The Effects Of Wall Roughness On Magnetohydrodynamic And Electroosmotic Flows Between Two Micro-Parallel Plates

With the development of micro total ananysis system (μTAS) and micro electro mechanical system (MEMS), microfluid actuation and manipulation techniques have gained considerable attention. In microfluidic system, external electric and magnetic fields are often used to propel and manipulate electrically conducting fluids (electrolyte solution or liquid metal) in micchannel. The flow generated by the external electric and magnetic fields is termed electromagnetically driven flow or magnetohydrodynamic (MHD) flow. The advantage of MHD flow is that it have high flow rate at relatively small electrode potential and an excellent biocompatibility. Since the end of the 20th century, many researches in domestic and overseas studied theoretically and experimentally HMD flows, and obtained many important results. MHD flow has many applications in biology, medicine and chemistry. However, the effects of wall roughness on MHD flow were not taken into account. Fabrication process or the adsorption of other species such as macromolecule can cause wall roughness. Additionally, surface roughness can be designed artificially to promote mixing in microchannels. The relative wall roughness (the ratio of roughness height to channel height) in microchannel is much larger than that in macrochannel. Therefore, the velocity perturbation due to wall roughness can reach the main flow region, and further affects the whole microflow. In addition, wall slip can occur when a fluid flows. The wall slip velocity is proportional to the shear rate acting on the fluid: uslip=uslip-uwall=b|αu/αy|wall. The slip length b is the order of micrometer. Hence, the wall slip phenomenon can be neglected in macrochannel, but have significient influence on the flow in microchannel. Hence, wall slip is one of important factors which should be considered.Based on the above discussion, the effects of wall roughness and slip on MHD flow are studied in this paper using perturbation method:(1) The effects of wall roughness on DC MHD flow between two microparallel plates with longitudinally sinusoidal wall roughness.The longitudinal wall roughness indicates that the flow is parallel to the corrugation grooves. In the microchannel with longitudinally sinusoidal wall roughness, the channel section perpendicular to the flow direction does not change along the flow direction. In this paper, approximate analytical solutions for the velocity and flow rate of the DC MHD flow through the microchannel with longitudinally sinusoidal wall roughness are obtained using perturbation method. Our results show that the effect of wall roughness on the flow decreases with increase in Hartmann number. The phase difference of two walls becomes immaterial when Hartmann number or the wavenumber is large enough. The decreasing effect of wall roughness on the flow increases with increase in the wavenumber. When the wavenumber is smaller than the threshold wavenumber and the phase difference between the two walls equals π, the wall roughness can enhance the mean velocity of DC MHD flow.(2) The effects of wall roughness on DC MHD flow between two microparallel plates with transeversely sinusoidal wall roughness.The transverse wall roughness indicates that the flow is perpendicular to the corrugation grooves. In the microchannel with transversely sinusoidal wall roughness, the channel section perpendicular to the flow direction changes along the flow direction. Approximate analytical solution of the streamfunction of the DC MHD flow through the microchannel with transversely sinusoidal wall roughness is obtained using perturbation method, and further a relation between flow rate and roughness is obtained. Our results show that the flow rate always decreases due to the wall roughness irrespective of the phase difference. The flow resistance increases with increases in the wavenumber, the phase difference between the two walls,and decreases with increase in Hartmann number. The effect of the phase difference on the flow is ignorable if the wavenumber is large enough.(3) The effects of wall roughness and slip on AC MHD flow between two microparallel plates with longitudinally sinusoidal wall roughness.Approximate analytical solutions of the velocity and electric potential distributions of an AC MHD slip flow through the microchannel with longitudinally sinusoidal wall roughness are obtained using perturbation method, and further a relation between complex velocity amplitude and roughness is obtained. Our results show that the velocity and electric potential distributions are obviously disturbed by the wall roughness. A phase lag between the velocity and the electric potential is found. The phase lag increases with increases in the frequency and the slip length, and decreases with increases in Hartmann number, the wavenumber and the phase difference of the wall corrugations. But, the phase lag is almost nonexistent when the frequency is large enough, and is not influenced by the phase difference of the wall corrugations when the weavenumber is large enough. The velocity amplitude increases with the slip length and decreases with the frequency, the wavenumber and the phase difference.However, the velocity amplitude is not influenced by the phase difference when the wavenumber is sufficiently large and is not also influenced by the slip length when the frequency is sufficiently large.Also, a combined electromagnetohydrodynamic flow through the microchannel with longitudinally sinusoidal wall roughness and a pure EOF through a microchannel with three-dimensional wall roughness are studied in this paper. Approximate analytical solutions for velocity, electric potential and flow rate are obtained using perturbation method. The effects of the wavenumber, zeta potential, Hartmann number and the normalized reciprocal thickness of the electric double layer on the flow are analyzed. The results obtained in the present paper can provide a foundational basis for the design, optimization and development of the microfluidic devices.