Pulsatile flow of a chemically-reacting non-linear fluid

Abstract

Many complex biological systems, such as blood and polymeric materials, can be approximated as single constituent homogeneous fluids whose properties can change because of the chemical reactions that take place. For instance, the viscosity of such fluids could change because of the chemical reactions and the flow. Here, I investigate the pulsatile flow of a chemically-reacting fluid whose viscosity depends on the concentration of a species (constituent) that is governed by a convection-reaction-diffusion equation and the velocity gradient, which can thicken or thin the fluid. I study the competition between the chemical reaction and the kinematics in determining the response of the fluid. The solutions to the equations governing the steady flow of a chemicallyreacting, shear-thinning fluid are obtained analytically. The solution for the velocity exhibits a parabolic-type profile reminiscent of the Newtonian fluid profile, if the fluids are subject to the same boundary conditions. The full equations associated with the fluid undergoing a pulsatile flow are studied numerically. A comparison of the shear-thinning/chemical-thinning fluid to the shear-thinning/chemicalthickening fluid using a new non-dimensional parameter–the competition number (CN) shows that both the shear-thinning effects and the chemical-thinning/thickening effects play a vital role in determining the response of the fluid. For the parameter values chosen, the effects of chemical-thinning/thickening dominate the majority of the domain, while the effects due to shear-thinning are dominant only in a small region near the boundary.