InterPore2025

Swelling Porous Media – The Effect of Swelling Pressure on Modeling Flow and Wave Propagation

22 May 2025, 09:20

15m

Oral Presentation (MS04) Swelling and shrinking porous media MS04

Speaker

Lynn Schreyer (Washington State University)

Description

The ability of a saturated swelling porous medium to swell can be measured using a reverse osmotic swelling experiment [3]. This experiment demonstrates that the liquid pressure inside a swelling porous medium (termed vicinal fluid) is different from that of fluid outside the porous medium in equilibrium with it (termed bulk fluid), and this in turn affects the flow of fluid and the speed of pressure waves. Here we use hybrid mixture theory to show how swelling pressure affects flow and swelling [1,5], and how it also affects the speed of pressure waves (Biot wave equations [2]), typically used to determine material properties. For flow, the classical Darcy’s law incorporates additional terms involving the gradient of porosity [1], and we illustrate an application by modeling a swelling polymer used for drug delivery such as Aleve [5]. For wave propagation the speed is modified by the swelling pressure and its significance is determined by the ratio of the swelling pressure and the P-wave modulus. Thus for soft swelling materials, the pressure wave speeds are significantly impacted, influencing e.g. the measurement of material parameters using pressure wave speeds [4].

1. Bennethum, L.S., Cushman, J.H.: Multicomponent, Multiphase Thermodynamics of Swelling Porous Media with Electroquasistatics: II. Constitutive Theory. Transport in Porous Media 47, 337- 362 (2002)

2. Biot, M.A.: Theory of Propagation of Elastic Waves in a Fluid-Saturated Porous Solid I. Low Frequency Range. The Journal of the Acoustical Society of America, 28, 168-178 (1956)

3. Low, P.F.: The Swelling of Clay: II. Montmorillonites. Soil Science Society of America Journal, 44, 667-676 (1980)

4. Whitehead, R.J., Modeling Mechanical Behavior in Swelling Porous Media, Washington State University, PhD Thesis, Ryan J. Whitehead (2024): Chapter 4.

5. Wojciechowski, K.J., Chen J., Schreyer-Bennethum, L., and K. Sandberg: Well-posedness and Numerical Solution of a Nonlinear Volterra Partial Integro-Differential Equation Modling a Swelling Porous Material, Journal of Porous Media, 17, 763-784 (2014)