New simple analytical method for flow enhancement predictions of pulsatile flow of a structured fluid

Abstract

In this work, a new simplified method to find the fluidity enhancement of a non-Newtonian liquid under a pulsating (time-dependent) pressure gradient is analyzed. The fluidity enhancement is predicted by means of a Taylor series expansion of the flow rate in the vicinity of the applied wall stress. This expansion is shown to render the same results as several perturbation techniques used at length in the literature. Both new and the conventional perturbation methods are equivalent in their predictions of the fluidity enhancement. Even though the flow and rheology behavior are modeled using the Bautista-Manero-Puig constitutive equation, it is shown that the prediction of the fluidity enhancement does not depend on the constitutive model employed, but a condition of shear thinning behavior of the fluid is necessary for it. Flow enhancement is predicted using rheological data for blood since this fluid naturally flows under a pulsatile pressure gradient. The flow enhancement equation is found to have a similar form as the equation of the Rabinowitsch formalism in fully developed Poiseuille flow. This simplified technique will help in saving machine time for numerical predictions in computational blood flow simulations.