Transient membrane kinematic model for viscoplastic fluids: periodic contraction in the microchannel
Department of Mathematics, National Institute of Technology Uttarakhand, 246174, Srinagar, India
2 Department of Mathematics, GITAM Deemed to be University, 502329, Hyderabad, India
Accepted: 9 August 2022
Published online: 5 September 2022
A linear viscoplastic fluid model is considered to analyze the viscoplastic effects in membrane-based pumping flow through the microchannel in mathematical framework. The pressure is generated by the time-dependent wall deformation due to membrane motion. This selective wall compression (expansion) approach drives fluid to unidirectional. The motivation behind this mathematical analysis is to derive the flow visualization of the concentrated and chemical composite (viscoplastic) fluid in the microchannel. The creeping nature of flow analysis in an inelastic microchannel has been modeled using lubrication theory and the long-wavelength approximation. The analytical solutions of dimensionless boundary value problem are obtained to derive the closed-form solutions. The computational results have shown the rheological effects on flow analysis and pumping characteristics. The streamlines of the velocity vector help to understand the flow visualization of viscoplastic fluid. It is observed that the pressure distribution for the viscoplastic fluid is extremely high which is 30.7% more as compared to Newtonian fluid. The magnitude of the volumetric flow rate is reduced by 18.5% as the width of plug flow region is increased from 0 to 0.05.
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