Effect of patterned hydrodynamic slip on electromagnetohydrodynamic flow in parallel plate microchannel

doi:10.1088/1674-1056/abab71

Abstract

A fully developed electromagnetohydrodynamic (EMHD) flow through a microchannel with patterned hydrodynamic slippage on the channel wall is studied. The flow is driven by the Lorentz force which originates from the interaction between an externally imposed lateral electric field and a perpendicular magnetic field. The governing equations for the velocity with patterned slip boundary conditions are solved analytically by perturbation techniques under the assumption of small Reynolds number Re. In addition, the numerical solutions for the velocity are obtained by using the finite-difference method, and they are found to be in good agreement with the analytical solutions within admissible parameter range. The effects of different parameters on the velocity and volume flow rate due to patterned hydrodynamic slippage are discussed in detail, including wave-number K, Hartmann number Ha, amplitude δ of the patterned slip length, and normalized electric field strength S. The results show that patterned slippage over microchannel walls can induce transverse flows, which will increase the mixing rates in microfluidic devices. In addition, we also find that precise flow control can be achieved by controlling the magnetic flux and the wave-number and also by well choosing the electric field intensity. Our analysis can be used for designing the efficient micro-fluidic mixers.

Keywords: electromagnetohydrodynamic (EMHD) flow patterned slip wall

Received: 03 April 2020
Revised: 24 May 2020
Accepted manuscript online: 01 August 2020

Fund: the National Natural Science Foundation of China (Grant Nos. 11772162 and 11472140), the Natural Science Foundation of Inner Mongolia Autonomous Region, China (Grant Nos. 2016MS0106 and 2018MS01015), and the Inner Mongolia Grassland Talent, China (Grant No. 12000-12102013).

Corresponding Authors: ^†Corresponding author. E-mail: jianyj@imu.edu.cn

Cite this article:

Chun-Hong Yang(杨春红) and Yong-Jun Jian(菅永军) Effect of patterned hydrodynamic slip on electromagnetohydrodynamic flow in parallel plate microchannel 2020 Chin. Phys. B 29 114101

Fig. 1.

Schematic diagram of physical modeling.

Fig. 2.

Contours plots for dimensionless velocity variations of (a) axial velocity u₁, (b) vertical velocity v₁ with a cosine wave variation in slip length on wall at Re = 0.01, Ha = 1, S = 1, Ω = 0, δ = 0.1, and K = 1.

Fig. 3.

Comparison between analytical and numerical solutions for the first-order (a) axial velocity u₁ and (b) vertical velocity v₁ at three different values of wave-number K (x = 0.0628, Re = 0.01, Ha = 1, S = 1, Ω = 0, δ = 0.1).

Fig. 4.

First-order velocity distributions for different values of non-dimensional slip length δ at K = 1 (x = 0.0628, Re = 0.01, Ha = 1, S = 1, Ω = 0), sowing (a) axial velocity u₁ and (b) vertical velocity v₁ varying with y.

Fig. 5.

First-order velocity distributions for different values of Hartmann number Ha (x = 0.2096, Re = 0.01, S = 1, Ω = 0, K = 1, δ = 0.1, α = 0.01), showing (a) axial velocity u₁ and (b) vertical velocity v₁ versus y.

Fig. 6.

Variations of total axial velocity u = u₀ + α u₁ with y for different values of Hartmann number Ha and electric field strength S: [(a), (b)] S = 1 and (c) Ha = 0.1 at x = 0.2096, Re = 0.01, Ω = 0, K = 1, δ = 0.1, α = 0.01.

Fig. 7.

Variations of total axial volume flow rate with Ha for different values of slip length δ and electric field strength S: (a) S = 1 and (b) δ = 0.1 at x = 0.2096, Re = 0.01, Ω = 0, K = 1, and α = 0.01.

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Effect of patterned hydrodynamic slip on electromagnetohydrodynamic flow in parallel plate microchannel

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