  Various biological and chemical processes lead to the nucleation and growth
of non-wetting fluid bubbles within the pore space of a granular medium, such
as the formation of gas bubbles in liquid-saturated lake-bed sediments. In
sufficiently soft porous materials, the non-wetting nature of these bubbles can
result in the formation of open cavities within the granular solid skeleton.
Here, we consider this process through the lens of phase separation, where
thermomechanics govern the separation of the non-wetting phase from a
fluid-fluid-solid mixture. We construct a phase-field model informed by
large-deformation poromechanics, in which two immiscible fluids interact with a
poroelastic solid skeleton. Our model captures the competing effects of
elasticity and fluid-fluid-solid interactions. We use a phase-field damage
model to capture the mechanics of the granular solid. As a model problem, we
consider an initial distribution of non-wetting fluid in the pore space that
separates into multiple cavities. We use simulations and linear-stability
analysis to identify the key parameters that control phase separation, the
conditions that favour the formation of cavities, and the characteristic size
of the resulting cavities.
