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Description:
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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 parameterâ  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 . |