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

A novel magnetic Fe3O4/cellulose nanofiber/polyethyleneimine/thiol-modified montmorillonite aerogel for efficient removal of heavy metal ions: Adsorption behavior and mechanism study

To efficiently remove heavy metals from wastewater, designing an adsorbent with high adsorption capacity and ease of recovery is necessary. This paper presents a novel magnetic hybridized aerogel, Fe3O4/cellulose nanofiber/polyethyleneimine/thiol-modified montmorillonite (Fe3O4/CNF/PEI/SHMMT), and explores its adsorption performance and mechanism for Pb2+, Cu2+, and Cd2+ in aqueous solutions. The hybrid aerogel has a slit-like porous structure and numerous exposed active sites, which facilitates the uptake of metal ions by adsorption. Pb2+, Cu2+, and Cd2+ adsorption by the hybridized aerogel followed the second-order kinetics and the Langmuir isotherm model, the maximum adsorption of Pb2+, Cu2+, and Cd2+ at 25 °C, pH = 6, 800 mg/L was 429.18, 381.68 and 299.40 mg/g, respectively. The adsorption process was primarily attributed to monolayer chemical adsorption, a spontaneous heat-absorption reaction. FTIR, XPS and DFT studies confirmed that the adsorption mechanisms of Fe3O4/CNF/PEI/SHMMT on Pb2+, Cu2+, and Cd2+ were mainly chelation, coordination, and ion exchange. The lowest adsorption energy of Pb2+ on the hybrid aerogel was calculated to be -2.37 Ha by DFT, which indicates that the sample has higher adsorption affinity and preferential selectivity for Pb2+. After 5 cycles, the adsorption efficiency of the aerogel was still >85 %. The incorporation of Fe3O4 improved the mechanical properties of the aerogel. The Fe3O4/CNF/PEI/SHMMT has fast magnetic responsiveness, and it is easy to be separated and recovered after adsorption, which is a promising potential for the treatment of heavy metal ions.

Fluid-Solid Reaction in Porous Media as a Chaotic Restart Process

Chemical and biological reactions at fluid-solid interfaces are central to a broad range of porous material applications and research. Pore-scale solute transport limitations can reduce reaction rates, with marked consequences for a wide spectrum of natural and engineered processes. Recent advances show that chaotic mixing occurs spontaneously in porous media, but its impact on surface reactions is unknown. We show that pore-scale chaotic mixing significantly increases reaction efficiency compared to nonchaotic flows. We find that reaction rates are well described in terms of diffusive first-passage times of reactants to the solid interface subjected to a stochastic restart process resulting from Lagrangian chaos. Under chaotic mixing, the shear layer at no-slip interfaces sets the restart rate and leads to a characteristic scaling of reaction efficiency with Péclet number, in excellent agreement with numerical simulations. Reaction rates are insensitive to the flow topology as long as flow is chaotic, suggesting the relevance of this process to a broad range of porous materials.

Mixing Controlled Adsorption at the Liquid-Solid Interfaces in Unsaturated Porous Media

The unsaturated zone, located between the soil surface and the phreatic level, plays an important role in defining the fate of any substance entering the subsoil. In addition to the processes of flow and transport taking place in the liquid phase, surface reactions such as adsorption to the solid phase may occur and increase the residence time of the substance entering the system. In this study, we aim to understand the pore-scale mechanisms that control adsorption in unsaturated systems. We combine 2D pore-scale experimental images with numerical simulations to analyze flow, transport, and adsorption under different liquid saturation degrees. We demonstrate the role of mixing on adsorption at the liquid-solid interfaces by analyzing the deformation in time of a pulse-injected surfactant. We also analyze the impact of the isotherm functional shape and the inclusion of the liquid-gas interfaces as adsorption sites on this surface reaction. The enhancement of mixing as saturation decreases is accompanied by a reduction in the amount of adsorbed mass, located mainly along preferential flow paths, where the solute is primarily transported. For the same isotherm, a nonlinear behavior of adsorption as a function of liquid saturation has been observed. This is explained by the nonlinear variation of the volume fraction of liquid behaving as preferential path or stagnation zone as liquid saturation decreases, despite the linear decrease in the surface area of solids accessible for adsorption.

Supplementary Information

The online version contains supplementary material available at 10.1007/s11242-022-01747-x.

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.

Modification Strategies of Kapok Fiber Composites and Its Application in the Adsorption of Heavy Metal Ions and Dyes from Aqueous Solutions: A Systematic Review

Kapok fiber (Ceiba pentandra) belongs to a group of natural fibers that are mainly composed of cellulose, lignin, pectin, and small traces of inorganic compounds. These fibers are lightweight with hollow tubular structure that is easy to process and abundant in nature. Currently, kapok fibers are used in industry as filling material for beddings, upholstery, soft toys, and nonwoven materials. However, kapok fiber has also a potential application in the adsorptive removal of heavy metal ions and dyes from aqueous systems. This study aims to provide a comprehensive review about the recent developments on kapok fiber composites including its chemical properties, wettability, and surface morphology. Effective and innovative kapok fiber composites are analyzed with the help of characterization tools such as scanning electron microscopy, X-ray diffraction, X-ray photoelectron spectroscopy, thermogravimetric analysis, Fourier transform infrared spectroscopy, energy-dispersive X-ray spectroscopy, and Brunauer-Emmett-Teller analysis. Different pre-treatment methods such as alkali and acid pre-treatment, oxidation pre-treatment, and Fenton reaction are discussed. These techniques are applied to enhance the hydrophilicity and to generate rougher fiber surfaces. Moreover, surface modification and synthesis of kapok fiber-based composites and its environmental applications are examined. There are various methods in the fabrication of kapok fiber composites that include chemical modification and polymerization. These procedures allow the kapok fiber composites to have higher adsorption capacities for selective heavy metal and dye removal.

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 new metric for relating macroscopic chromatograms to microscopic surface dynamics: the distribution function ratio (DFR)

Heterogeneous stationary phase chemistry causes chromatographic tailing that lowers separation efficiency and complicates optimizing mobile phase conditions. Model-free metrics are attractive for assessing optimal separation conditions due to the low quantity of information required, but often do not reveal underlying mechanisms that cause tailing, for example, heterogeneous retention modes. We report a new metric, which we call the Distribution Function Ratio (DFR), based on a graphical comparison between the chromatogram and Gaussian cumulative distribution functions, achieving correspondence to ground truth surface dynamics with a single chromatogram. Using a Monte Carlo framework, we show that the DFR can predict the prevalence of heterogeneous retention modes with high precision when the relative desorption rate between modes is known, as in during surface dynamics experiments. Ground truth comparisons reveal that the DFR outperforms both the asymmetry factor and skewness by yielding a one-to-one correspondence with heterogeneous retention mode prevalence over a broad range of experimentally realistic values. Perhaps of more value, we illustrate that the DFR, when combined with the asymmetry factor and skewness, can estimate microscopic surface dynamics, providing valuable insights into surface chemistry using existing chromatographic instrumentation. Connecting ensemble results to microscopic quantities through the lens of simulation establishes a new chemistry-driven route to measuring and advancing separations.

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.

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.