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Concept: Mass transfer


We have suggested a novel approach for classification of flow methods according to the conditions under which the mass transfer processes and chemical reactions take place in the flow mode: dispersion-convection flow methods (1) and forced-convection flow methods (2). The first group includes continuous flow analysis, flow injection analysis, all injection analysis, sequential injection analysis, sequential injection chromatography, cross injection analysis, multicommutated flow analysis, multisyringe flow injection analysis, multi-pumping flow systems, loop flow analysis and simultaneous injection effective mixing flow analysis. The second group includes segmented flow analysis, zone fluidics, flow batch analysis, sequential injection analysis with a mixing chamber, stepwise injection analysis and multicommutated stepwise injection analysis. The offered classification allows to systematize a large number of the flow methods. Recent development and application of dispersion-convection flow methods and forced-convection flow methods are presented. [Figure: see text].

Concepts: Series, According to Jim, Chemical substance, AutoAnalyzer, Mass transfer, Limit of a sequence, Chemical engineering, Chemical reaction


One of the targets of the experiment IVIDIL (Influence Vibrations on Diffusion in Liquids) conducted on-board ISS was to study the response of binary mixtures to vibrational forcing when the density gradient results from thermal and compositional variations. Compositional variations were created by the Soret effect and can strengthen or weaken the overall density gradient and, consequently, the response to vibrational forcing. We present the results of two experimental runs conducted on-board ISS in the frame of the experiment IVIDIL for low and strong vibrational forcing. The experimental observations revealed that a significant mean flow is set within 2 minutes after imposing vibrations and later in time it varies weakly and slowly due to the Soret effect. A mathematical model has been developed to compute the thermal and concentration fields in the experiment IVIDIL and verify the accuracy of picture processing based on the classical approach used in non-convective systems with the Soret effect. The effect of temperature and concentrations perturbations by joint action of vibrational convection and Soret effect on long time scale are carefully examined. The model demonstrates that image processing used for non-convective systems is suitable for the systems with vibration-affected thermodiffusion experiment.

Concepts: Experimental physics, Weak interaction, Diffusion, Fundamental physics concepts, Mathematics, Mass transfer, Convection, Temperature


The intense interactions of guest molecules with the pore walls of nanoporous materials is the subject of continued fundamental research. Stimulated by their thermal energy, the guest molecules in these materials are subject to a continuous, irregular motion, referred to as diffusion. Diffusion, which is omnipresent in nature, influences the efficacy of nanoporous materials in reaction and separation processes. The recently introduced techniques of microimaging by interference and infrared microscopy provide us with a wealth of information on diffusion, hitherto inaccessible from commonly used techniques. Examples include the determination of surface barriers and the sticking coefficient’s analogue, namely the probability that, on colliding with the particle surface, a molecule may continue its diffusion path into the interior. Microimaging is further seen to open new vistas in multicomponent guest diffusion (including the detection of a reversal in the preferred diffusion pathways), in guest-induced phase transitions in nanoporous materials and in matching the results of diffusion studies under equilibrium and non-equilibrium conditions.

Concepts: Matter, Fundamental physics concepts, Kinetic theory, Chemical substance, Chemical engineering, Thermodynamics, Mass transfer, Separation process


Alkali exchanged SSZ-13 adsorbents were investigated for their applicability in separating N2 from CO2 in flue gas streams using a dynamic breakthrough method. In contrast to IAST calculations based on equilibrium isotherms, K+ exchanged SSZ-13 was found to yield the best N2 productivity, comparable to Ni-MOF-74, under dynamic conditions where diffusion properties play a significant role. This was attributed to the selective, partial blockage of access to the chabazite cavities, enhancing the separation potential in a 15/85 CO2/N2 binary gas mixture.

Concepts: Partial differential equation, Separation, Mass transfer, PH, Nitrogen, Chemical engineering, Carbon dioxide, Adsorption


We present a general mechanistic model of mass diffusion for a composite sphere placed in a large ambient medium. The multi-layer problem is described by a system of diffusion equations coupled via interlayer boundary conditions such as those imposing a finite mass resistance at the external surface of the sphere. While the work is applicable to the generic problem of heat or mass transfer in a multi-layer sphere, the analysis and results are presented in the context of drug kinetics for desorbing and absorbing spherical microcapsules. We derive an analytical solution for the concentration in the sphere and in the surrounding medium that avoids any artificial truncation at a finite distance. The closed-form solution in each concentric layer is expressed in terms of a suitably-defined inverse Laplace transform that can be evaluated numerically. Concentration profiles and drug mass curves in the spherical layers and in the external environment are presented and the dependency of the solution on the mass transfer coefficient at the surface of the sphere analyzed.

Concepts: Gaussian curvature, Sphere, Injective function, Transport phenomena, Mass transfer, Torus, Real projective plane, Laplace transform


Although crucial for designing separation processes little is known experimentally about multi-component adsorption isotherms in comparison with pure single components. Very few binary mixture adsorption isotherms are to be found in the literature and information about isotherms over a wide range of gas-phase composition and mechanical pressures and temperature is lacking. Here, we present a quasi-one-dimensional statistical mechanical model of binary mixture adsorption in metal-organic frameworks (MOFs) treated exactly by a transfer matrix method in the osmotic ensemble. The experimental parameter space may be very complex and investigations into multi-component mixture adsorption may be guided by theoretical insights. The approach successfully models breathing structural transitions induced by adsorption giving a good account of the shape of adsorption isotherms of CO2and CH4adsorption in MIL-53(Al). Binary mixture isotherms and co-adsorption-phase diagrams are also calculated and found to give a good description of the experimental trends in these properties and because of the wide model parameter range which reproduces this behaviour suggests that this is generic to MOFs. Finally, a study is made of the influence of mechanical pressure on the shape of CO2and CH4adsorption isotherms in MIL-53(Al). Quite modest mechanical pressures can induce significant changes to isotherm shapes in MOFs with implications for binary mixture separation processes.This article is part of the theme issue ‘Modern theoretical chemistry’.

Concepts: Chemistry, Adsorption, Mass transfer, Mixture, Experiment, Chemical engineering, Thermodynamics, Separation process


Sequestered mass in low permeability zones has been increasingly recognized as an important source of organic chemical contamination that acts to sustain downgradient plume concentrations above regulated levels. However, few modeling studies have investigated the influence of this sequestered mass and associated (coupled) mass transfer processes on plume persistence in complex dense nonaqueous phase liquid (DNAPL) source zones. This paper employs a multiphase flow and transport simulator (a modified version of the modular transport simulator MT3DMS) to explore the two- and three-dimensional evolution of source zone mass distribution and near-source plume persistence for two ensembles of highly heterogeneous DNAPL source zone realizations. Simulations reveal the strong influence of subsurface heterogeneity on the complexity of DNAPL and sequestered (immobile/sorbed) mass distribution. Small zones of entrapped DNAPL are shown to serve as a persistent source of low concentration plumes, difficult to distinguish from other (sorbed and immobile dissolved) sequestered mass sources. Results suggest that the presence of DNAPL tends to control plume longevity in the near-source area; for the examined scenarios, a substantial fraction (43.3-99.2%) of plume life was sustained by DNAPL dissolution processes. The presence of sorptive media and the extent of sorption non-ideality are shown to greatly affect predictions of near-source plume persistence following DNAPL depletion, with plume persistence varying one to two orders of magnitude with the selected sorption model. Results demonstrate the importance of sorption-controlled back diffusion from low permeability zones and reveal the importance of selecting the appropriate sorption model for accurate prediction of plume longevity. Large discrepancies for both DNAPL depletion time and plume longevity were observed between 2-D and 3-D model simulations. Differences between 2- and 3-D predictions increased in the presence of sorption, especially for the case of non-ideal sorption, demonstrating the limitations of employing 2-D predictions for field-scale modeling.

Concepts: Zone, Plume, Computer graphics, Chemistry, Diffusion, Mass transfer, 3D computer graphics, Concentration


A two-step solution based on the boundary conditions of Crank’s equations for mass transfer in a film was developed. Three driving factors, the diffusion (D), partition (Kp,f) and convective mass transfer coefficients (h), govern the sorption and/or desorption kinetics of migrants from polymer films. These three parameters were simultaneously estimated. They provide in-depth insight into the physics of a migration process. The first step was used to find the combination of D, Kp,fand h that minimized the sums of squared errors (SSE) between the predicted and actual results. In step 2, an ordinary least square (OLS) estimation was performed by using the proposed analytical solution containing D, Kp,fand h. Three selected migration studies of PLA/antioxidant-based films were used to demonstrate the use of this two-step solution. Additional parameter estimation approaches such as sequential and bootstrap were also performed to acquire a better knowledge about the kinetics of migration. The proposed model successfully provided the initial guesses for D, Kp,fand h. The h value was determined without performing a specific experiment for it. By determining h together with D, under or overestimation issues pertaining to a migration process can be avoided since these two parameters are correlated.

Concepts: Convection, Transport phenomena, Statistics, Binomial coefficient, Diffusion, Mass transfer coefficient, Estimation theory, Mass transfer


Motivated by important applications in materials science and geophysics, we consider the steady-state growth of anisotropic needle-like dendrites in undercooled binary mixtures with a forced convective flow. We analyse the stable mode of dendritic evolution in the case of small anisotropies of growth kinetics and surface energy for arbitrary Péclet numbers andn-fold symmetry of dendritic crystals. On the basis of solvability and stability theories, we formulate a selection criterion giving a stable combination between dendrite tip diameter and tip velocity. A set of nonlinear equations consisting of the solvability criterion and undercooling balance is solved analytically for the tip velocityVand tip diameterρof dendrites withn-fold symmetry in the absence of convective flow. The case of convective heat and mass transfer mechanisms in a binary mixture occurring as a result of intensive flows in the liquid phase is detailed. A selection criterion that describes such solidification conditions is derived. The theory under consideration comprises previously considered theoretical approaches and results as limiting cases. This article is part of the theme issue ‘From atomistic interfaces to dendritic patterns’.This article is part of the theme issue ‘From atomistic interfaces to dendritic patterns’.

Concepts: Anisotropy, Dendrite, Diffusion, Fluid dynamics, Mass transfer, Heat, Convection, Fundamental physics concepts


Phenol recovery from phenol-laden saline wastewater plays an important role in the waste reclamation and pollution control. A membrane aromatic recovery system-like membrane contactor (MARS-like membrane contactor) was set up in this study using electrospun polydimethylsiloxane/polymethyl methacrylate (PDMS/PMMA) membrane with 0.0048 m2effective area to separate phenol from saline wastewater. Phenol and water contact angles of 0° and 162° were achieved on this membrane surface simultaneously, indicating its potential in the separation of phenol and water-soluble salt. Feed solution (500 mL) of 0.90 L/h and receiving solution (500 mL) of 1.26 L/h were investigated to be the optimum conditions for phenol separation, which corresponds to the employed Reynolds number of 14.6 and 20.5. During 108-h continuous separation for feed solution (2.0 g/L phenol, 10.0 g/L NaCl) under room temperature (20 °C), 42.6% of phenol was recycled in receiving solution with a salt rejection of 99.95%. Meanwhile, the mean phenol mass transfer coefficient (Kov) was 6.7 × 10-7 m s-1. As a membrane-based process, though the permeated phenol increased with the increase of phenol concentration in feed solution, the phenol recovery ratio was determined by the membrane properties rather than the pollutant concentrations. Phenol was found to permeate this membrane via adsorption, diffusion and desorption, and therefore, the membrane fouling generated from pore blockage in other membrane separation processes was totally avoided.

Concepts: Analytical chemistry, Pollution, Transport phenomena, Solution, Separation process, Concentration, Mass transfer, Chemical engineering