Modeling Geometric State for Fluids in Porous Media: Evolution of the Euler Characteristic

Growth regimes in three-dimensional phase separation of liquid-vapor systems

The liquid-vapor phase separation is investigated via lattice Boltzmann simulations in three dimensions. After expressing length and time scales in reduced physical units, we combined data from several large simulations (on 512^{3} nodes) with different values of viscosity, surface tension, and temperature, to obtain a single curve of rescaled length l[over ̂] as a function of rescaled time t[over ̂]. We find evidence of the existence of kinetic and inertial regimes with growth exponents α_{d}=1/2 and α_{i}=2/3 over several time decades, with a crossover from α_{d} to α_{i} at t[over ̂]≃1. This allows us to rule out the existence of a viscous regime with α_{v}=1 in three-dimensional liquid-vapor isothermal phase separation, differently from what happens in binary fluid mixtures. An in-depth analysis of the kinetics of the phase separation process, as well as a characterization of the morphology and the flow properties, are further presented in order to provide clues into the dynamics of the phase-separation process.

Effects of hole shape and bottom gap on the flow characteristics behind butterfly porous fence and its application in dust diffusion control in large open-air piles

In view of the possible dust pollution of atmospheric caused by large open-air piles, a scheme of using butterfly porous fences is proposed. Based on the actual cause of large open-air piles, this study makes an in-depth study on the wind shielding effect of butterfly porous fences. The effects of hole shape and bottom gap on the flow characteristics are investigated behind the butterfly porous fence with the porosity of 0.273 through the combined methods of computational fluid dynamics and validating PIV experiments. The streamlines distribution and X-velocity behind the porous fence of numerical simulation are in good agreement with the experimental results and based on the research group's previous work, the numerical model is feasible. The concept of the wind reduction ratio is proposed to quantitatively evaluate the wind shielding effect of the porous fence. The results show that the butterfly porous fence with circular holes provided the best shelter effect with the wind reduction ratio of 78.34%, and the optimal bottom gap ratio is about 0.075 with the highest wind reduction ratio of 80.1%. When a butterfly porous fence is applied on site, the diffusion range of dust in open-air piles is significantly reduced compared with that without a fence. In conclusion, the circular holes with the bottom gap ratio of 0.075 are suitable for the butterfly porous fence in practical applications and provide a solution for wind-induced control in large open-air piles.

Strain-Driven Mixed-Phase Domain Architectures and Topological Transitions in Pb1- x Srx TiO3 Thin Films

The potential for creating hierarchical domain structures, or mixtures of energetically degenerate phases with distinct patterns that can be modified continually, in ferroelectric thin films offers a pathway to control their mesoscale structure beyond lattice-mismatch strain with a substrate. Here, it is demonstrated that varying the strontium content provides deterministic strain-driven control of hierarchical domain structures in Pb_{1- x} Sr_x TiO₃  solid-solution thin films wherein two types, c/a and a₁ /a₂ , of nanodomains can coexist. Combining phase-field simulations, epitaxial thin-film growth, detailed structural, domain, and physical-property characterization, it is observed that the system undergoes a gradual transformation (with increasing strontium content) from droplet-like a₁ /a₂  domains in a c/a domain matrix, to a connected-labyrinth geometry of c/a domains, to a disconnected labyrinth structure of the same, and, finally, to droplet-like c/a domains in an a₁ /a₂  domain matrix. A relationship between the different mixed-phase modulation patterns and its topological nature is established. Annealing the connected-labyrinth structure leads to domain coarsening forming distinctive regions of parallel c/a and a₁ /a₂  domain stripes, offering additional design flexibility. Finally, it is found that the connected-labyrinth domain patterns exhibit the highest dielectric permittivity.

Fluctuation-Dissipation Theorems for Multiphase Flow in Porous Media

A thermodynamic description of porous media must handle the size- and shape-dependence of media properties, in particular on the nano-scale. Such dependencies are typically due to the presence of immiscible phases, contact areas and contact lines. We propose a way to obtain average densities suitable for integration on the course-grained scale, by applying Hill's thermodynamics of small systems to the subsystems of the medium. We argue that the average densities of the porous medium, when defined in a proper way, obey the Gibbs equation. All contributions are additive or weakly coupled. From the Gibbs equation and the balance equations, we then derive the entropy production in the standard way, for transport of multi-phase fluids in a non-deformable, porous medium exposed to differences in boundary pressures, temperatures, and chemical potentials. Linear relations between thermodynamic fluxes and forces follow for the control volume. Fluctuation-dissipation theorems are formulated for the first time, for the fluctuating contributions to fluxes in the porous medium. These give an added possibility for determination of the Onsager conductivity matrix for transport through porous media. Practical possibilities are discussed.

Coupling between internal and external mass transfer during stage-1 evaporation in capillary porous media: Interfacial resistance approach

The coupling boundary condition to be imposed at the evaporative surface of a porous medium is studied from pore network simulations considering the capillary regime. This paper highlights the formation of a thin edge effect region of smaller saturation along the evaporative surface. It is shown that this thin region forms in the breakthrough period at the very beginning of the drying process. The size of this region is studied and shown to be not network size dependent. This region is shown to be the locus of a nonlocal equilibrium effect. The features lead to the consideration of a coupling boundary condition involving an interfacial mass transfer resistance and an external mass transfer resistance. Contrary to previous considerations, it is shown that both resistances depend on the variation of the saturation, i.e., the fluid topology, and the size of the external mass transfer layer, i.e., the mass transfer rate. This is explained by the evolution of the vapor partial pressure distribution at the surface which becomes increasingly heterogeneous during evaporation and depends on both the evolving fluid distribution in the interfacial region and the mass transfer rate. However, the geometric effects due to the configuration of the fluids can be separated from rate effects that arise due to the nonequilibrium mass transport.

Capillary equilibrium of bubbles in porous media

In geologic, biologic, and engineering porous media, bubbles (or droplets, ganglia) emerge in the aftermath of flow, phase change, or chemical reactions, where capillary equilibrium of bubbles significantly impacts the hydraulic, transport, and reactive processes. There has previously been great progress in general understanding of capillarity in porous media, but specific investigation into bubbles is lacking. Here, we propose a conceptual model of a bubble's capillary equilibrium associated with free energy inside a porous medium. We quantify the multistability and hysteretic behaviors of a bubble induced by multiple state variables and study the impacts of pore geometry and wettability. Surprisingly, our model provides a compact explanation of counterintuitive observations that bubble populations within porous media can be thermodynamically stable despite their large specific area by analyzing the relationship between free energy and bubble volume. This work provides a perspective for understanding dispersed fluids in porous media that is relevant to CO₂ sequestration, petroleum recovery, and fuel cells, among other applications.