We show that the return-point memory of cyclic macroscopic trajectories enables the derivation of a thermodynamic framework for quasistatically driven dissipative systems with multiple metastable states. We use this framework to sort out and quantify the energy dissipated in quasistatic fluid-fluid displacements in disordered media. Numerical computations of imbibition--drainage cycles in a quasi-2D medium with gap thickness modulations (imperfect Hele-Shaw cell) show that energy dissipation in quasistatic displacements is due to abrupt changes in the fluid-fluid configuration between consecutive metastable states (Haines jumps), and its dependence on microstructure and gravity. The relative importance of viscous dissipation is deduced from comparison with quasistatic experiments.

Pockmarks are morphological depressions commonly observed in ocean and lake floors. Pockmarks form by fluid (typically gas) seepage thorough a sealing sedimentary layer, deforming and breaching the layer. The seepage-induced sediment deformation mechanisms, and their links to the resulting pockmarks morphology, are not well understood. To bridge this gap, we conduct laboratory experiments in which gas seeps through a granular (sand) reservoir, overlaid by a (clay) seal, both submerged under water. We find that gas rises through the reservoir and accumulates at the seal base. Once sufficient gas over-pressure is achieved, gas deforms the seal, and finally escapes via either: (i) doming of the seal followed by dome breaching via fracturing; (ii) brittle faulting, delineating a plug. The gas lifts the plug and seeps through the bounding faults; or (iii) plastic deformation by bubbles ascending through the seal. The preferred mechanism is found to depend on the seal thickness and stiffness: in stiff seals, a transition from doming and fracturing to brittle faulting occurs as the thickness increases, whereas bubbles rise is preferred in the most compliant, thickest seals. Seepage can also occur by mixed modes, such as bubbles rising in faults. Repeated seepage events suspend the sediment at the surface and create pockmarks. We present a quantitative analysis that explains the tendency for the various modes of deformation observed experimentally. Finally, we connect simple theoretical arguments with field observations, highlighting similarities and differences that bound the applicability of laboratory experiments to natural pockmarks.

A document by Ran Holtzman. Click on the document to view its contents.

Solute transport in unsaturated porous media is of interest in many engineering and environmental applications. The interplay between small-scale, local forces and the porous microstructure exerts a strong control on the transport of fluids and solutes at the larger, macroscopic scales. Heterogeneity in pore geometry is intrinsic to natural material across a large range of scales. This multiscale nature, and the intricate links between two-phase flow and solute transport, remain far from well understood, by and large. Here, we use Direct Numerical Simulation (DNS) to quantify the effects of correlated heterogeneity on solute transport during drainage under an unfavorable viscosity ratio. We find that increasing spatial correlations in pore sizes increases the size of the required Representative Elementary Volume (REV). We also show that increasing the correlation length enhances solute dispersivity through its impact on the spatial distribution of low-velocity (diffusion-dominated) and high-velocity (advection-dominated) regions. Fluid saturation is shown to directly affect diffusive mass flux among high-and low-velocity zones. Another indirect effect of correlated heterogeneity on solute transport is through its control of the drainage patterns via rearrangements of mobile-immobile zones. Our findings improve quantitative understanding of solute mixing and dispersion in unsaturated conditions, highly relevant to some of our most urgent environmental problems.