  We analyzed effects of elasticity on the dynamics of fluids in porous media
by studying a flow of a Maxwell fluid in a tube, which oscillates
longitudinally and is subject to oscillatory pressure gradient. The present
study investigates novelties brought about into the classic Biot's 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
$F(\kappa)$ that measures the deviation from Poiseuille flow friction as a
function of frequency parameter $\kappa$. This provides a more complete theory
of flow of Maxwell fluid through the longitudinally oscillating cylindrical
tube with the oscillating pressure gradient, which has important practical
applications. This study has clearly shown transition from dissipative to
elastic regime in which sharp enhancements (resonances) of the flow are found.
