Solute Mass Transfer Research Articles

Molecular advection–diffusion through graphene nanopores

Nanoporous graphene promises extremely high flow rates in membrane separation applications owing to its single atom thickness. While sub-nanometer graphene pores are desirable for rejecting ions and small molecules, transport through larger graphene nanopores is relevant in nanofiltration applications and to leakage flow through membrane defects. The permeance of these pores is commonly estimated using continuum transport relationships in graphene membrane modeling, although errors are expected due to sub-continuum behavior that emerges for smaller nanopores. In this paper we perform molecular dynamics simulations to understand the departure of solute advection–diffusion through graphene nanopores from continuum theory. We find that the same diameter dependent effective pore thickness can be used to adjust continuum models for both the net flow rate and solute mass transfer rate to match simulations. The increased resistance to both modes of transport is attributed to reduced molecule mobility in the dense layers of fluid that form on either side of the graphene and within the pore. The results further indicate the extent of deviations from continuum solute mass transfer that can be expected through graphene nanopores, toward more accurate modeling of nanoporous atomically thin membranes.

Mechanism of coalbed methane migration and production based on micro-pore overpressure environment

A complete understanding of the mechanism and characteristics of the migration and output of coalbed methane (CBM) is of great significance for CBM development. For the coal reservoir in a micropore overpressure environment, the “Reservoir inner surface desorption-micropore diffusion-natural fracture seepage” cannot completely describe the CBM production process. To this end, starting from the three stages of CBM production, based on the microporous overpressure environment of coal reservoirs to reveal CBM's migration and production mechanism. The results show that: (1) In the stage of saturated single-phase water flow, CBM was transported by “solution mass transfer”; (2) At the single-phase unsaturated water flow stage, CBM become “microporous drainage”; (3) At the two-phase gas-water flow stage, CBM is transported and produced traditionally.

Mass transfer from a sheared spherical rigid capsule

Solute mass transfer from a spherical fluid-filled rigid capsule subjected to shear flow is studied numerically, while considering unsteady, continuous, and nonuniform boundary conditions on its surface. Here, the capsule acts as a reservoir with its initially encapsulated solute concentration decaying over time. This scenario differs from the classical case study of either constant concentration or constant mass flux at the surface of the particle. The flow and the concentration field are computed using fully three-dimensional lattice Boltzmann simulations, where the fluid-structure two-way coupling is achieved by the immersed boundary method. The effects of the flow and the boundary conditions on mass transfer efficacy are quantified by the Sherwood number (the dimensionless mass transfer coefficient), which is found to increase due to the combined effects of forced convection and the rotation of the capsule. Having continuity of both the concentration and the mass flux on the capsule significantly decreases the Sherwood number as compared to the case with constant and uniform boundary condition. All the obtained results can be applied to heat transfer in the case of cooling an initially hot spherical particle, for which the concentration must be replaced by the temperature and the Sherwood number by the Nusselt number.

Understanding the Importance of Labile Fe(III) during Fe(II)-Catalyzed Transformation of Metastable Iron Oxyhydroxides.

Transformation of metastable Fe(III) oxyhydroxides is a prominent process in natural environments and can be significantly accelerated by the coexisting aqueous Fe(II) (Fe(II)aq). Recent evidence points to the solution mass transfer of labile Fe(III) (Fe(III)labile) as the primary intermediate species of general importance. However, a mechanistic aspect that remains unclear is the dependence of phase outcomes on the identity of the metastable Fe(III) oxyhydroxide precursor. Here, we compared the coupled evolution of Fe(II) species, solid phases, and Fe(III)labile throughout the Fe(II)-catalyzed transformation of lepidocrocite (Lp) versus ferrihydrite (Fh) at equal Fe(III) mass loadings with 0.2-1.0 mM Fe(II)aq at pH = 7.0. Similar to Fh, the conversion of Lp to product phases occurs by a dissolution-reprecipitation mechanism mediated by Fe(III)labile that seeds the nucleation of products. Though for Fh we observed a transformation to goethite (Gt), accompanied by the transient emergence and decline of Lp, for initial Lp we observed magnetite (Mt) as the main product. A linear correlation between the formation rate of Mt and the effective supersaturation in terms of Fe(III)labile concentration shows that Fe(II)-induced transformation of Lp into Mt is governed by the classical nucleation theory. When Lp is replaced by equimolar Gt, Mt formation is suppressed by opening a lower barrier pathway to Gt by heterogeneous nucleation and growth on the added Gt seeds. The collective findings add to the mechanistic understanding of factors governing phase selections that impact iron bioavailability, system redox potential, and the fate and transport of coupled elements.

Facile Synthesis of MOFs-Templated Carbon Aerogels with Enhanced Tetracycline Adsorption Performance

Three-dimensional aerogels have great potential for antibiotic removal from aqueous solution due to their excellent solution mass transfer channels and special morphology. Herein, the metal ions were bound with alginate to form alginate-Fe, alginate-Cu, and alginate-Fe-Cu hydrogels, then they were used as nucleation sites for metal organic framework (MOF) growth to obtain MAlgs gels, respectively. Considering the aqueous environmental stability of MOFs particles, the alginate and MOF particles in MAlgs aerogels were pyrolyzed as templates to obtain the derived carbon aerogel CMAlgs. The results showed that the adsorption capacity of MAlgs-Fe-Cu aerogel was higher than that of MAlg-Cu and MAlg-Fe aerogels, up to ~130 mg·g−1. The adsorption performance of carbon aerogel CMAlg-Cu decreased obviously because of the decrease of pore size and oxygen-containing functional groups. The adsorption process is a combination of physical adsorption and chemical adsorption. In addition, CMAlgs aerogels exhibit better recyclability than MAlgs aerogels. This work provides a new strategy for fabricating MOFs-templated in-situ grown carbon aerogels for water purification.

SPONTANEOUS ORDERING OF CHEMOCONVECTIVE FINGERING NEAR AN INTERFACE IN A REACTING SOLUTION

In this work, we develop a mathematical model of buoyancy-driven mass transfer in an aqueous alkali solution filling a Hele-Shaw cell. The upper boundary of the layer is free and nondeformable. The acid flux through the interface is determined by the constant value of the acid concentration set at the interface. Thus, the neutralization reaction proceeds near the interface and is accompanied by the formation of salt and water. We neglect the heat release of the exothermic reaction and the Marangoni effect, assuming that all substances do not exhibit surface activity. The ratio of the initial concentrations of acid and base is the control parameter of the system, which unambiguously determines the onset of various types of chemoconvection. The described model reproduces the main properties of a two-layer system of immiscible reacting liquids if the interface is impermeable to base and salt. Based on recent experimental observations, we modify the equation of solvent motion, introducing an integral term that describes the reaction-induced production of water. We demonstrate that such an assumption drastically changes the density distribution in the system because of the depletion of solutions in the reaction zone. In particular, this effect leads to spontaneous stabilization of fingering process in the parameter range, where numerical simulation of the standard model predicts the development of disordered Rayleigh-Taylor convection. Finally, we present a bifurcation diagram for the ratio of initial concentrations. The obtained results are in good agreement with the experimental data.

Mass Advection–Diffusion in Creeping Flow Through an Orifice Plate: A Model for Nanoporous Atomically Thin Membranes

Abstract Continuum transport equations are commonly applied to nanopores in atomically thin membranes for simple modeling. Although these equations do not apply for nanopores approaching the fluid or solute molecule size, they can be reasonably accurate for larger nanopores. Relatively large graphene nanopores have applications in small particle filtration and appear as unwanted defects in large-area membranes. Solute transport rates through these nanopores determine the rejection performance of the membrane. Atomically thin membranes commonly operate in a regime where advection and diffusion both contribute appreciably to transport. Solute mass transfer rates through larger nanopores have previously been modeled by adding continuum estimates for pure diffusion and pure advection through an infinitesimally thick orifice plate, as if the separate contributions were independent. We show here that estimating the transport rate in this way is accurate to within 30%. We further derive an expression for the net mass transfer rate in advection–diffusion through an infinitesimal thickness orifice plate at low Reynolds numbers that is accurate to within 1% for positive Péclet numbers (where diffusion is in the same direction as advection) and applies for negative Péclet numbers as well. Based on our expression, we devise an equation for the net mass transfer rate in creeping flow through orifice plates of arbitrary thickness that matches finite volume calculations to within 3% for positive Péclet numbers. These simple but accurate analytical equations for mass transfer rates in creeping flow through an orifice plate are useful tools in constructing approximate transport models.

Mass transfer from small spheroids suspended in a turbulent fluid

By coupling direct numerical simulation of homogeneous isotropic turbulence with a localised solution of the convection–diffusion equation, we model the rate of transfer of a solute (mass transfer) from the surface of small, neutrally buoyant, axisymmetric, ellipsoidal particles (spheroids) in dilute suspension within a turbulent fluid at large Péclet number, $\textit {Pe}$ . We observe that, at $\textit {Pe} = O(10)$ , the average transfer rate for prolate spheroids is larger than that of spheres with equivalent surface area, whereas oblate spheroids experience a lower average transfer rate. However, as the Péclet number is increased, oblate spheroids can experience an enhancement in mass transfer relative to spheres near an optimal aspect ratio $\lambda \approx 1/4$ . Furthermore, we observe that, for spherical particles, the Sherwood number $\textit {Sh}$ scales approximately as $\textit {Pe}^{0.26}$ over $\textit {Pe} = 1.4\times 10^{1}$ to $1.4\times 10^{4}$ , which is below the $\textit {Pe}^{1/3}$ scaling observed for inertial particles but consistent with available experimental data for tracer-like particles. The discrepancy is attributed to the diffusion-limited temporal response of the concentration boundary layer to turbulent strain fluctuations. A simple model, the quasi-steady flux model, captures both of these phenomena and shows good quantitative agreement with our numerical simulations.

Ice Templating Soft Matter: Fundamental Principles and Fabrication Approaches to Tailor Pore Structure and Morphology and Their Biomedical Applications.

Porous scaffolds are widely used in biomedical applications where pore size and morphology influence a range of biological processes, including mass transfer of solutes, cellular interactions and organization, immune responses, and tissue vascularization, as well as drug delivery from biomaterials. Ice templating, one of the most widely utilized techniques for the fabrication of porous materials, allows control over pore morphology by controlling ice formation in a suspension of solutes. By fine-tuning freezing and solute parameters, ice templating can be used to incorporate pores with tunable morphological features into a wide range of materials using a simple, accessible, and scalable process. While soft matter is widely ice templated for biomedical applications and includes commercial and clinical products, the principles underpinning its ice templating are not reviewed as well as their inorganic counterparts. This review describes and critically evaluates fundamental principles, fabrication and characterization approaches, and biomedical applications of ice templating in polymer-based biomaterials. It describes the utility of porous scaffolds in biomedical applications, highlighting biological mechanisms impacted by pore features, outlines the physical and thermodynamic mechanisms underpinning ice templating, describes common fabrication setups, critically evaluates complexities of ice templating specific to polymers, and discusses future directions in this field.

Effect of nanoparticles on interfacial mass transfer characteristics and mechanisms in liquid-liquid extraction by molecular dynamics simulation

The addition of nanoparticles is a promising strategy to intensify interfacial mass transfer, which possess a wide array of potential applications in considerable industrial processes. In order to elucidate interfacial mass transfer characteristics and mechanisms, the effects of functional group, particle size and volume fraction of silica nanoparticle on dimethyl sulfoxide (DMSO) transfer across the water/hexane interface were investigated by molecular dynamics simulation. The results manifested that hydrophilic nanoparticles are beneficial to mass transfer enhancement. Due to the increase of mass transfer path and steric hindrance of nanoparticles at the liquid-liquid interface, however, hydrophobic and amphiphilic nanoparticles inhibit solute mass transfer. Moreover, the smallest size nanoparticle at the maximum concentration of 10 vol% leads to the highest enhancement, namely the decrease of mass transfer resistance by 36%. By analyzing the mean square displacement and size effect of nanoparticle, it is found that Brownian motion rather than micro-convection is probably the dominant mechanism.

Experimental research on heat and mass transfer characteristics of membrane energy accumulator used in solar refrigeration

• Hollow fiber and flat membrane energy accumulators are designed and tested. • Compared with HFMEAs, FMEAs have higher mass transfer efficiency. • The mass transfer mechanism in MEA is analyzed. • Effects of thermodynamic characters on solution mass transfer are obtained. An experimental platform was set up to test the heat and mass transfer performance inside the membrane energy accumulator (MEA). Hollow fiber MEAs (HFMEAs) and flat MEAs (FMEAs) were designed and tested. Compared with HFMEAs, FMEAs have higher mass transfer efficiency. The average mass transfer speed of the water vapor increased by 108.34% when the evaporation temperature increased from 4.5 °C to 12.3 °C for HFMEA. When the evaporation temperature increased from 7.88 °C to 19.51 °C, the change in mass fraction of lithium bromide (LiBr) in FMEA increased by 62.36%. Compared with a 60% solution, the average mass transfer rate of water vapor molecules in a 70% LiBr solution increased by 49.83% for FMEA. In addition, the water vapor absorbed by the 70% LiBr solution in 30 min increased by 18.63% compared to that of the 60% solution for FMEA. The effect of the initial solution temperature on the mass transfer rate is closely related to the mass fraction of LiBr. Both the mass transfer rate and crystallization melting process of the LiBr solution will accelerate by increasing the initial mass fraction and evaporation temperature.

Multi-physics analysis of the galvanic corrosion of Mg-steel couple under the influence of time-dependent anisotropic deposition film

Abstract The anisotropic deposit film formed during the galvanic corrosion can impede the mass transfer of the involved species, thereby affecting the electro-chemical behavior and the evolution of galvanic corrosion. The limitations of experimental studies in the spatial-temporal scales restrict a deeper understanding of the corrosion mechanism, which can be complemented by numerical simulation. A multi-physics coupled model is proposed in this work to systematically investigate the temporal and spatial evolution of galvanic corrosion of the Mg-steel couple with the growing anisotropic deposition layer. By utilizing the multi-physics field coupled technique, various coupled physical-chemical processes underlying the corrosion behavior are built into the model, including chemical reactions, ionic mass transfer in the bulk solution and the deposition layer, interfacial reaction, deposition of corrosion products as well as the morphological transitions caused by metal dissolution and deposition. In particular, the anisotropic deposit film is considered to be a porous layer with a porosity varying in time and space as the corrosion evolves. The predicted corrosion morphology by this model is better than the previous models. The coupled relationship between the electrochemical behavior (e.g., electrode reaction kinetics, current density, surface potential) and the physical processes (e.g., ionic transport, geometric evolution of metal surface and film interface) is revealed. The results indicate that a porous deposition layer with a denser inner layer and a loose outer layer is generated, leading to more significant inhibition of mass transfer in the inner layer than the outer layer. The anisotropism of the deposition layer results in a non-uniform conductivity distribution and a discontinuous current density distribution in the electrolyte. The current density on the electrode surface is inhibited by the deposition layer and the variation in the cathode/anode area ratio during the corrosion process. The competition between the transport process and the electrochemical reaction determines the spatial-temporal evolution of the ion concentration.

Butterfly Baffles Enhanced Solution Mixing and Mass Transfer to Improve Microalgae Growth in Double Column Photobioreactor

Butterfly Baffles Enhanced Solution Mixing and Mass Transfer to Improve Microalgae Growth in Double Column Photobioreactor

Photocatalytic Destruction of Caffeine on Sepiolite-Supported TiO2 Nanocomposite

The study is about the degradation of a common pharmaceutical and personal care product (PPCP) caffeine by photocatalysis under UV–visible light using pristine TiO2 (P-25) and a lab-made nanocomposite of sepiolite–TiO2. It was found that the dark adsorption of caffeine on P-25 was insignificant, but considerably high on the nanocomposite, owing to the high porosity and unique structure of sepiolite. The degradation of the compound in the presence of P-25 and Sep–TiO2 followed the pseudo-first order and exponential decay kinetics, with a rate constant of 0.12 min−1 and 0.50 min−1, respectively. The efficiency of both catalysts for carbon mineralization was better at acidic pH, but that of the nanocomposite was significantly higher at all pH than that of the unmodified P-25 (36.1 against 9.6% at pH 6.0). The loading of TiO2 on sepiolite was an important factor in the activity of the catalyst, as the maximum activity was observed at a loading ratio of 12.5 mmol per g sepiolite, which decreased at higher ratios of the semiconductor to sepiolite. Exposure of the treated samples to high-frequency ultrasound at pH 6 was found to enhance the degree of mineralization to 65.1 and 52.1% in the presence of the nanocomposite and P-25, respectively. The outcome was attributed to the unique properties of ultrasound for the cleaning of solid surfaces, for enhancing the mass transfer of solutes to heterogeneous interfaces, and for generation of excess hydroxyl radicals. Finally, the nanocomposite was found to be considerably stable, as it was easily recovered and used four times without a significant loss in activity.

Experimental and numerical study of liquid–liquid interphase mass transfer in a pilot-scale extraction column

Liquid–liquid interphase mass transfer was experimentally and numerically studied in a pilot-scale pulsed disc-and-doughnut column (PDDC). The mass transfer coefficients, which were determined by analyzing experimental data through a transient axial dispersion model, increased from 2.27 × 10–6 to 3.06 × 10–6 m/s with an increase in the pulsation intensity from 0.0065 to 0.0105 m/s. The Euler–Euler two-fluid model was applied to simulate the interphase mass transfer in the PDDC. Three key issues, including the formulation of governing equations, selection of the mesh size, and determination of the mass transfer coefficient, which significantly influence the numerical accuracy, were discussed in detail. The simulated concentration profiles accorded well with that predicted by the experimentally verified mass transfer model. Local mass transfer performance was uncovered based on simulation results to elucidate the spatial and temporal variation of the solute concentrations, hold-up, and mass transfer coefficients in the PDDC.

Effect of agitation on batch adsorption process facilitated by using nanobubbles

Pb2+ adsorption onto activated carbon was studied as a function of the different liquid medium during batch adsorption process without shaking/agitation of flasks (where adsorbate and adsorbent coexist). As liquid medium deionized water (DW) enhanced with gases bulk nanobubbles (bNBs) was used. The adsorbent material used was activated carbon from potato peels. The maximum Pb2+ adsorption capacity (Qm) was 9 mg/g in the case of adsorption process in DW without agitation, whereas the respective Qm was 94 mg/g by using DW-bNBs as medium without agitation. It was also found that Qm increased to 171 mg/g in the adsorption process with DW-bNBs and agitation (150 rpm). This finding was the start point of a new experimental design where after re-agitation (intense shaking of 225 rpm) of the respective experimental case (94 mg/g), the final Qm was 163 mg/g i.e. very close to the one corresponding to simultaneous adsorption and agitation from the beginning. The results are analyzed and discussed intensively to lead in several important implications on the influence of bNBs to the bulk solute mass transfer. Based on our experimental equilibrium data a modified-Langmuir equation was developed, applied and proposed so as to better simulate the whole (complicated) process.

Performance Assessment of an NH3/LiNO3 Bubble Plate Absorber Applying a Semi-Empirical Model and Artificial Neural Networks

In this study, ammonia vapor absorption with NH3/LiNO3 was assessed using correlations derived from a semi-empirical model, and artificial neural networks (ANNs). The absorption process was studied in an H-type corrugated plate absorber working in bubble mode under the conditions of an absorption chiller machine driven by low-temperature heat sources. The semi-empirical model is based on discretized heat and mass balances, and heat and mass transfer correlations, proposed and developed from experimental data. The ANN model consists of five trained artificial neurons, six inputs (inlet flows and temperatures, solution pressure, and concentration), and three outputs (absorption mass flux, and solution heat and mass transfer coefficients). The semi-empirical model allows estimation of temperatures and concentration along the absorber, in addition to overall heat and mass transfer. Furthermore, the ANN design estimates overall heat and mass transfer without the need for internal details of the absorption phenomenon and thermophysical properties. Results show that the semi-empirical model predicts the absorption mass flux and heat flow with maximum errors of 15.8% and 12.5%, respectively. Maximum errors of the ANN model are 10.8% and 11.3% for the mass flux and thermal load, respectively.

Mixing Ratios With Age: Application to Preasymptotic One‐Dimensional Equilibrium Bimolecular Reactive Transport in Porous Media

AbstractAnalysis of reactive transport in natural and engineered porous media has benefited from the concept of mixing ratios, in particular as a basis for mathematical separation of transport and reactions processes. General use of solute age has also been recently explored as a way to describe solute mass transfer and/or as a proxy for reaction extent. Age here is defined as exposure time to the flow field. Pairing these concepts, we develop mixing ratio models that are structured on age. One‐dimensional transport is cast in terms of age‐structured mixing ratios in general and compared with conventional formulations of mixing ratio models, demonstrating that age is often a more natural independent variable than absolute time. Using this modeling framework, we then apply age‐structured mixing ratios to the problem of mixing‐limited reactive transport in one‐dimension by explicitly considering unmixed and mixed phases. In order to address mixing limitations under the entirety of transport including the preasymptotic dispersion timeframe, we use the same age variable to define the dispersion coefficient value in a local formulation of transport. Establishing an age‐dependent dispersion coefficient allows simulation of the whole transport time including both preasymptotic and asymptotic dispersion conditions with one model. In our application we explore use of this modeling approach to both synthetic preasymptotic data and experimental asymptotic data pertaining to one famous experiment.

Enhancing microalgal biomass productivity with an optimized flow field generated by double paddlewheels in a flat plate photoreactor with CO2 aeration based on numerical simulation

Computational fluid dynamics were used to analyze the flash light effect and CO2 bubble behavior in an optimized flow field generated by double paddlewheels in a flat plate photoreactor to enhance microalgal biomass productivity. The increased D/w ratio significantly enhanced the average turbulent kinetic energy and flash cycle frequency. However, the effects became weak when the D/w ratio was over 0.67. Appliance of double paddlewheels increased flash cycle frequency from 0.035 to 0.121 Hz and increased light time ratio from 8.3% to 31.5%. Meanwhile, the bubble dynamic behavior was characterized using population balance model. The average bubble size reduced by 24.4% and the bubble rising velocity reduced by 10.6%, which facilitated CO2 mixing and mass transfer in microalgal solution. Therefore, biomass accumulation of microalgae Chlorella in the photoreactor with double paddlewheels increased by 62.3% under 15% CO2.

Laser-based 3D microscopic gauging of soil aggregate coating thickness and volume

In structured soils, clay-organic coatings are spatially distributed along macropore surfaces. Information on thickness and volume of coating material is essential for macropore-matrix mass exchange of water and solutes. However, their determination is difficult and fraught with uncertainty due to irregular shapes of macropore surfaces. The objective of this study was to test the use of a three-dimensional (3D) confocal laser scanning microscope for gauging soil macropore coatings. For this test, coating material was manually separated from the surface of intact soil clods (5 cm edge length) sampled from Bt horizons (with illuvial clay) of till-derived and loess-derived Haplic Luvisols. The resulting coating thicknesses ranged between approx. 0.1 and 0.5 mm and volumes between 0.057 and 2.9 mm3 with mean densities of 1.96 g cm−3 for loess-derived and 2.67 g cm−3 for till-derived coatings. The 3D laser microscopic method yielded data based on micro-topographic information. The key benefits of the 3D confocal laser scanning microscope are the information on the mm-scale spatial distribution of coating thickness and bulk density. These additional parameters of the clod surface or aggregate micro-topography can be useful for improved quantification of accessibility of sorption surfaces and for describing macropore-matrix mass transfer of reactive solutes.