Blood Flow in Multi-Sinusoidal Curved Passages with Biomimetic Rheology: An Application of Blood Pumping

The unsteady flow of biological liquid through non-uniform pumps under porosity impacts is considered. The Jeffrey fluid is used as blood in the current study, which is also characterized as viscoelastic fluid because of its dual characteristics: on the one hand, its viscosity in nature; on the other hand, its elastic effect. Rheological equations are framed in a curvilinear coordinates system, and porosity influences are simulated with the body force term in momentum equations. The flow system has been transformed from fixed to wave frame using a linear–mathematical transformation between these two frames. In the next mathematical steps, these transformed equations are given in non-dimensional form using physical variables. The system of PDE is reduced to an ODE under lubrication theory and long wavelength approximation. Solutions to reduced ordinary differential equations are obtained numerically in MATLAB software via a BVP4C scheme. The physical impacts of the involved parameters on flow features, such as curvature, porosity (Darcy’s number), non-uniformity, and viscoelastic parameters, have been visualized graphically. Multi-sinusoidal waves are used in the boundary wall of the curved pump for peristaltic pumping. The magnitude of velocity profile for a saw-tooth wave (trapezoidal wave) is larger (smaller) than all other natures of peristaltic waves. The larger intensity of Darcy’s number has a dynamic role in the reduction of peristaltic pumping, whereas the opposite behavior is noticed when increasing the non-uniform nature of a channel. A comparison between all multi-sinusoidal waves is also addressed. The results of the present research shall be very productive for the manufacture of peristaltic pumps for drug delivery and bio-medical systems.