Validating the Transition Criteria from the Cassie-Baxter to the Wenzel State for Periodically Pillared Surfaces with Lattice Boltzmann Simulations.

Microfabrication techniques allow the development and production of artificial superhydrophobic surfaces that possess a precisely controlled roughness at the micrometer level, typically achieved through the arrangement of micropillar structures in periodic patterns. In this work, we analyze the stability and energy barrier of droplets in the Cassie-Baxter (CB) state on such periodic patterns. In addition, we further develop a transition criterion using the CB equation and derive an improved version which allows predicting for which pillar geometries, equilibrium contact angles, and droplet volumes the CB state switches from a metastable to an unstable state. This enables a comparison with existing experiments and three-dimensional multiphase Lattice Boltzmann simulations for different pillar distances, two contact angles, and two droplet volumes, where a good agreement has been found.

Microfluidic investigation of pore-size dependency of barite nucleation.

The understanding and prediction of mineral precipitation processes in porous media are relevant for various energy-related subsurface applications. While it is well known that thermodynamic effects can inhibit crystallization in pores with sizes <0.1 µm, the retarded observation of mineral precipitation as function of pore size is less explored. Using barite as an example and based on a series of microfluidic experiments with well-defined pore sizes and shapes, we show that retardation of observation of barite crystallite can already start in pores of 1 µm size, with the probability of nucleation scaling with the pore volume. In general, it can be expected that mineralization occurs preferentially in larger pores in rock matrices, but other parameters such as the exchange of the fluids with respect to reaction time, as well as shape, roughness, and surface functional properties of the pores may affect the crystallization process which can reverse this trend.

Diffusion and Gas Flow Dynamics in Partially Saturated Smectites.

Clays and clay rocks are considered good natural and engineered barriers for deep geological disposal of nuclear waste worldwide. Metal corrosion and organic waste degradation in underground repositories generate significant amounts of gas that should be able to migrate through the multibarrier system to avoid potential pressure buildup, which could be compromising the integrity of the barriers and host rocks. The gas is expected to accumulate in larger pores and eventually form an interconnected network. Under such conditions, the migration of gas molecules takes place both in pore water films and gas-filled macropores. Therefore, mass fluxes depend on the distribution of gas molecules between the water-rich and gas-rich phases and their mobility in both compartments. Classical molecular dynamics (MD) simulations were employed to investigate the mobilities of He, H2, CO2, Ar, and CH4 in a Na-montmorillonite mesopore as a function of the degree of saturation, as well as evaluate the hydrodynamic behavior of the pore fluid in partially saturated clays. The diffusivity of the gas molecules was determined by observing the asymptotic behavior of the mean square displacement in the gas-rich phase and at the gas-water interface. The partition coefficient and Gibbs free energy were analyzed to investigate the transfer of gas molecules between the gas-rich and water-rich phases by observing the molecular trajectories as they cross the vapor-liquid interface. The results revealed that the diffusion coefficient in the gas phase increased with increasing gas-filled pore width and converged asymptotically toward the diffusion coefficient in the bulk state. It could be shown that the diffusion coefficient of gas molecules dissolved in the water films remained constant as long as the interacting water surface was in the bulk-liquid-like phase. This behavior changes in very thin water films. It was observed that the partitioning coefficient of gas molecules at the solid-liquid interface is nearly the same as that in the bulk-liquid-like phase. Partitioning is observed to be strongly dependent on the temperature and gas molecular weights. In the second part of the study, nonequilibrium molecular dynamics (NEMD) simulations were performed to investigate the mobility of gases in pressure-driven decoupled gas-phase dynamics (DGPD) and coupled gas and water phase dynamics (CGWPD) in a partially saturated Na-montmorillonite slit mesopore. The dynamic viscosity of the gas phase was calculated from NEMD simulations and indicated that the viscosity of the gas phase was almost the same in both methods (DGPD and CGWPD). The average slip length for gas molecules at the gas-water interface was also calculated, revealing that the slip-free boundary condition assumed in continuum models is generally invalid for microfluidics and that a slip boundary condition exists at the microscale for specific surface interactions. Finally, a Bosanquet-type equation was developed to predict the diffusion coefficient and dynamic viscosity of gas as a function of the average pore width, gas mean-free path, geometric factor, and thickness of the adsorbed water film.

Pore-Level Multiphase Simulations of Realistic Distillation Membranes for Water Desalination.

Membrane distillation (MD) is a thermally driven separation process that is operated below boiling point. Since the performance of MD modules is still comparatively low, current research aims to improve the understanding of the membrane structure and its underlying mechanisms at the pore level. Based on existing realistic 3D membrane geometries (up to 0.5 billion voxels with 39nm resolution) obtained from ptychographic X-ray computed tomography, the D3Q27 lattice Boltzmann (LB) method was used to investigate the interaction of the liquid and gaseous phase with the porous membrane material. In particular, the Shan and Chen multi-phase model was used to simulate multi-phase flow at the pore level. We investigated the liquid entry pressure of different membrane samples and analysed the influence of different micropillar structures on the Wenzel and Cassie-Baxter state of water droplets on rough hydrophobic surfaces. Moreover, we calculated the liquid entry pressure required for entering the membrane pores and extracted realistic water contact surfaces for different membrane samples. The influence of the micropillars and flow on the water-membrane contact surface was investigated. Finally, we determined the air-water interface within a partially saturated membrane, finding that the droplet size and distribution correlated with the porosity of the membrane.

Deciphering the molecular mechanism of water boiling at heterogeneous interfaces.

Water boiling control evolution of natural geothermal systems is widely exploited in industrial processes due to the unique non-linear thermophysical behavior. Even though the properties of water both in the liquid and gas state have been extensively studied experimentally and by numerical simulations, there is still a fundamental knowledge gap in understanding the mechanism of the heterogeneous nucleate boiling controlling evaporation and condensation. In this study, the molecular mechanism of bubble nucleation at the hydrophilic and hydrophobic solid-water interface was determined by performing unbiased molecular dynamics simulations using the transition path sampling scheme. Analyzing the liquid to vapor transition path, the initiation of small void cavities (vapor bubbles nuclei) and their subsequent merging mechanism, leading to successively growing vacuum domains (vapor phase), has been elucidated. The molecular mechanism and the boiling nucleation sites' location are strongly dependent on the solid surface hydrophobicity and hydrophilicity. Then simulations reveal the impact of the surface functionality on the adsorbed thin water molecules film structuring and the location of high probability nucleation sites. Our findings provide molecular-scale insights into the computational aided design of new novel materials for more efficient heat removal and rationalizing the damage mechanisms.

Lattice Boltzmann model with generalized wall boundary conditions for arbitrary catalytic reactivity.

A lattice Boltzmann model for multispecies flows with catalytic reactions is developed, which is valid from very low to very high surface Damköhler numbers (Da_{s}). The previously proposed model for catalytic reactions [S. Arcidiacono, J. Mantzaras, and I. V. Karlin, Phys. Rev. E 78, 046711 (2008)PLEEE81539-375510.1103/PhysRevE.78.046711], which is applicable for low-to-moderate Da_{s} and encompasses part of the mixed kinetics and transport-controlled regime, is revisited and extended for the simulation of arbitrary kinetics-to-transport rate ratios, including strongly transport-controlled conditions (Da_{s}→∞). The catalytic boundary condition is modified by bringing nonlocal information on the wall reactive nodes, allowing accurate evaluation of chemical rates even when the concentration of the deficient reactant at the wall becomes vanishingly small. The developed model is validated against a finite volume Navier-Stokes CFD (Computational Fluid Dynamics) solver for the total oxidation of methane in an isothermal channel-flow configuration. CFD simulations and lattice Boltzmann simulations with the old and new catalytic reaction models are compared against each other. The new model demonstrates a second order accuracy in space and time and provides accurate results at very high Da_{s} (∼10^{9}) where the old model fails. Moreover, to achieve the same accuracy at moderate-to-high Da_{s} of O(1), the new model requires ∼2^{d}×N coarser grid than the original model, where d is the spatial dimension and N the number of species.

Coupling of multiscale lattice Boltzmann discrete-element method for reactive particle fluid flows.

Reactive particulate systems are of prime importance in varieties of practical applications in process engineering. As an example this study considers extraction of phosphorous from waste water by calcium silicate hydrate particles in the P-RoC process. For such systems modeling has a large potential to help to optimize process conditions, e.g., particle-size distributions or volume flows. The goal of this study is to present a new generic modeling framework to capture relevant aspects of reactive particle fluid flows using combined lattice Boltzmann method and discrete-element method. The model developed is Euler-Lagrange scheme which consist of three-components viz., a fluid phase, a dissolved reactive substance, and suspended particles. The fluid flow and reactive mass transport are described in a continuum framework using volume-averaged Navier-Stokes and volume-averaged advection-diffusion-reaction equations, respectively, and solved using lattice Boltzmann methods. The volume-averaging procedure ensures correctness in coupling between fluid flow, reactive mass transport, and particle motion. The developed model is validated through series of well-defined benchmarks. The benchmarks include the validation of the model with experimental data for the settling of a single particle in a cavity filled with water. The benchmark to validate the multi-scale reactive transport involves comparing the results with a resolved numerical simulation. These benchmarks also prove that the proposed model is grid convergent which has previously not been established for such coupled models. Finally, we demonstrate the applicability of our model by simulating a suspension of multiple particles in fluid with a dissolved reactive substance. Comparison of this coupled model is made with a one-way coupled simulation where the influence of particles on the fluid flow and the reactive solution transport is not considered. This elucidates the need for the two-way coupled model.

Thermal multicomponent lattice Boltzmann model for catalytic reactive flows.

Catalytic reactions are of great interest in many applications related to power generation, fuel reforming and pollutant abatement, as well as in various biochemical processes. A recently proposed lattice Boltzmann model for thermal binary-mixture gas flows [J. Kang, N. I. Prasianakis, and J. Mantzaras, Phys. Rev. E. 87, 053304 (2013)] is revisited and extended for the simulation of multispecies flows with catalytic reactions. The resulting model can handle flows with large temperature and concentration gradients. The developed model is presented in detail and validated against a finite volume Navier-Stokes solver in the case of channel-flow methane catalytic combustion. The surface chemistry is treated with a one-step global reaction for the catalytic total oxidation of methane on platinum. In order to take into account thermal effects, the catalytic boundary condition of S. Arcidiacono, J. Mantzaras, and I. V. Karlin [Phys. Rev. E 78, 046711 (2008)] is adapted to account for temperature variations. Speed of sound simulations further demonstrate the physical integrity and unique features of the model.

Lattice Boltzmann model for thermal binary-mixture gas flows.

A lattice Boltzmann model for thermal gas mixtures is derived. The kinetic model is designed in a way that combines properties of two previous literature models, namely, (a) a single-component thermal model and (b) a multicomponent isothermal model. A comprehensive platform for the study of various practical systems involving multicomponent mixture flows with large temperature differences is constructed. The governing thermohydrodynamic equations include the mass, momentum, energy conservation equations, and the multicomponent diffusion equation. The present model is able to simulate mixtures with adjustable Prandtl and Schmidt numbers. Validation in several flow configurations with temperature and species concentration ratios up to nine is presented.

Lattice Boltzmann method for simulation of compressible flows on standard lattices.

The recently introduced lattice Boltzmann model for thermal flow simulation on a standard lattice [Prasianakis and Karlin, Phys. Rev. E 76, 016702 (2007)] is studied numerically in the case where compressibility effects are essential. It is demonstrated that the speed of sound and shock propagation are described correctly in a wide temperature range, and that it is possible to take into account additional physics such as heat sources and sinks. A remarkable simplicity of the model makes it viable for engineering applications in subsonic flows with large temperature and density variations.

Lattice Boltzmann method for thermal flow simulation on standard lattices.

The recently introduced consistent lattice Boltzmann model with energy conservation [S. Ansumali and I. V. Karlin, Phys. Rev. Lett. 95, 260605 (2005)] is extended to the simulation of thermal flows on standard lattices. The two-dimensional thermal model on the standard square lattice with nine velocities is developed and validated in the thermal Couette and Rayleigh-Bénard natural convection problems.