We analyzed the effects of elasticity on the dynamics of fluids in porous media by studying the flow of a Maxwell fluid in a tube, which oscillates longitudinally and is subject to an oscillatory pressure gradient. The present study investigates novelties brought about in the classic Biot theory of propagation of elastic waves in a fluid-saturated porous solid by inclusion of non-Newtonian effects that are important, for example, for hydrocarbons. Using the time Fourier transform and transforming the problem into the frequency domain, we calculated (a) the dynamic permeability, and (b) the function $F\left(\kappa \right)$ that measures the deviation from Poiseuille flow friction as a function of frequency parameter $\kappa .$ This provides a more complete theory of the flow of Maxwell fluid through a longitudinally oscillating cylindrical tube with an oscillating pressure gradient, which has important practical applications. This study clearly shows the transition from a dissipative regime to an elastic regime in which sharp enhancements (resonances) of the flow are found.

• Received 9 October 2000

DOI:https://doi.org/10.1103/PhysRevE.63.046304