Electroosmotic flow of a power-law fluid through an asymmetrical slit microchannel with gradually varying wall shape and wall potential

Abstract

h i g h l i g h t s• Non-parallel electroosmotic flow of power-law fluid in a microchannel.• Lubrication theory for slowly varying channel height and wall potential.• Linear superposition of forces invalidated by asymmetry of channel.• Nonlinear interaction between wall undulation and wall charge modulation.• Flow-rate sensitive to phase shift of wall patterns and power-law index. g r a p h i c a l a b s t r a c t a b s t r a c tThis study aims to investigate electroosmotic flow of a power-law fluid through a slit channel with walls asymmetrically patterned with periodic variations in shape and zeta potential. On taking into account the near-wall depletion layer, the present problem is simplified on the basis of the lubrication approximation, and through the use of the Helmholtz-Smoluchowski slip boundary condition. Nonlinear equations are to be solved for two unknown functions of axial dependence, one being the induced pressure gradient, and another being an undetermined stress component. An efficient numerical scheme is devised in this work to solve the nonlinear problem. Results are generated to check whether the principle of linear superposition of forces, for electrokinetic flow of a non-Newtonian fluid in the presence of a Newtonian depletion layer, is still applicable to flow in an asymmetric channel. It is also found that phase shifts between the geometrical and electric potential patterns on the two walls may lead to qualitatively disparate effects, depending on the power-law behavior index of the fluid and the applied pressure gradient.

Viscoelastic Effects on Dispersion due to Electroosmotic Flow with Variable Zeta Potential

“…Similar results with high zeta potentials in the walls of the micro-channel are found in [2]. The analysis of the electrokinetic flow of a power-law fluid through a slit channel with gradually varying wall potential and channel height was reported in [3,4]. They found that the interaction between the wall undulation and the wall potential modulation, under the combined action of hydrodynamic and electric forces, may give rise to a rich set of nonlinear behaviors for flow of a non-Newtonian fluid in the channel.…”

Electroosmotic flow of a power-law fluid in a slit microchannel with gradually varying channel height and wall potential

“…The pressure as a function of the axial coordinate, which is internally induced so as to maintain a constant flow rate through a channel with axial non-uniformities, has to be found numerically owing to the nonlinear interaction between the hydrodynamic and electric forcings for a non-Newtonian fluid. This distinguishes the present study from previous studies by the authors [26,27], which also look into EO flow of power-law fluid in a non-uniform channel, but are simplified by the use of the Newtonian Helmholtz-Smoluchowski slip boundary condition on taking into account a near-wall Newtonian depletion layer.…”

“…Thanks to the conditionκ 1, Eqs. (26) and (27) should admit only one real root, thereby avoiding ambiguity in solving these equations forP x .…”

Rotating electroosmotic flow of viscoplastic material between two parallel plates

“…Denoting the axial and transverse velocity components byû us andv us , we may get the stress components in the unsheared region by integrating Eqs. (17) and (18):…”

“…The increasing need to understand the behaviors of complex fluids (e.g., blood, DNA solutions, colloidal and cell suspensions) in microfluidic analysis has spurred many researchers to study EO flow of non-Newtonian fluids through microchannels in recent years. These studies include, among others, Das and Chakraborty [3], Zimmerman et al [4], Zhao et al [5], Olivares et al [6], Zhao and Yang [7,8], Babaie et al [9], Vakili et al [10], Ng [11], Ng and Qi [12,13], Dhar et al [14], Zhu et al [15], and Qi and Ng [16,17]. A variety of models, such as power-law, Carreau and viscoplastic models, have been used by these authors to describe the non-Newtonian rheology of the material under investigation.…”