Pore morphological identification of hydrotalcite from nitrogen adsorption

The characteristic energy of nitrogen adsorption in a meso-porous hydrotalcite at 77 K demonstrates the fractality over wider range of pore sizes including meso and macro-pores. More irregular, wider pore-size distribution exhibits higher adsorption potential than that with more regular, narrower pore-size distribution. The changes in differential molar entropy during the adsorption indicate that an irreversibly chaotic process associated with transition from a disordered gaseous state to a more ordered adsorbed state occurs. The differential entropy of adsorption decreases at increasing fractality. The increase in ‘pure’ isosteric enthalpy of adsorption with increasing fractality indicates that the energy is closely related to the pore-size distribution.     

Numerical solution of the mathematical model of internal-diffusion kinetics of adsorption

A numerical method is proposed for solving a nonlinear weakly singular Volterra integral equation of the second kind which arises in the study of the mathematical model of internal-diffusion kinetics of adsorption of a substance from an aqueous solution of constant and bounded volume. The efficiency of the method is demonstrated using prototype examples and in application to inverse problems of adsorption kinetics.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 63, pp. 30–38, 1987.     

Numerical study of the adsorption of dyes from textile effluents

The textile industry is one of the greatest generators of liquid effluents, due to the high quantities of water used in the dyeing process. Fixed bed adsorption columns using activated carbon have been widely used in industrial processes for the removal of contaminants from textile effluents. In this study we present the modelling of an adsorption process applied to textile dyes, using fixed bed columns. This model permits the prediction of the dye concentration at the adsorption column outlet, considering the influence of various operational parameters. The adsorption isotherms of the dye Basic Green 4, over granular activated carbon at 25 °C in an aqueous solution, were determined experimentally through a comprehensive series of tests. The Langmuir and Radke–Prausnitz models gave the best results for the adsorption isotherms. Tests were carried out in fixed bed columns to determine the breakthrough curves, with variations in feed rate, feed concentration, diameter of the column and mass transfer coefficient. The experimental conditions were simulated using a transient mathematical model. The data obtained numerically and experimentally were compared to validate the mathematical model proposed.     

Finite-difference solution of a nonlinear initial-boundary-value problem for a nonlinear parabolic equation of second order

An implicit finite-difference scheme is constructed for solving a nonlinear initial-boundary-value problem for a nonlinear homogeneous parabolic equation of second order with a nonlinear boundary condition that contains the time derivative of the sought function. The results are used for numerical solution of the mathematical model of internal-diffusion kinetics of adsorption from a constant bounded volume.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 65, pp. 34–46, 1988.     

Specific surface area of mercuric sulphide

The specific surface area of mercuric sulphide (a) has been determined by three methods: (a) gas adsorption method (N₂ adsorption), (b) air permeability method and (c) microscopic method. The area values are compared. In the gas adsorption method, the effect of degassing temperature on the surface area of solid was studied. In the permeability method the porosity range over which the specific surface area remains constant was also determined.     

Tensammetric studies of thiourea and its derivatives

Adsorption of thiourea and some of its derivatives at the mercurysolution interface has been studied by the tensammetric technique. It has been found that adsorption of thiourea increased the differential capacity rather than decreasing it. However the adsorption of S-methyl derivative of thiourea decreased the differential capacity. The N-substituted derivatives depressed the tensammetric curve of the supporting electrolyte to a greater extent than the N, N¹-substituted derivatives. The different behaviours of thiourea and its derivatives are discussed.     

A regularizing Kohn–Vogelius formulation for the model-free adsorption isotherm estimation problem in chromatography

Competitive adsorption isotherms must be estimated in order to simulate and optimize modern continuous modes of chromatography in situations where experimental trial-and-error approaches are too complex and expensive. The inverse method is a numeric approach for the fast estimation of adsorption isotherms directly from overloaded elution profiles. However, this identification process is usually ill-posed. Moreover, traditional model-based inverse methods are restricted by the need to choose an appropriate adsorption isotherm model prior to estimate, which might be very hard for complicated adsorption behavior. In this study, we develop a Kohn–Vogelius formulation for the model-free adsorption isotherm estimation problem. The solvability and convergence for the proposed inverse method are studied. In particular, using a problem-adapted adjoint, we obtain a convergence rate under substantially weaker and more realistic conditions than are required by the general theory. Based on the adjoint technique, a numerical algorithm for solving the proposed optimization problem is developed. Numerical tests for both synthetic and real-world problems are given to show the efficiency of the proposed regularization method.     

Homogenization of a convection–diffusion equation in perforated domains with a weak adsorption

The aim of this paper is to study the asymptotic behavior of the solution of a convection–diffusion equation in perforated domains with oscillating velocity and a Robin boundary condition which describes the adsorption on the bord of the obstacles. Without any periodicity assumption, for a large range of perforated media and by mean of variational homogenization, we find the global behavior when the characteristic size ε of the perforations tends to zero. The homogenized model, is a convection–diffusion equation but with an extra term coming from the weak adsorption boundary condition. An example is presented to illustrate the methodology.     

Homogenization of a convection–diffusion equation in perforated domains with a weak adsorption

The aim of this paper is to study the asymptotic behavior of the solution of a convection–diffusion equation in perforated domains with oscillating velocity and a Robin boundary condition which describes the adsorption on the bord of the obstacles. Without any periodicity assumption, for a large range of perforated media and by mean of variational homogenization, we find the global behavior when the characteristic size ε of the perforations tends to zero. The homogenized model, is a convection–diffusion equation but with an extra term coming from the weak adsorption boundary condition. An example is presented to illustrate the methodology.     

The step-wise adsorption of nitrogen on carbon black

Adsorption measurements have been carried out for nitrogen on the commercial carbon blacks Spheron 6 and Vulcan. The adsorption on Spheron 6 is step-wise in the pressure range 0 to 45 mm. (fraction of surface covered approximately 10^?5), and on Vulcan to at least 0.16 mm. Calorimetric measurements of differential heats of adsorption on Spheron 6 have shown that they vary with the amount of surface covered being greatest at low coverages and decreasing toward the heats of liquefaction as a limit. 1,2 This indicates that the surface of such materials contains various types of adsorption sites, having different heats of adsorption, and suggests that sufficiently refined measurements would show a step-wise adsorption isotherm. This paper reports the results of experimental studies of the adsorption of nitrogen on the carbon blacks Spheron 6 and Vulcan in the pressure range 0.00 to 75 mm., and at 0° and 100° C.     

Effect of electrophysical activation of components on adhesive interaction in polymer composites

The key problem in designing polymeric composites is ensuring a sufficiently strong adhesive bond between the polymer and the filler (or the reinforcement). One method for strengthening the intermolecular interaction at the phase interface is electrophysical activation of the particle surface. We have investigated the absorption activity and adhesiveness of powdered inorganic fillers and polymeric binders with triboelectric activation and activation in a corona discharge. We consider a broad class of disperse materials. We show that electrophysical activation of powdered materials causes changes in the concentration of donor and acceptor centers on the particle surface and in the adsorption activity of the materials as a whole. The presented results can be used for goal-directed selection of the most effective method of activation for disperse materials; they also are evidence for the important role of adsorption forces in the adhesion phenomenon.Report presented at the Ninth International Conference on the Mechanics of Composite Materials (Riga, October 1995).Translated from Mekhanika Kompozitnykh Materialov, Vol. 31, No. 6, pp. 734–741, November–December, 1995.     

A transfer function technique to describe odor causing VOCs transport in a ventilated airspace with mixing/adsorption heterogeneity

A model describing odor causing volatile organic compounds (VOC-odor) transport in a ventilated airspace influenced by heterogeneity of adsorption surface of ambient aerosol and air mixing pattern is proposed and analyzed based on a transfer function modeling technique. In this study an advection–reaction impulse/step response function for VOC-odor is assumed. The system process presented by an ensemble transfer function is solved analytically in the Laplace domain. The analytical results are then numerically inverted using a modified fast Fourier transform algorithm. The model requires the specification of probability density function for residence time of airflow and for both equilibrium linear partitioning and first-order mass transfer rate parameters to quantify the specific air mixing pattern and transport processes. The model predicts the ensemble mean VOC-odor concentrations for a variety of adsorption kinetics and mixing pattern combinations as a function of the boundary impulse/step response inputs as well as residence time and adsorption rate statistics. The general behavior of output VOC-odor profiles is analyzed through the effects of mean adsorption rate coefficient, mean linear partitioning constant, mixing efficiency, mean residence time and coefficient of variations of both linear partitioning and rate coefficients. It indicates that when mixing/adsorption heterogeneity exists, simple complete mixing assumption and simple distribution of rate constant is inherently not sufficient to represent a more generally distributed mixing/adsorption process of VOC-odor transport in a ventilated airspace.     

A transfer function model to describe odor causing VOCs transport in a ventilated airspace with mixing/adsorption heterogeneity

The ability of a transfer function modeling technique is evaluated to explain the odor causing VOCs (VOC-odor) transport processes influenced by heterogeneity of adsorption surface of ambient aerosol and air mixing pattern in a ventilated airspace. An advection–reaction impulse/step response function is used to generalize the dynamic transport of VOC-odor in heterogeneous mixing/adsorption ventilated airspace. The system process presented by an ensemble transfer function is solved analytically in the Laplace domain. The model requires the specification of probability density function (pdf) for residence time of airflow and for both equilibrium linear partitioning and first-order mass transfer rate parameters of gas/solid phase to quantify the specific air mixing pattern and transport processes. The model predicts the ensemble mean VOC-odor concentrations for a variety of adsorption kinetics and mixing pattern combinations as a function of the boundary impulse/step response inputs as well as residence time and adsorption rate statistics. The general behavior of output VOC-odor profiles is analyzed through the effects of mean adsorption rate coefficient, mean linear partitioning constant, mixing efficiency, mean residence time and coefficient of variations of both linear partitioning and rate coefficients. This study indicates that when mixing/adsorption heterogeneity exists, simple complete mixing assumption and simple distribution of rate constant are inherently not sufficient to represent a more generally distributed mixing/adsorption process of VOC-odor transport in a ventilated airspace.     

Inverse Problem for a Mathematical Model of Adsorption Dynamics

A mixed problem is considered for a system of partial differential equations modeling the process of adsorption dynamics. An existence and uniqueness theorem is proved for this problem, and the solution properties are investigated. The inverse problem is posed, involving the determination of the system coefficient given additional information about the solution. A uniqueness theorem is proved for the solution of the inverse problem.__________Translated from Prikladnaya Matematika i Informatika, No. 16, pp. 5 – 14, 2004.     

Uniqueness of a solution to the stationary problem of kinetics of growth of thin film of vapor phase on solid bases

A mathematical model of many-layer adsorption is considered. Sufficient conditions for the uniqueness of a solution of the class of periodic functions are found. The solvability and the uniqueness theorems for the Dirichlet problem are established for sufficiently small values of a parameter. Bibliography: 1 title. Translated fromProblemy Matematicheskogo Analiza, No. 16. 1997, pp. 193–203.     

Adsorbing staircase walks and staircase polygons

The adsorption of staircase walks and staircase polygons on the main diagonal in the square lattice is reviewed. We draw attention to the connection between adsorbing random walks in subsets of the integers and the square lattice, and this problem. The generating functions of adsorbing staircase walks and polygons are determined using several techniques, and information about the adsorption transition is found by the calculation of a critical exponent associated with it.This work is supported by operating and equipment grants from NSERC, Canada.     

Iterative Method of Solving the Inverse Problem for a Quasilinear Hyperbolic Equation

We consider the inverse problem for the quasilinear hyperbolic equation connected with the mathematical model of adsorption dynamics with a concentration-dependent kinetic coefficient. An iterative method is proposed that reduces the inverse problem to a nonlinear operator equation.__________Translated from Prikladnaya Matematika i Informatika, No. 17, pp. 5–12, 2004.     

Exchange relations, Dyck paths and copolymer adsorption

We consider a lattice model of fully directed copolymer adsorption equivalent to the enumeration of vertex-coloured Dyck paths. For two infinite families of periodic colourings we are able to solve the model exactly using a type of symmetry we call an exchange relation. For one of these families we are able to find an asymptotic expression for the location of the critical adsorption point as a function of the period of the colouring. This expression describes the effect of a regular inhomogeneity in the polymer on the adsorption transition.     

A new multiscale model for flow and transport in unconventional shale oil reservoirs

A new multiscale computational model for two-phase gas/oil flow in a multiporosity shale formation composed of three levels of porosity associated with nano/micro pores and hydraulic fractures is rigorously constructed within the framework of the homogenization procedure in conjunction with the Discrete Fracture Modeling, where fractures are treated as (n-1) interfaces (n=2, 3) immersed in the domain occupied by the matrix. Effective equations are obtained by upscaling the microstructural information of the shale oil formation with matrix composed of three distinct solid phases: the organic matter, constituted by kerogen aggregates containing particles and nanopores with adsorbed gas, and the pyrobitumen network, also containing an organic solid with micropores filled by tight oil and dissolved gas, along with the inorganic solid composed of clay, quartz and calcite, assumed impermeable and free of adsorption. Such distinct solid phases are separated from each other by the network of interparticle pores. Together with the pyrobitumen such a network form the pathways for multiphase flow in the matrix whereas the kerogen aggregates are treated as disconnected inclusions playing the role of storage sites for adsorbed gas. The homogenization of the multiphase flow model of black oil type gives rise to new pressure and saturation equations with effective coefficients strongly correlated with the shale microstructure, volume fractions and total organic content (TOC). Constitutive laws for the effective hydraulic conductivity and retardation parameter, which captures adsorption of methane in the nanopores, are numerically reconstructed by solving the local cell problems arising from the homogenization procedure. In particular the partition coefficient is computed from adsorption isotherms rigorously constructed within the framework of the Thermodynamics of confined gases seated on the Density Functional Theory (DFT). The effective equations in the matrix resemble in form of a generalized black oil model coupled with the two-phase flow model posed in the subdomain occupied by the network of hydraulic fractures. A macroscopic model is obtained by averaging the mass conservation equation across the fracture aperture giving rise to reduced balance laws posed in a network of reduced (n-1)-dimension (n=2, 3) supplemented by a source term arising from the jump in the oil/gas fluxes in the shale matrix. The resultant coupled Discrete Fracture/Multiscale model consists of a first attempt at constructing a rigorous correlation between the nature of the macroscopic multiphase flow equations and the local shale-microstructure mainly characterized by the simultaneous presence of inorganic and organic matters with the latter containing nanopores. Numerical simulations of gas/oil withdrawal are performed to accurately predict hydrocarbon movement in stimulated shale oil formations.