Unexpected coupling between flow and adsorption in porous media

From Transient to Stationary Transport in Porous Networks under Various Adsorption Conditions and Kinetics

We investigate the interplay between adsorption and transport in a two-dimensional porous medium by means of an extended Lattice Boltzmann technique within the Two-Relaxation-Time framework. We focus on two canonical adsorption thermodynamics and kinetics formalisms: (1) the Henry model in which the adsorbed amount scales linearly with the free adsorbate concentration and (2) the Langmuir model that accounts for surface saturation upon adsorption. We simulate transport of adsorbing and nonadsorbing particles to investigate the effect of the adsorption/desorption ratio k, initial free adsorbate concentration c₀, surface saturation Γ^∞, and Peclet numbers Pe on their dispersion behavior. In all cases, despite marked differences between the different adsorption models, the three following transport regimes are observed: diffusion-dominated regime, transient regime and Gaussian or nearly Gaussian dispersion regime. On the one hand, at short times, the intermediate transient regime strongly depends on the system's parameters with the shape of the concentration field at a given time being dependent on the amount of particles adsorbed shortly after injection. On the other hand, at longer times, the influence of the initial condition attenuates as particles sample sufficiently the adsorbed and nonadsorbed states. Once such dynamical equilibrium is reached, transport becomes Gaussian (i.e., normal) or nearly Gaussian in the asymptotic regime. Interestingly, the characteristic time scale to reach equilibrium, which varies drastically with the system's parameters, can be much longer than the actual simulation time. In practice, such results reflect many experimental situations such as in water treatment where dispersion is found to remain anomalous (non-Gaussian), even if transport is considered over long macroscopic times.

Lattice Boltzmann method for adsorption under stationary and transient conditions: Interplay between transport and adsorption kinetics in porous media

A numerical method based on the Lattice Boltzmann formalism is presented to capture the effect of adsorption kinetics on transport in porous media. Through the use of a general adsorption operator, canonical models such as Henry and Langmuir adsorption as well as more complex adsorption mechanisms involving collective behavior with lateral interactions and surface aggregation can be investigated using this versatile model. By extending the description of adsorption phenomena to kinetic regimes with any underlying adsorption model, this effective technique allows assessing the coupled dynamics resulting from advection, diffusion, and adsorption in pores not only in stationary conditions but also under transient conditions (i.e., in regimes where the adsorbed amount evolves with time due to diffusion and advection). As illustrated in this paper, the development of such an approach provides a simple tool to determine the reciprocal effect of molecular flow and dispersion on adsorption kinetics. In this context, the use of a Lattice Boltzmann-based approach is important as it allows considering porous media of any morphology and topology. Beyond fundamental implications, this efficient method allows treating real engineering conditions such as pollutant dispersion or surfactant injection in a flowing liquid in soils and porous rocks.

A multi-scale model for fluid transport through a bio-inspired passive valve

Tillandsia landbeckii is a rootless plant thriving in the hyper-arid Atacama Desert of Chile. These plants use unique cellulose-based microscopic structures called trichomes to collect fresh water from coastal fog. The trichomes rely on a passive mechanism to maintain an asymmetrical transport of water: they allow for the fast absorption of liquid water deposited by sporadic fog events while preventing evaporation during extended drought periods. Inspired by the trichome's design, we study fluid transport through a micrometric valve. Combining Grand Canonical Monte Carlo with Non-Equilibrium Molecular Dynamics simulations, we first analyze the adsorption and transport of a fluid through a single nanopore at different chemical potentials. We then scale up the atomic results using a lattice approach, and simulate the transport at the micrometric scale. Results obtained for a model Lennard-Jones fluid and TIP4P/2005 water were compared, allowing us to identify the key physical parameters for achieving a passive hydraulic valve. Our results show that the difference in transport properties of water vapor and liquid water within the cellulose layer is the basis for the ability of the Tillandsia trichome to function as a water valve. Finally, we predict a critical pore dimension above which the cellulose layer can form an efficient valve.

Modelling of framework materials at multiple scales: current practices and open questions

The last decade has seen an explosion of the family of framework materials and their study, from both the experimental and computational points of view. We propose here a short highlight of the current state of methodologies for modelling framework materials at multiple scales, putting together a brief review of new methods and recent endeavours in this area, as well as outlining some of the open challenges in this field. We will detail advances in atomistic simulation methods, the development of material databases and the growing use of machine learning for the prediction of properties. This article is part of the theme issue 'Mineralomimesis: natural and synthetic frameworks in science and technology'.

Entropy production in thermal phase separation: a kinetic-theory approach

Entropy production during the process of thermal phase-separation of multiphase flows is investigated by means of a discrete Boltzmann kinetic model. The entropy production rate is found to increase during the spinodal decomposition stage and to decrease during the domain growth stage, attaining its maximum at the crossover between the two. Such behaviour provides a natural criterion to identify and discriminate between the two regimes. Furthermore, the effects of heat conductivity, viscosity and surface tension on the entropy production rate are investigated by systematically probing the interplay between non-equilibrium energy and momentum fluxes. It is found that the entropy production rate due to energy fluxes is an increasing function of the Prandtl number, while the momentum fluxes exhibit an opposite trend. On the other hand, both contributions show an increasing trend with surface tension. The present analysis inscribes within the general framework of non-equilibrium thermodynamics and consequently it is expected to be relevant to a broad class of soft-flowing systems far from mechanical and thermal equilibrium.

From a Protein's Perspective: Elution at the Single-Molecule Level

Column chromatography is a widely used analytical technique capable of identifying and isolating a desired chemical species from a more complicated mixture. Despite the method's prevalence, theoretical descriptions have not advanced to accommodate today's common analyte, proteins. Proteins are increasingly used as biologics, a term that refers to biological pharmaceuticals, and present new complexities for chromatographic separation. Large variations in surface charge, chemistry, and structure among protein analytes expose the limits in the current theoretical framework's ability to predict the efficiency of a column without empirical data. The bottleneck created by empirical optimization is a strong motivation for a renewed effort to achieve an in-depth understanding of the range of interactions that occur between a protein analyte and the stationary phase that together enable its selective separation from other constituents of a mixture. The physical and chemical processes that dictate the amount of time an analyte spends in the column are often abstracted by theory and treated as statistical distributions. Until recently, these distributions could not be mapped experimentally as traditional experimental techniques could not reveal underlying heterogeneity in structure, charge, and dynamics. Aligning the latest experimental and theoretical advances is thus a hurdle to be overcome so that significant progress can be made toward a predictive chromatographic theory. In this Account, we detail the work of the Landes Lab in developing single-molecule techniques that refine the stochastic theory of chromatography as a first step toward predictive chromatographic column design. We provide a brief review of the development of stochastic theory and establish a mathematical framework to put the discussed physical chemistry in context. We describe our investigations of three pertinent phenomena: mobile/stationary phase exchange, adsorption/desorption kinetics, and hindered diffusion. We highlight experimental evidence that points to nonuniform behavior. Then, we describe our work in developing single-molecule techniques that can evaluate these effects on a protein-by-protein basis. We highlight two developments: fast imaging via super temporal-resolved microscopy (STReM) and visualizing diffusion within pores via a combination of fluorescence correlation spectroscopy and super-resolution optical fluctuation imaging (fcsSOFI). Both methods offer new ways to study chromatographic elution at the single-protein level. Such methods can identify the rare heterogeneities that prevent efficient separations and advance the field closer to predictively optimized protein separations.

Kinetic Accessibility of Porous Material Adsorption Sites Studied through the Lattice Boltzmann Method

We present here a computational model based on the lattice Boltzmann scheme to investigate the accessibility of active adsorption sites in hierarchical porous materials to adsorbates in a flowing liquid. By studying the transport and adsorption of tracers after they enter the pore space of the virtual sample, we characterize their kinetics as they pass through the pore space and adsorb on the solid-liquid interface. The model is validated on simple geometries with a known analytical solution. We then use it to investigate the influence of regular grooves or disordered roughness on the walls of a slit pore geometry, looking at the impact on adsorption and transport. In particular, we highlight the importance of adsorption site accessibility, which depends on the shape and connectivity of the pore space as well as the fluid flow profile and velocity.

Transport and adsorption under liquid flow: the role of pore geometry

We study here the interplay between transport and adsorption in porous systems with complex geometries under fluid flow. Using a lattice Boltzmann scheme extended to take into account the adsorption at solid/fluid interfaces, we investigate the influence of pore geometry and internal surface roughness on the efficiency of fluid flow and the adsorption of molecular species inside the pore space. We show how the occurrence of roughness on pore walls acts effectively as a modification of the solid/fluid boundary conditions, introducing slippage at the interface. We then compare three common pore geometries, namely honeycomb pores, inverse opal, and materials produced by spinodal decomposition. Finally, we quantify the influence of those three geometries on fluid transport and tracer adsorption. This opens perspectives for the optimization of materials' geometries for applications in dynamic adsorption under fluid flow.

Multiscale adsorption and transport in hierarchical porous materials

This review presents the state-of-the-art of multiscale adsorption and transport in hierarchical porous materials.