Periodic Reporting for period 4 - DEFTPORE (Deformation control on flow and transport in soft porous media)
Reporting period: 2023-08-01 to 2024-09-30
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.
With regard to solute transport and mixing, we focused specifically on one research question: How does compressing or stretching a soft porous medium alter the spreading of solute through its pore space? We tackled this question both theoretically and experimentally. Theoretically, we used formal mathematical homogenisation to calculate how distorting the pore geometry changes the basic transport properties, such as the rate of solute diffusion. We then used an existing mathematical model to study how the repeated squeezing of a soft porous medium drives the in-and-out motion of both fluid and solute. Experimentally, we developed a technique for manufacturing custom sponges out of transparent rubber and then used these sponges to measure the impact of squeezing on solute motion. Our results are relevant to household experiences like cleaning dirty water from a kitchen sponge by squeezing it repeatedly, but also to nutrient transport in tissues like cartilage.
With regard to the interactions between two different fluids, we focused specifically on understanding the evolution of gas bubbles in a soft, liquid-saturated porous medium. This problem is relevant to the growth and venting of gas bubbles in lakebed sediments, seabed sediments, and industrial waste ponds. We first performed an experimental study of gas migration and venting. Our results reinforced and broadened a key finding from previous work: in a stiff medium, gas bubbles will migrate through the pore space; in a soft medium, gas bubbles will instead push the solid apart and create macroscopic openings or "cavities". This observation motivated us to develop the first model that can reproduce the formation of these gas cavities. We then developed a series of experiments that allowed for the first detailed measurements of the behavior of these gas cavities during the compression of the medium.
Our results were widely disseminated across numerous international scientific seminars, workshops, and conferences, at an international summer school, and via attention from the popular-science media.
With regard to the interactions between two different fluids, we focused specifically on understanding the evolution of gas bubbles in a soft, liquid-saturated porous medium. This problem is relevant to the growth and venting of gas bubbles in lakebed sediments, seabed sediments, and industrial waste ponds. We first performed an experimental study of gas migration and venting. Our results reinforced and broadened a key finding from previous work: in a stiff medium, gas bubbles will migrate through the pore space; in a soft medium, gas bubbles will instead push the solid apart and create macroscopic openings or "cavities". This observation motivated us to develop the first model that can reproduce the formation of these gas cavities. We then developed a series of experiments that allowed for the first detailed measurements of the behavior of these gas cavities during the compression of the medium.
Our results were widely disseminated across numerous international scientific seminars, workshops, and conferences, at an international summer school, and via attention from the popular-science media.
In both prongs of the project, we advanced the state of the art by performing novel, high-resolution experiments that reveal both macroscopic and pore-scale features of the problem. Our experiments were intentionally minimal, avoiding application-specific complications to allow us to focus on the underlying physical mechanisms in the simplest possible setting. We used these experimental observations to inform the development of new continuum models for solute transport and two-fluid-phase flow. For solute transport, we developed an improved understanding of the deformation-driven mixing and spreading of solutes and took important steps toward a new model that captures the role of changing pore structure; no such model currently exists. For the flow of different fluid phases, we developed a new theoretical framework that allows for the prediction of flow rates, pressure drops, and phase distributions in soft porous media -- including the formation of macroscopic gas cavities. We identified latter phenomenon as the hallmark feature of this problem. No other current model can make these predictions or capture these features. Together, these advances in our understanding and predictive capabilities have the potential to contribute to improved product and process design, resource management, and medical diagnosis and treatment.