A porous medium is a solid structure that is permeated with a connected network of fluid-filled pores. In stiff porous media such as rock, wood, or bone, this solid structure is only weakly responsive to the flow; in soft porous media, in contrast, this solid structure is highly responsive to the flow. Soft porous media are ubiquitous in nature, industry, and everyday life, including granular materials such as sand and mud, fibrous materials such as paper and cloth, and biomaterials such as cartilage and brain tissue. In these materials, the motion of the internal fluid(s) is central to processes such as wetting and drying, processing and cleaning, and the transport of nutrients. Our ability to understand and work with these systems from a scientific, engineering, or medical perspective -- such as estimating methane emissions from seabed sediments, processing pulp into paper, or treating disease -- relies on the ability to make quantitative predictions about flow and the transport of dissolved substances (solutes) in these systems. For stiff porous media, a variety of mathematical models are available that enable reasonable predictions. Soft porous media are much less well understood; existing models can predict, for example, the compression of a woven filter as liquid is pumped through it, or the rate at which sediment will consolidate over time due to gravity. However, we have no clear framework for predicting the impact of filter compression on the transport and mixing of solutes, which controls the filtration efficiency, or for the impact of sediment consolidation on the motion of gas bubbles, which controls the venting of gas to the surrounding environment. The central goal of this project was to fill these gaps in our understanding -- and in our predictive capabilities -- by making high-resolution experimental observations to inform a set of new mathematical models for flow and transport in soft porous media. Specifically, we studied the impact of deforming pore structure on the transport and mixing of solutes (eg, the motion of dissolved minerals or nutrients) and on the interactions between two different fluid phases (eg, gas bubbles in wet sediment). We produced first-of-kind datasets on deformation-driven solute spreading; compression-driven fluid-fluid displacement; and gas invasion into soft, liquid-saturated granular media. We developed a new modelling framework for the growth and collapse of gas bubbles in soft porous media. Our work provides new physical insight into these complex processes and has kindled new research interest in these topics across a diverse community of scientists and engineers.
