Imbibition dynamics under dissolution-driven fluid thickening
The imbibition of milk into a biscuit provides an example of a broader class of processes in which a liquid invades a porous material, dissolving components of the solid and thereby modifying its own rheology. This coupling between imbibition, dissolution, and evolving fluid rheology also occurs in food processing, filtration, and reactive porous media. While the resulting changes in fluid viscosity are known to affect imbibition, a quantitative description of how this evolving rheology determines the imbibition dynamics is still lacking. Here, we establish such a description for dissolution-driven fluid thickening. For a capillary tube in the well-mixed limit, we derive a generalized Washburn law showing that the evolving viscosity can be incorporated through a rescaled time given by the accumulated inverse viscosity. This predicts a collapse of the imbibition dynamics for different dissolution rates, which we confirm numerically using coupled free-surface and solute-transport simulations. When diffusion is slower, concentration and viscosity become spatially heterogeneous, resulting in a weaker retardation of the advancing liquid than predicted by the well-mixed theory. We then consider disordered porous media and quantify how dissolution-driven thickening and variations in pore geometry affect the dynamics. Our results extend the classical Washburn description to imbibition with evolving fluid properties and provide a quantitative basis for understanding fluid uptake when interactions with the solid progressively modify the rheology of the invading liquid.