Fluid flows through deformable porous media are ubiquitous throughout nature. Examples include methane venting from seabed sediments, meltwater flow through compacting snow, and solute transport within biological tissues. Despite extensive studies of flow through stiff or rigid porous media, flow through highly deformable porous media remains poorly understood. A key reason for this lack of understanding is the physical and conceptual complexity induced by the strong two-way coupling between flow and deformation: flow can deform the pore structure, which in turn affects the flow.
A major challenge in modelling multiphase flow in highly deformable systems is that deformation enables the emergence of completely new flow phenomena that do not have an analogue in the rigid case, the most striking of which is the ability of the non-wetting fluid to form open (solid-free) pathways and cavities. Additionally, capillary compression of the solid skeleton by an invading fluid phase can itself deform the pore structure, potentially leading to a 'self-clogging' behaviour. We have explored these phenomena by combining theoretical approaches with simple table-top experiments using packings of hydrogel beads or soft fibrillar sponges as the deformable porous medium.
Various biological and chemical processes lead to the nucleation and growth of non-wetting fluid bubbles within the pore space of a soft granular medium. The non-wetting nature of these bubbles makes it energetically costly for them to invade narrow pore throats between solid grains. If the solid skeleton is sufficiently deformable, these non-wetting bubbles can instead displace the solid to form macroscopic cavities that are much larger than the pore size.Â
During my PhD, I used a combination of theoretical and experimental approaches to build towards a quantitative understanding of the parameters that control the total volume of cavities, their size distribution, and the dynamics of their formation and collapse. Understanding these processes is important for explaining the macroscopic mechanics of the composite three-phase system and its interactions with the surrounding environment.
See here for a recorded talk I gave as part of the Porous Media Tea Time Talks series, and here for our paper on the thermo-mechanics of cavity formation.
The passing of sand through an hourglass is an everyday example of the flow of granular material through a complex surrounding environment. Similar processes occur widely in both industrial (e.g. grain silos) and geophysical (e.g. subsurface faults and fractures) settings. Frictional interactions between solid grains and confining walls can also give rise to spectacular pattern formation.
In work lead by Liam Morrow, we explore the piston-driven bulldozing of a dense granular material through a confined channel. Comparing the predictions of a reduced-order continuum model with a series of experiments in a millifluidic setup, we highlight how the rheology of the granular packing and frictional interactions with the confining walls control the resultant flow profile as well as the force required to advance the piston.
Capillary-driven compression and relaxation of a soft sponge
H. Wei, O. W. Paulin, C. Cuttle, C. W. MacMinn (in prep)
Deformation-driven collapse of non-wetting cavities in a soft porous medium
O. W. Paulin, L. C. Morrow, M. G. Hennessy, and C. W. MacMinn (in prep)
L. C. Morrow, O. W. Paulin, M. G. Hennessy, D. R. Hewitt, M. L. Morgan, B. Sandnes, and C. W. MacMinn (submitted)
O. W. Paulin
DPhil Thesis, University of Oxford (2023)
O. W. Paulin, L. C. Morrow, M. G. Hennessy, and C. W. MacMinn
Journal of the Mechanics and Physics of Solids, 164:104892 (2022)