Analytical Prediction of Flow Field in Magnetohydrodynamic-Based Microfluidic Devices

Abstract

A new approximate solution for the velocity profile of steady incompressible magnetohydrodynamic (MHD) flows in a rectangular microchannel driven by the Lorentz force is proposed. Mean velocity and mass flow rate in a channel, subsequently derived, can be used efficiently for many MHD-based microfluidic applications, including the design of a MHD-based microfluidic network without resorting to costly full-scale computational fluid dynamics. The closed-form solutions, provided for both direct-current (dc) and alternating-current (ac) electric and magnetic fields, are in simple forms, without any series or functions to evaluate, and so can be readily used for inverse or control problems associated with MHD-based lab-on-a-chip (LOC) devices. Extensive comparisons with previous analytical, computational, and experimental results are performed, and summarized in the present study. The proposed solutions are shown to agree better with existing experimental and computational reports than previous approximations and are to be used in a broad range of MHD-based LOC applications with both dc and ac fields with required accuracy.

Ultrasensitive detection of mercury (II) ions using electrochemical surface plasmon resonance with magnetohydrodynamic convection

“…The induced MHD convection plays a significant role in the electrochemical system even though the dimensions of the electrochemical cell are quite small [63][64][65]71]. Since the MHD convection increases with the increase in the strength of the magnetic field [62,72], one expects that the MHD convection effects increase in importance as the strength of the magnetic field increases.…”

“…Mechanical stirring, however, may be inefficient and inappropriate in the analysis of small-volume samples, such as those in a microscale electrochemical cell. MHD convection can induce extremely fine mixing [55][56][57][58][59][60][61][62], and is nonintrusive, obviating the need to insert any moving part into the electrochemical cell. The fluid motion is generated by the Lorenz force, induced by the interaction of an external magnetic field and the electric current in the cell.…”

Lattice Boltzmann simulation of thermofluidic transport phenomena in a DC magnetohydrodynamic (MHD) micropump

“…The magnetic field can be generated by either a permanent magnet or an electromagnet. It should be mentioned that the uniform flux density assumption is an appropriate approximation when the size of the magnet is much larger than that of the microfluidic device (Kabbani et al 2008). The magnetic field interacts with the electric field to produce the electromagnetic Lorentz force σE Z B x along the y direction that drives the flow.…”

“…In a subsequent effort, Abdullah and Duwairi (2008) studied the effect of fluctuating Lorentz force on the AC MHD micropump with the same numerical technique. Recently, Kabbani et al (2008) proposed an approximate analytical model for the steady incompressible MHD flows in a rectangular microchannel driven by the Lorentz force.…”

Transient rotating electromagnetohydrodynamic micropumps between two infinite microparallel plates

“…Ho (2007) obtained analytical solution of MHD micropump in rectangular ducts and compared the analytical results of flow rate and average flow velocity with those of experiments. Kabbani et al (2008) proposed the closed-form solutions of flow field in a rectangular MHD micropump under both DC and AC electric and magnetic fields. Recently, Moghaddam (2012) reported an unsteady analytical solution for both DC and AC MHD micropump in a circular microchannel.…”