Transient Membrane Kinematic Model for Viscoplastic Fluids: Periodic Contraction in the Microchannel

A coupled model of viscoplastic fluid and membrane contraction mechanism is presented mathematically. The time-dependent wall deformation due to membrane motion through the microchannel is retained in the analysis. Further, we examined the rheological effects on flow analysis, pressure distribution, wall shear stress, and discuss their importance for the physiological transport phenomena. In the membrane pumping mechanism, the expansion and compression phases are used for the micropump actuator simulation. Propagation of membrane as a motion of actuation is embedded in the middle of the microchannel. With the creeping nature of physical transport, a lubrication approach has been used. An analytical approach is adopted to derive the closed-form solutions. Numerical results indicate that the flow characteristics and pumping characteristics are significantly affected by the plasticity of the fluids and membrane shape. Such results provide the initial idea for designing the novel micro-valveless pumping actuator to control the microscale transport phenomena of physiological systems.