Enhancement in the dynamic response of a viscoelastic fluid flowing in a tube

Abstract

In order to gain insight into the effects of elasticity on the dynamics of fluids in porous media, we have analyzed the flow of a Maxwell fluid in a tube. The entire problem is transformed to the frequency domain through a time Fourier transform and this allows for the derivation of a dynamic generalization of Darcy's law. Analytical results are provided showing a dramatic enhancement at certain frequencies. We present a parametric analysis of the dissipative and elastic behavior of the system, and we obtain an analytic expression for the maximum value of the permeability and the frequency at which this maximum occurs in terms of the physical properties of the fluid and the radius of the tube. With these results, we show that the human pulse occurs at a frequency that produces a permeability in the neighborhood of the maximum permeability.