Statistical mechanics of unsaturated porous media

Statistical Mechanics of Electrowetting

We derive the ab initio equilibrium statistical mechanics of the gas-liquid-solid contact angle on planar periodic, monodisperse, textured surfaces subject to electrowetting. To that end, we extend an earlier theory that predicts the advance or recession of the contact line amount to distinct first-order phase transitions of the filling state in the ensemble of nearby surface cavities. Upon calculating the individual capacitance of a cavity subject to the influence of its near neighbors, we show how hysteresis, which is manifested by different advancing and receding contact angles, is affected by electrowetting. The analysis reveals nine distinct regimes characterizing contact angle behavior, three of which arise only when a voltage is applied to the conductive liquid drop. As the square voltage is progressively increased, the theory elucidates how the drop occasionally undergoes regime transitions triggering jumps in the contact angle, possibly changing its hysteresis, or saturating it at a value weakly dependent on further voltage growth. To illustrate these phenomena and validate the theory, we confront its predictions with four data sets. A benefit of the theory is that it forsakes trial and error when designing textured surfaces with specific contact angle behavior.

Neighborhood Relationships of Widely Distributed and Irregularly Shaped Particles in Partially Dewatered Filter Cakes

A more thorough understanding of the properties of bulk material structures in solid–liquid separation processes is essential to understand better and optimize industrially established processes, such as cake filtration, whose process outcome is mainly dependent on the properties of the bulk material structure. Here, changes of bulk properties like porosity and permeability can originate from local variations in particle size, especially for non-spherical particles. In this study, we mix self-similar fractions of crushed, irregularly shaped Al2O3 particles (20 to 90 µm and 55 to 300 µm) to bimodal distributions. These mixtures vary in volume fraction of fines (0, 20, 30, 40, 50, 60 and 100 vol.%). The self-similarity of both systems serves the improved parameter correlation in the case of multimodal distributed particle systems. We use nondestructive 3D X-ray microscopy to capture the filter cake microstructure directly after mechanical dewatering, whereby we give particular attention to packing structure and particle–particle relationships (porosity, coordination number, particle size and corresponding hydraulic isolated liquid areas). Our results reveal widely varying distributions of local porosity and particle contact points. An average coordination number (here 5.84 to 6.04) is no longer a sufficient measure to describe the significant bulk porosity variation (in our case, 40 and 49%). Therefore, the explanation of the correlation is provided on a discrete particle level. While individual particles < 90 µm had only two or three contacts, others > 100 µm took up to 25. Due to this higher local coordination number, the liquid load of corresponding particles (liquid volume/particle volume) after mechanical dewatering increases from 0.48 to 1.47.

Can an Off-Nominal Landing by an MMRTG-Powered Spacecraft Induce a Special Region on Mars When No Ice Is Present?

This work aims at addressing whether a catastrophic failure of an entry, descent, and landing event of a Multimission Radioisotope Thermoelectric Generator-based lander could embed the heat sources into the martian subsurface and create a local environment that (1) would temporarily satisfy the conditions for a martian Special Region and (2) could establish a transport mechanism through which introduced terrestrial organisms could be mobilized to naturally occurring Special Regions elsewhere on Mars. Two models were run, a primary model by researchers at the Lawrence Berkeley National Laboratory and a secondary model by researchers at the Jet Propulsion Laboratory, both of which were based on selected starting conditions for various surface composition cases that establish the worst-case scenario, including geological data collected by the Mars Science Laboratory at Gale Crater. The summary outputs of both modeling efforts showed similar results: that the introduction of the modeled heat source could temporarily create the conditions established for a Special Region, but that there would be no transport mechanism by which an introduced terrestrial microbe, even if it was active during the temporarily induced Special Region conditions, could be transported to a naturally occurring Special Region of Mars.

Statistical mechanics of the triple contact line

We outline a statistical mechanics of the triple gas-solid-liquid contact line on a rough plane. The analysis regards the neighborhood of the line as a solid dotted with cavities. It adopts the simplest mean-field statistical mechanics, in which each cavity is either full or empty, while being connected to near neighbors by thin necks. The theory predicts equilibrium angles for advance and recession in terms of the Young contact angle and the joint statistical distribution of two quantifiable geometrical parameters representing specific neck cross-section and specific cavity opening. It attributes contact angle hysteresis to first-order phase transitions among adjacent cavities, as they collectively imbibe or reject liquid. It also calculates the potential energy barriers that hysteresis erects against overcoming contact line pinning. By determining whether the phase transitions can release latent energy, this ab initio analysis distinguishes six regimes, including two metastable recession states. We compare predictions with data for superhydrophobia on microscopic rods; for hysteresis in the "Wenzel state"; and for variations of the advancing contact angle with surface energies of the liquid.

Beyond Darcy's law: The role of phase topology and ganglion dynamics for two-fluid flow

In multiphase flow in porous media the consistent pore to Darcy scale description of two-fluid flow processes has been a long-standing challenge. Immiscible displacement processes occur at the scale of individual pores. However, the larger scale behavior is described by phenomenological relationships such as relative permeability, which typically uses only fluid saturation as a state variable. As a consequence pore scale properties such as contact angle cannot be directly related to Darcy scale flow parameters. Advanced imaging and computational technologies are closing the gap between the pore and Darcy scale, supporting the development of new theory. We utilize fast x-ray microtomography to observe pore-scale two-fluid configurations during immiscible flow and initialize lattice Boltzmann simulations that demonstrate that the mobilization of disconnected nonwetting phase clusters can account for a significant fraction of the total flux. We show that fluid topology can undergo substantial changes during flow at constant saturation, which is one of the underlying causes of hysteretic behavior. Traditional assumptions about fluid configurations are therefore an oversimplification. Our results suggest that the role of fluid connectivity cannot be ignored for multiphase flow. On the Darcy scale, fluid topology and phase connectivity are accounted for by interfacial area and Euler characteristic as parameters that are missing from our current models.