Analysis of heat and mass transport in a complex PDMS-based porous medium

Effective thermal conductivity of flows in porous media is one of the most fundamental properties required for industrial applications such as combustion, heat exchange or enhanced novel oil recovery techniques. Its estimation is not an easy task since thermal dispersion must be considered accurately. In this study, we determine numerically the thermal dispersion of a fluid flow within a polydimethylsiloxane (PDMS) porous medium at different Reynolds and Péclet numbers. The geometry is created by casting the polymer onto a sugar cube replacing its crystalline structure in negative. A three-dimensional model is then reconstructed using microtomography images, enabling the characterization of the main geometric properties of the fluid and solid phases. Two configurations are tested: in the first one, temperature gradient is introduced along the longitudinal direction of the flow, while in the second, the gradient is perpendicular to the flow. The microscopic flow and temperature fields obtained for both cases are subsequently used to evaluate the effective thermal conductivity of the utilized porous medium, considering the physical solid (polymer) to fluid (water) phase conductivity ratio ($\lambda_s/\lambda_f$). The simulations examine velocity fields, pressure drop and shear rates along the PDMS sponge, comparing them to a Kelvin cell geometry with well-characterized properties and transport mechanisms. Additionally, we investigate the effect of compressing the pores of the PDMS sponge on its thermal properties, highlighting the influence of structural deformation on heat transfer. In the last part we investigate how these findings related to the heat transport can affect the mass transport, examining the influence of thermal effects on the mixing process of two miscible fluids within the PDMS structure. The study offers thus also insights into the interplay between thermal and mixing processes in complex porous media.