Extension of Biot's theory to porous materials saturated by a non-Newtonian fluid
Résumé
The Biot model is the most comprehensive framework for describing acoustic wave propagation in porous media, as it accounts for wave propagation in both the solid matrix and the fluid phases. However, the classic Biot theory assumes that the saturating fluid is Newtonian, whereas many real world fluids, exhibit non-Newtonian behavior characterized by viscoelastic effects. This study explores the modifications introduced to Biot's classical theory when the saturating fluid is modeled as non Newtonian fluid (Maxwell fluid). Specifically, it examines the impact of viscoelasticity on the propagation of dilatational elastic waves by analyzing their phase velocities and attenuation coefficients as functions of frequency. The results, for cylindrical pores with circular cross section, show that replacing a Newtonian fluid with a Maxwell fluid leads to: (a) Increased phase velocities for both dilatational waves, particularly at high frequencies. (b) Decreased attenuation coefficients with rising frequency, especially at low Deborah numbers (De). (c) Oscillatory behavior in all physical quantities in the strongly non-Newtonian regime. These findings offer new insights into elastic wave propagation in fluid-saturated porous materials with viscoelastic fluids.
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