Abstract
In this paper, the effects of asymmetrically modulated charged surfaces on streaming potential, velocity field and flow rate are investigated under the axial pressure gradient and vertical magnetic field. In a parallel-plate microchannel, modulated charged potentials on the walls are depicted by the cosine function. The flow of incompressible Newtonian fluid is two-dimensional due to the modulated charged surfaces. Considering the Debye–Hückel approximation, the Poisson–Boltzmann (PB) equation and the modified Navier-Stokes (N-S) equation are established. The analytical solutions of the potential and velocities (u and v) are obtained by means of the superposition principle and stream function. The unknown streaming potential is determined by the condition that the net ionic current is zero. Finally, the influences of pertinent dimensionless parameters (modulated potential parameters, Hartmann number and slip length) on the flow field, streaming potential, velocity field and flow rate are discussed graphically. During the flow process and under the impact of the charge-modulated potentials, the velocity profiles present an oscillating characteristic, and vortexes are generated. The results show that the charge-modulated potentials are beneficial for the enhancement of the streaming potential, velocity and flow rate, which also facilitate the mixing of fluids. Meanwhile, the flow rate can be controlled through the use of a low-amplitude magnetic field.
Highlights
Ding and Jian [32] studied the flow of viscoelastic fluid under an oscillating pressure gradient and concluded the resonances that are generated for the streaming potential field and for the flow rate
Based on the above analysis of the advancements that have been achieved in fluid mechanics, this paper studies the streaming potential and velocity field through a microchannel under the condition that the potentials on the walls are modulated, and the pressure gradient and magnetic field are applied
Where up is the characteristic velocity of the fluid flow driven by pressure, ur is the characteristic velocity of the electric flow, δ is the nondimensional slip length, P0 is the characteristic pressure, Ha is the Hartmann number, E0 is the characteristic scale of the electric field
Summary
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. Micromachines 2022, 13, 66 of vertical ion concentration In this sense, the modulated charged potentials will be considered in this study. Bandopadhyay and Mandalb et al [29] studied the flow of two immiscible fluids under pressure drive They analyzed the influence of changing the net conductivity on the concomitant streaming potential. Ding and Jian [32] studied the flow of viscoelastic fluid under an oscillating pressure gradient and concluded the resonances that are generated for the streaming potential field and for the flow rate. Based on the above analysis of the advancements that have been achieved in fluid mechanics, this paper studies the streaming potential and velocity field through a microchannel under the condition that the potentials on the walls are modulated, and the pressure gradient and magnetic field are applied. The influences of the related parameters on the flow field, streaming potential, velocity field and flow rate are discussed in the form of graphs
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