluid and the viscosity of the conducting fluid. Additionally, the heat that is dissipated trough the external surface of the microchannel and the sensitivity of the viscosity to temperature changes play important roles, which modify the flow field.

Editorial for the Special Issue on Micro/Nano-Chip Electrokinetics, Volume II

“…Mei et al [ 9 ] studied the electroosmotic flow of a linear Phan–Thien–Tanner fluid in a nanoslit by solving numerically the nonlinear Poisson–Nernst–Planck equations. Matías et al [ 10 ] presented a perturbation analysis of Joule heating effects on electroosmotic flow in a microcapillary tube filled with immiscible Newtonian and power-law fluids. Lu et al [ 11 ] used a molecular dynamics simulation to study the electroosmotic flow in rough nanochannels, with particular attention to the fluid–solid interactions.…”

Start-Up Electroosmotic Flow of Multi-Layer Immiscible Maxwell Fluids in a Slit Microchannel

“…Therefore, for about two decades, the research to understand the physical mechanisms for moving parallel flows of immiscible fluids under electrokinetic effects has considered the transport of two layers [ 35 , 36 , 37 , 38 , 39 , 40 , 41 , 42 ] and three layers [ 43 ]. In these investigations, the arrangement of fluids considers that one fluid layer is non-conducting and the other(s) fluid(s) layer(s) if, being the electrolytic fluid(s) which is(are) under electroosmotic effects.…”

Transient analysis of combined electroosmotic and pressure driven flow with multi-layer immiscible fluids in a narrow capillary

“…Their study reports an analytical solution for the velocity profiles into a two-phase electroosmotic-viscous pump in a circular microchannel. About this theme, other investigations under electroosmotic effects to pumping a nonconducting fluid by viscous drag due to electroosmotic effects over a conducting liquid in cylindrical channels can be reviewed in the works conducted by Movahed et al [23], Moghadam [24] and Matías et al [25]; moreover, in parallel flat plates by Huang et al [26] and Afonso et al [27], and rectangular channels by Gao et al [28]; all of them in steadystate. Concerning the transient-state analysis of pumping of non-conducting liquids by viscous drag induced by electroosmotic effects, we can cite the investigation realized by Gao et al [29] in a rectangular channel.…”