Alteration in membrane-based pumping flow with rheological behaviour: A mathematical model

Blood is complex fluids exhibits the non-Newtonian characters and rheological properties of the blood vary person to person. Typically, the rheological properties of blood are very similar to Carreau fluids which is considered in the present model. The main objective of this study is to examine how a typical membrane-based pumping model will function with varying rheological properties (shear-thinning, Newtonian, and shear-thickening) of fluids.

A mathematical formulation is constructed for the membrane-based pumping model using the conservation principles of mass and momentum, and stress-strain relationship based on Carreau fluids model. Velocity slip condition is adopted for this model to discuss the possibility of fluids velocity at the wall surface. The perturbation method is employed to derive the series solution for the governing equations subjected to physical boundary conditions with suitable assumptions.

From numerical results, it is found that the pressure inside the microchannel reduces for the shear-thinning fluid and increases for the shear-thickening fluid with increasing the Weissenberg. In the membrane region, the chaos of the flow field is occurred due to the local pressure gradient by the rhythmic membrane propagation. It is further reported that shear-driven flow is responsible for the decrement in fluid velocity.

This model provides a framework for estimating the effects of rheological properties and velocity slip for membrane-based pumping model which help in designing the smart pumps for various needs in the fields of biomedical engineering and fluid industries.