DEFTPORE: Deformation controls flow and transport in soft porous media

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 is to fill these gaps in our understanding — and in our predictive capabilities — by using high-resolution experimental observations to inform a set of new mathematical models for flow and transport in soft porous media. The key output of the project will be a coherent, first-of-its-kind framework of experimental observations, mathematical models, and physical insights into these complex processes. Our work will also attract attention to this under-explored field, spurring interest from a diverse research community.

Research topics

  • Transport and mixing: We are working to understand how an imposed deformation — such as repeated squeezing — drives motion of solute. This problem is directly relevant to household experiences like cleaning dirty water from a kitchen sponge by squeezing it repeatedly, as well as to nutrient transport in cartilage. To develop a big-picture understanding of this problem, we are performing a thorough theoretical exploration of deformation-driven mixing and spreading using a continuum (Darcy-scale) mathematical model. To understand the small-scale details of this problem, we have been developing an experimental system for performing high-resolution measurements of solute motion due to repeated squeezing; we will soon begin an extensive experimental program. We have also been developing formal mathematical tools for linking the detailed, pore-scale motion of solute in a deforming pore structure with the resulting macroscopic transport and mixing, which will help us to connect our experimental observations with our modelling work.

  • Phase separation: The interactions of two fluids within a porous medium depend strongly on flow conditions, wettability, and the structure of the pore space. At the pore scale, these interactions are characterised by the formation of wetting films that coat solid surfaces and occupy corners and throats, and the formation of non-wetting blobs that occupy larger pore bodies. The invasion of non-wetting blobs into narrow throats is energetically unfavorable, but it can be forced with a sufficiently high pressure gradient. In a soft porous medium, where the pore structure can deform in response to the flow, the most striking feature of two-fluid-phase flow is the tendency of the non-wetting phase to enlarge the pore space by pushing the solid grains apart, to the point of forming macroscopic cavities in the medium. These cavities can be much larger than the pore scale, and they form spontaneously when the energetic benefit of reducing the Laplace pressure exceeds the energetic cost of deforming the solid skeleton. We are reframing this process through the lens of phase separation, where a non-wetting phase separates (or not) from a fluid-fluid-solid mixture. We are constructing a phase-field model in which two immiscible fluids interact with a poroelastic solid skeleton, and we are complementing this model with high-resolution experiemntal observations. Our work has implications for a wide variety of natural and industrial systems, such as the nucleation and growth of gas bubbles in lake beds and waste ponds.

  • Compression and inflation: Compressibility refers to the increase in a material's density with pressure (ie, that a given mass of material occupies less volume as pressure the increases). "Inflatability" refers to the increase of a container's internal volume with pressure (ie, that the container expands as the pressure increases). In both soft and rigid porous media, the compressibility of the fluids and the inflatability of the system have similar effects, in that they both increase the mass of fluid and/or solid that can fit in the system. We are exploring the similar roles of these two phenomena to better understand how compression and inflation interact with flow and transport in soft systems.

Outputs