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Paper is a stochastic network of fibres, water and additives, and in that sense it may be envisaged as a composite material. Since fibres are much longer than the thickness of the paper sheet, the network is planar and almost two-dimensional. The two-dimensional structure governs many paper properties but the three-dimensional porous structure is also important. Insight into the structural changes that take place when paper is compressed in the paper machine may be gained by modelling and simulation of its viscoelastoplastic behaviour. The present work describes a mathematical model based on the cellular solids theory, characterising the nonlinear rheologic behaviour of the material. This approach results in an unsteady state problem and the resulting set of ODEs is solved by means of the DLSODES subroutine, which uses an integrator based in the Gear method. Experiments were conducted on a laboratory-scale dynamic press in order to validate the mechanical model. [Copyright &y& Elsevier]

The MaCKiE-2002 conference discussed scientific problems that arise in applied chemistry, and for which advanced mathematical methods are known or are still under development. In this introduction to the special issue dedicated to the conference, we discuss its background and give an overview of the contributions that were selected for publication. [Copyright &y& Elsevier]

• A promising platform for gene delivery clinical trial simulations is provided. • PK/PD analysis is performed for both individual and population modelling approaches. • Model predictions are consistent with the clinical data for haemophilia patients. • A simulation-based modelling approach is proposed to guide initial dose selection. • Simulations show that the increase in FIX activity and ALT level is dose-dependent. Haemophilia B is a bleeding disorder resulting from a deficiency of coagulation factor IX (FIX). Although gene therapy is a potentially curative treatment option, optimising the dosing of therapeutic genes for patients remains a challenge. Detailed simulation of gene delivery systems is required for an improved understanding of the system. Hence, the purpose of this paper is to develop a modelling framework to predict the physiological response of a subject affected by type B haemophilia to a dose of the vector. To address this, an integrated pharmacokinetic/pharmacodynamic (PK/PD) modelling platform was developed based on in vivo clinical data for three patients with severe haemophilia B, whose functional plasma levels of FIX are less than 1% of the normal value. The plasma FIX activity was considered as the pharmacological effect, while the level of serum alanine aminotransferase (ALT) demonstrated the hepatocellular toxicity. Both an individual-based modelling approach and a population modelling approach were used to estimate the physiological parameters of the developed PK/PD models. The models were then validated using data from the clinical study before being used in a simulation-based modelling approach to provide dosing recommendations. The results obtained from the study demonstrate a good prediction of the pharmacokinetics and pharmacodynamics of the vector. Model-based simulations were subsequently performed to guide initial dose selection to provide clinicians with better tools to simplify the decision-making process for designing more effective treatment plans. [ABSTRACT FROM AUTHOR]

• Recently discovered oscillations during CO oxidation over Ni were modeled. • The first mathematical model producing oscillations in excess CO was developed. • The T range of the oscillations and their waveforms and amplitudes were simulated. • Ni color variation during oscillations is caused by the O dissolution in the bulk. This paper presents the first mathematical model simulating the recently discovered oscillatory behavior during CO oxidation on a Ni foil in a continuous-flow catalytic reactor. These oscillations occur in the presence of excess CO; thus, the well-known Sales–Turner–Maple model, simulating oscillations in oxygen excess, cannot be applied. We suggest a modification of the Sales–Turner–Maple model by introducing the precursor-mediated adsorption of CO. This made it possible to simulate the oscillations under reducing conditions. The suggested microkinetic model coupled with a continuous-flow reactor model predicts that the oscillations proceed on the partially oxidized catalyst because of the periodic formation and reduction of the surface oxide. The introduction of oxygen diffusion into the subsurface layers allows the description of the experimentally observed variation in Ni color during the oscillatory cycle. The developed model successfully reproduces experimental data as the temperature range of the oscillations together with their shape and amplitudes. [ABSTRACT FROM AUTHOR]

Abstract: In many different fields of research, the interactions between two immiscible fluids are of importance. To study these flows in industrial equipment, a multi-scale modeling approach is often used. In this approach, the smallest scale models apply detailed information in the form of closure equations for the larger scale models, which can model complete industrial equipment. This paper will focus on the improvement of the smallest scale model; direct numerical simulations employing the Volume of Fluid model. In this model, mass is inherently conserved because of the surface treatment, but this treatment also poses a challenge in calculating the surface properties like the surface tension. In this paper, three different surface tension models for the Volume of Fluid were tested: the generally used Continuum Surface Force (CSF) model, the height function model and the novel tensile force method. From the verification tests, it was concluded that both the height function model and the tensile force method are an improvement of the CSF model. The single bubble simulations showed that the height function method works best for small bubble . This is due to problems with connectivity for the tensile force method. While for the larger bubbles , the tensile force method is the best functioning surface tension model, because the calculation of the curvature in the height function method uses a stencil in which the distance between two interfaces in the direction of the normal should at least be four grid cells. In all the other tested cases, the height function model and the tensile force method perform equally well. The Morton number changes the ranges for the region of use of the surface tension models slightly when (the height function model can only be used when , while the tensile force method can only be used at ) and (the height function model can in this region also be used when ). [Copyright &y& Elsevier]

Abstract: Design and analysis of photoreactors is significantly more challenging than conventional reactors due to participation of radiation in chemical reactions. This problem is further compounded in case of photocatalytic reactors because of presence of photocatalytic particles, which not only produce complex light scattering effects but, in case of slurry systems, also act as an additional phase, the hydrodynamics of which is essential to characterize for evaluating the phase distribution of photocatalyst particles without which it is not possible to calculate the light intensity distribution. This then necessitates the use of a computational fluid dynamics (CFD)-based simulation approach which can simultaneously take into account the hydrodynamics of multiple phases, light intensity distribution and reaction kinetics. This paper presents a sequential review of all steps for CFD simulations of photocatalytic reactors. The hydrodynamic modeling has been considered first with an emphasis on the Eulerian–Eulerian model because of its ability to handle large-scale photocatalytic reactor systems with only relatively moderate computational resources. This has been followed by a review of lamp emission models, which in CFD models are used as boundary conditions for solving the radiation transport equation (RTE). Before discussing the kinetics of photocatalytic reactors, a review of numerical models for solving the RTE has also been presented for both slurry and immobilized reactor systems. Finally, the paper discusses important factors for setting up the boundary conditions for CFD modeling of photocatalytic reactors. [Copyright &y& Elsevier]

Abstract: This study is a sequel to the paper of Savage and Oger ( this issue) that reviewed experimental studies of airslides. These devices make use of fluidization to facilitate the transport of granular materials over long distances. The present paper describes a detailed and comprehensive consideration of the various contributions to the governing multiphase flow equations and proceeds to carry out numerical simulations of airslide flows and compare the results with laboratory experiments. It was carried out in part using the open source multiphase flow CFD program MFIX. Revisions and additions to the governing equations used in the distribution version of MFIX were made. The results of previously published molecular dynamics simulations were used to formulate a revised radial distribution function. The forms of the quasi-static stress contributions were designed to permit the development of higher concentration flows typical of experimentally observed airslide flows. Finally, additional terms were included in the particle fluctuation energy equation to account for (i) the viscous dissipation of the fluctuating particles due to the interstitial air, and (ii) the energy source term arising from the transfer of energy from the fluid to the particles. These expressions have been incorporated in the computational scheme and simulations of fluidized granular flows in a rectangular channel having frictional side walls were carried out. Some initial exploratory calculations were performed to examine the effects of various parameters on the mass flow rates and the velocity profiles. Different wall conditions were studied by varying the particle and wall restitution coefficients. The effects of varying the minimum fluidization velocity and the solid fraction thresholds were also examined. The simulation scheme was then applied to model two of the better documented fluidized chute flow experiments; those of Botterill and Bessant (1976), and the McGill University fluidized solids flow channel experiments of Liot (1979) and Chan (1979). Results of these computations and comparisons with observed experimental airslide behavior are discussed. Good agreement is found between the simulations and the experimental airslide flow characteristics. [Copyright &y& Elsevier]

Abstract: Airslides are commonly used to transport dry particulate materials over distances as long as 1km. Air is pumped through the porous bed of the transport channel to fluidize the granular material and to promote the flow down very small bed slopes. Current design of airslides is based on empirical design charts and past experiences. The present paper is the first of a two-part investigation of airslides. It reviews selected experimental studies of airslides with the goal of identifying characteristic features of these flows that we attempt to model in the numerical simulations described in the second companion paper. The experiments of Botterill and Bessant (1976) and a power-law, non-Newtonian finite element model that gave a good representation of the Botterill and Bessant (1976) velocity profiles are described. The McGill fluidized solids channel experimental setup and the associated measurements carried out by Liot (1979) and Chan (1979) are outlined. Some of these results were interpreted by means of simple, hydraulics type backwater analyses. As with the usual hydraulics type open channel flows, it was found that fully developed, uniform depth, granular airslide flows could develop. This is an important observation and it will be used as justification for the methodology employed in the calculations in the companion paper which proceeds to simulate fully developed, three-dimensional fluidized granular flows in a rectangular channel. The distinctive features identified in the review of the airslide flow experiments are summarized. [Copyright &y& Elsevier]

Abstract: Accurate estimation of the model parameters is required to obtain reliable predictions of the products end-use properties. However, due to the mathematical model structure and/or to a possible lack of measurements, the estimation of some parameters may be impossible. This paper will focus on the case where the main limitations to the parameters estimability are their weak effect on the measured outputs or the correlation between the effects of two or more parameters. The objective of the method developed in this paper is to determine the subset of the most influencing parameters that can be estimated from the available experimental data, when the complete set of model parameters cannot be estimated. This approach has been applied to the mathematical model of the emulsion copolymerization of styrene and butyl acrylate, in the presence of n-dodecyl mercaptan as a chain transfer agent. In addition, a new approach is used to better assess the true confidence regions and evaluate the accuracy of the parameters estimates in more reliable way. [Copyright &y& Elsevier]

Abstract: This paper presents a coupling of Discrete Element Method (DEM) and Constrained Interpolation Profile (CIP) mainly designed for simulations of the nucleation process in wet granulation. The governing equations for fluid (liquid and gas) phases are the volume averaged form of the Navier–Stokes equation, continuity and colour function equations. These equations are solved by use of a meso-scale fixed Cartesian grid whose cell is larger than individual particles. The solid–liquid–gas interfacial effects on both fluid and particle phases are taken into account in the simulation. The surface tension effect on the fluid motion was modelled in three different ways depending on the relative position of the liquid–gas interfaces to powder beds: the models outside, inside, and on the surface of powder beds correspond to a free surface, capillary action and bed surface wetting. A new model for the surface tension effect on the solid (particle) motion, i.e. the capillary force effect, is proposed in this paper. This capillary force model is particularly useful when using a meso-scale fixed grid, and it can be used with various types of multi-fluid scheme such as CIP, Volume of Fluid (VoF) and Level Set methods. The proposed models are validated by comparing the simulation results with theoretical and experimental results. It is also revealed that the capillary force model is crucial to obtain reasonable simulation results for nucleation process. [Copyright &y& Elsevier]

Highlights • H 2 is autothermally generated from ethanol in a parallel-plates reactor. • Adequate thermal coupling between combustion and reforming of ethanol is predicted. • Feasible integration between the reactor and heat exchangers is proved. • Splitting the fuel feed reduces hot spots while enables extra H 2 yields. • Importance of proper heat loss quantification is evidenced. Abstract This paper deals with the study of the integration of ethanol steam reforming and ethanol combustion in a parallel plates reactor aiming a hydrogen production of 1 kW th equivalent. The study was performed by means of a mathematical model of a non-adiabatic reactor and the associated heat exchangers used for preheating purposes. Focus is given here to the influence of the insulation of the reactor and heat exchangers, the fuel concentration, fuel distribution policy to the reactor, and reforming flowrate. Thermal coupling between combustion and reforming of ethanol in terms of energetic integration is feasible and an adequate behavior of the reactor and the heat exchangers is predicted. The importance of heat losses to the environment is evidenced since they represent about 35–50% of the heat released by the combustion. Ranges of ethanol fuel concentration (0.6–2.0% of ethanol fuel) and distribution (1 or 2 feed ports), and ethanol reforming load (0.37–0.63 kg/h) were studied to find windows for these variables where a satisfactory operation is possible. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents a novel Lagrangian approach to model fuel mixing in gas–solid fluidized beds. In the mixing process, fuel particles are considerably larger than the inert bed material and therefore, the present work proposes three grids to account for the difference in size between the fuel particles and inert solids. The information between the grids is exchanged using an algorithm presented in the paper. A statistical method has been developed to analyze the distribution of the fuel particles in the bed. The results for the preferential positions, velocity vectors and horizontal dispersion coefficients are compared with experimental data in a bed applying simplified scaling relationships for different operating conditions. The effects of initial bed height and inlet gas velocity on the fuel mixing are investigated. It is found that the proposed Lagrangian modeling can capture the complex pattern of the movement of the fuel particles, in spite of the large difference in diameter between inert and fuel particles. [Copyright &y& Elsevier]

Abstract: A modified direct simulation Monte Carlo (DSMC) method is proposed in the present paper for obtaining the particle motion behavior which is of essential importance for research of the transfer processes in a gas–particle two-phase impinging streams (GPIS). In GPIS, the particle concentration distribution is extremely nonuniform. The particle collisions play an important role in the particle motion behavior inside the impingement zone with high particle concentration, nevertheless, the interactions between gas phase and particle phase play an important role outside the impingement zone. And the volume of the impingement zone is relatively small, and the time required for a particle to pass through this zone is very short. According to these characteristics of multiple spatial scale and multiple time scale, the DSMC method is modified to be more suitable to the numerical study of GPIS. This modified DSMC method is not restricted to flow field cells in the calculation of particle motion and collisions, and the particle time step in this method is adaptive and calculated using local particle parameters. The algorithm and numerical solution method of this method are also given in this paper. The predicted results of the particle motion behavior in GPIS are in reasonable agreement with the experimental data, which indicates the validity of the present method. [Copyright &y& Elsevier]

Abstract: This paper explores the through-/in-plane characteristics of water transport in the cathode gas diffusion layer (GDL) of a polymer electrolyte fuel cell (PEFC). Theoretical analysis is performed on the non-isothermal two-phase flow under flow channels. A dimensionless group Da (Damkohler number for PEFC operation), defined as the ratio of water generation rate to water vapor-phase removal rate, is formulated to characterize the flow regimes in a PEFC. This group, lumping geometrical parameters and physical properties, compares the water vapor-phase removal capability (via water diffusion and holding capacity) with the rate of water production by the oxygen reduction reaction. We find that this dimensionless group can be used to characterize the non-isothermal, two-phase phenomena: when Da→0, the fuel cell is subjected to single-phase operation; while as Da→∞ we have full two-phase operation. A more precise expression is explored for the dimensionless group at the channel central line, i.e. Da 0: when Da 0>1 the entire cathode GDL–CL (catalyst layer) interface is in two-phase region, whereas part of the interface is free of liquid water for Da 0<1. The latter scenario is the concept that this paper proposes for improving fuel cell water management: the consequent co-occurrence of single- and two-phase flows in the in-plane direction at Da 0<1 is beneficial to avoid severe dryout and flooding. A two-phase transport model, describing the water and heat transport on the PEFC cathode side, is employed to perform a two-dimensional numerical study. Detailed liquid and temperature distributions are displayed. Simulation predictions are in reasonably good agreement with the dimensionless-group analysis. [Copyright &y& Elsevier]

Abstract: In gasification of biomass, coal and blended biomass and coal, there are two steps including an initial pyrolysis process followed by gasification of solid char. The latter process is a slow process and thus dominates the whole gasification. In our previous paper (), the differences between steam gasification of biomass chars and that of coal chars have experimentally been investigated and the results show that these differences are mainly due to the difference in microstructures of these two fuels. In this work, a mathematical model of char gasification is developed based on reaction kinetics and gas transportation of both the producer gas and the gasification agent (steam). The model also includes mass conservation equations for each of the gas components and solid carbon involved in the gasification process. This has resulted in a set of highly nonlinear differential equations which have been solved using a numerical technique to predict gas production rate, gas compositions and carbon consumption rate during the gasification. The developed mathematical model is validated using experimental results reported in previous paper (), and close agreement between the simulation results and the experimental values have been observed. From the modelling, it has been confirmed that the char gasification is mainly determined by the characteristics of char matrix including the exposed surface area and the micro-pore size. The former determines intrinsic reaction rate and the latter influences the intra-particle mass transportation. Biomass char has more amorphous structure, thus the intrinsic reaction rate is enhanced. For coal char, the larger pore size enables the high transport rate of the gasification agent (water vapour) into the char particles but the resultant gases have higher resistance to transfer through compact clusters. For simulation of the blended biomass and coal, the blend properties were determined based on the blend proportion of each fuel. The close agreement between the simulation results and experimental data suggests that the approach in this work can adequately quantify the gasification kinetics and the gas composition. [Copyright &y& Elsevier]

Abstract: Granular solids in silos experience considerable principal stress rotations, which result in the non-coaxiality between principal stresses and plastic strain rates. This paper discusses the influences of the use of elastoplastic non-coaxial models for granular solids on predictions of wall pressure distributions in silos by using the finite element method. A well established non-coaxial model in geomechanics, the yield vertex model, is employed. Simulations are performed on a steep hopper characterized with a mass flow and a flat-bottomed silo with a semi-mass flow. The simulations indicate that the non-coaxiality does not influence predictions of wall pressures after filling. On the other hand, the predicted discharge wall pressures with non-coaxial considerations are larger than those without it. Its mechanism is discussed in this paper. The suppressed shear-dilatancy of granular solids in silos leads to a larger increase of normal stress with non-coaxial models. [Copyright &y& Elsevier]

Abstract: The present paper investigates some families of simple 2D circuits or grids of intersecting tubes or channels (thus forming meshes) from the point of view of the fluid distribution and hydraulic characteristics in slow laminar flow. Square grids with a single inlet and a single outlet, and comprising from 4 to 100 meshes are considered, either with all channels identical, or with different channels along the borders of the circuit. Analytical resolution of the mesh and node relations to obtain the steady flow distributions are convenient up to 5×5 meshes, and formal computation furnishes numerical solutions for higher order circuits. This paper discusses some details of the flow and pressure distributions, in particular the symmetries, and also the behavior of some global properties such as overall or internal resistance and flow heterogeneity, as a function of the ratio of resistances of the two types of channels. [Copyright &y& Elsevier]

Abstract: This paper describes several improvements to a numerical model introduced by for collisional exchange and damping in dense particle flows. use a Bhatnagar, Gross, and Krook (BGK) approximation to the collision terms in a particle distribution function transport equation to model the effects of particle collisions on damping fluctuating particle velocities and, in gas/liquid/solid beds, fluctuating temperatures and compositions of liquid films on particle surfaces. In this paper we focus on particle flows in which the particles have no liquid films and report on an improved expression we have developed for the collision damping time of particle velocity fluctuations used in the BGK approximation. The improved expression includes the effects on the collision damping time of the particle material coefficient of restitution and of non-equilibrium particle velocity distributions. The collision model improvements are incorporated into the general-purpose computational-particle fluid dynamics (CPFD) numerical methodology for dense particle flows. Three computational examples show the benefits of using the new collision time in calculations of particle separation in polydisperse dense particle flows and calculations of colliding particle jets. [ABSTRACT FROM AUTHOR]

Abstract: In the last years, there has been a rapid growth of research and development activities on high temperature molten salts for nuclear and non-nuclear applications. The study of their heat transfer characteristics is a key issue in the current development of the molten salt reactor (MSR) that is one of the innovative nuclear reactors proposed by the Generation IV International Forum. The MSR is a sort of circulating fuel reactor (CFR), which adopts a molten halide salt mixture containing the fissile material and playing the distinctive role of both fuel and coolant. In a thermal-neutron-spectrum MSR, the reactor core is composed by a graphite matrix (neutron moderator), through which the liquid nuclear fuel flows and leads to a strong and intrinsic coupling between thermo-hydrodynamics and neutronics. This peculiar feature requires a suitable and qualified multi-physics simulation environment for a proper description of the system (fuel/coolant+graphite) behaviour. With reference to such complex and non-linear system, the present work is intended to give two different but linked contributions, in the perspective of a multi-physics modelling able to accurately describe the synergy of the involved different physical phenomena (e.g., by means of software). [(I)] On one hand, this work is aimed at establishing a useful validation framework for the assessment of computational fluid-dynamics (CFD) analyses of liquids with internal heat generation. For this purpose, an analytic approach for both fluid velocity and temperature fields in a circular pipe surrounded by a solid region has been developed. It is an extension of the approach elaborated for pipe flow in (Di Marcello, V., Cammi, A., Luzzi, L., 2010. A generalized approach to heat transfer in pipe flow with internal heat generation. Chemical Engineering Science 65, 1301−1310), in order to take into account the heat conduction in the solid domain (represented by the graphite matrix in the specific case of interest). [(II)] On the other hand, the paper presents a preliminary investigation of the thermal-hydraulic behaviour occurring in a typical graphite-moderated MSR core channel. The developed analytic approach has been conveniently applied to this case study: (i) by testing the capabilities of to evaluate the heat transfer characteristics and the hydrodynamic behaviour of such system; and (ii) by investigating the applicability of correlations for the Nusselt number to fluids with internal heat generation. For a deeper insight into the numerical solutions provided by COMSOL, a code-to-code comparison has been also carried out, adopting a dedicated CFD finite volume software (i.e., FLUENT®). As a result, a satisfactory agreement has been found between the analytic solution and the numerical computations provided by COMSOL and FLUENT for a wide range of Reynolds numbers. As concerns the Nusselt number evaluation, the correlations usually adopted for molten salts have been proved as unsuitable for the analysed system, whereas the correlation advanced in the above mentioned paper (that explicitly takes account of the internal heat source) appears more appropriate. The results of the present work are thought to be useful because they provide: (i) a “generalized” analytic approach to the heat transfer that is applicable in a more general context; (ii) an insight into the heat transfer characteristics of the considered graphite-moderated MSR core channel; and (iii) a preliminary assessment of computations that is essential in view of the adoption of multi-physics tools (like COMSOL) for more complex and representative simulations of the dynamic behaviour of the molten salt reactor, and more in general of other kinds of CFRs. [Copyright &y& Elsevier]

Abstract: The paper presents a novel quality-by-design framework for the design of optimal seed recipes for batch cooling crystallisation systems with the aim to produce a desired target crystal size distribution (CSD) of the product. The approach is based on a population balance model-based optimal control framework, which optimises the compositions of seed blends, based on seed fractions that result from standard sieve analysis. The population balance model is solved using a combined quadrature method of moments and method of characteristics (QMOM-MOCH) approach for the generic case of apparent size-dependent growth. Seed mixtures are represented as a sum of Gaussian distributions, where each Gaussian corresponds to the seed distribution in a particular sieve size range. The proposed methods are exemplified for the model system of potassium dichromate in water, for which the apparent size-dependent growth kinetic parameters have been identified from laboratory experiments. The paper also illustrates the simultaneous application of in situ process analytical tools, such as focused beam reflectance measurement (FBRM) for nucleation detection, attenuated total reflection (ATR) UV/Vis spectroscopy for concentration monitoring, as well as the in-line use of laser diffraction particle sizing for real-time CSD measurement. [Copyright &y& Elsevier]

This paper reports experimental investigation of mixing performances inside microfluidic liquid slugs using the Villermaux–Dushman reaction. Slug-based microfluidics offers rapid mixing by internal circulation and transport with narrow residence time distribution, making it suitable for precise reaction and mixing operations. The experimental investigation presents operation methods to form microfluidic liquid slugs having the reactant arrangements. Mixing performances of flows with and without internal circulation are compared and mixing rates for the axial and radial arrangements of reactants are also compared. Moreover, for the radial arrangement, mixing performances can be evaluated using a dimensionless number irrespective of flow rate and slug length, based on the novel method discussed in our previous paper, which proposes the modified Peclet number to estimate mixing rates and design liquid slugs to obtain desired mixing rates. These results give support to the suggestions by the previous simulation results. [Copyright &y& Elsevier]

Abstract: This paper addresses the problem of reducing insignificant or redundant information in parameter sets associated with fundamental models of dynamical systems. Whilst these parameters are important for describing physical or chemical relationships between the process variables, some of them only provide a marginal contribution to the input–output behavior of the system. Consequently, the identification of the latter parameters is difficult on the basis of recorded process data. Since this important issue has not attracted considerable attention over the past decade, the paper introduces and evaluates three techniques to assess the importance of each parameter to the overall input/output description of the process under study. The three presented methodologies include: (1) parameter reduction where the contribution is measured by Hankel singular values; (2) reduction of the parameter space via singular value decomposition; and (3) a combination of the two techniques, where the number of parameters is reduced in a first step followed by reduction of the parameter space of the remaining parameters. The techniques are first developed for linear systems and an extension to nonlinear models is presented. The three techniques are compared using two case studies, one of which is a benchmark example from the nonlinear control literature. [Copyright &y& Elsevier]

Abstract: Spout–fluid beds find a widespread application in the process industry for efficient contacting of large particles with a gas. However, detailed understanding of the complex behavior of these systems is lacking, which leads to significant scale-up problems in industry. In this paper we report results of a combined experimental and simulation study on the various regimes, which can be encountered during spout–fluid bed operation. A regime map for a 3D spout–fluid bed was composed employing spectral analysis of pressure drop fluctuations and fast video recordings. In addition 3D Euler–Lagrange computations were performed to assess the capability of the model to reproduce the experimentally observed flow regimes. The influence of the drag closure on the model results was assessed and the influence of the computational grid was studied using a new method for the implementation of the two-way coupling, which is proposed in this paper. For most regimes our model is able to predict the appropriate regime. The frequency, at which the largest power is found, is overpredicted by the model. Contrary to the experimental observations, our model did not predict any large slugs in the slugging bed regime. The remaining differences between the simulated and experimentally observed bed behavior is most likely related to the representation of the effective fluid–particle interaction in our model, which relies on local spatial homogeneity. [Copyright &y& Elsevier]

A new variable-density plastic flow model is developed, in which the Drucker Prager yield condition holds identically, but the corresponding flow condition contains the time derivative of density (or the divergence of mass flux), in order to satisfy mass conservation. This “softening” model is applied to the steady radial flow of a cohesionless granular material from steep-walled wedge and conical hopper. Density is assumed to vary with pressure. The variation of density within the hopper is shown to decrease the mass discharge rate, relative to the incompressible model, by a similar amount to the fractional reduction in voidage about the orifice. The predicted mass discharge decreased with increasing internal friction angle. This paper assumed that the inclination of the stagnant region in hopper flow is described by regression curves fitted to data from Brown and Richards. Approximate agreement between the theory of this paper and voidage measurements by Fickie et al. was obtained. Approximate agreement was also obtained with the published mass discharge rates of Nedderman and Beverloo for wedge and conical hoppers, respectively, and our results were insensitive to variations in internal angles of friction between about 25° and 35°. The steady equations considered here can only be satisfied approximately, supporting observations that granular flows are intrinsically transient. [Copyright &y& Elsevier]

This paper proposes a new mathematical model describing the diffusion-controlled release of an active ingredient (AI) from a cylindrical product, followed by convection-dispersion transport in a wind tunnel through which air flows. The model aims to support the development of products with targeted AI release profiles. It was motivated by the particular case of a new product formulation releasing phytochemicals with insecticide activity. The well-known analytical solution for the AI transient release from the product is coupled with the analytical solution for the convection-dispersion transport along the tunnel through a simple approximation that introduces a negligible error. An overall analytical solution is thus obtained, having obvious advantages against numerical approximations, particularly for intensive computational tasks such as model fitting to experimental data, uncertainty analysis and product composition optimization. • Mathematical modelling of the release of a volatile active ingredient (AI) from a solid product. • Unified model to describe AI release and subsequent dispersion in a wind tunnel. • Analytical solution of the unified model. • Model applied to simulation of wind tunnel tests, used to develop a porous solid product releasing an insecticvide. [ABSTRACT FROM AUTHOR]

It is well understood that during the pharmaceutical aqueous film coating process the amount of liquid water that interacts with the porous tablet core can affect the quality of the final product. Therefore, understanding and simulating the mechanisms of water droplet spreading, absorption and evaporation is crucial for controlling the process and optimising the shelf-life of the tablets. The purpose of the work presented in this paper is to define and describe the spreading, absorption and evaporation phenomena after droplet impingement on a tablet. We divided the droplet behaviour into three phases of different dynamics and duration: the kinematic, capillary and evaporation phases. To model the kinematic phase, we combined and modified 1-D spreading models from the literature which solve the kinetic energy balance equation for the first milliseconds of spreading. For the capillary phase, we simplified and solved the continuity and Navier-Stokes equations using the lubrication approximation theory. Finally, for the evaporation phase, we adopted a modelling approach for the second drying stage of slurry droplets inside a spray dryer. During this stage, one can no longer describe the droplet as a liquid system containing solids, having to regard it as a wet particle with a dry crust and a wet core. In our work, we represented in a novel way the crust as the dry surface of the tablet and the wet core as the wetted area inside the porous matrix. We implemented the mathematical model presented in this work in gPROMS, employing the Modelbuilder platform. Our numerical results (droplet height and spreading, wetting, evaporation front profiles) are in good agreement with recent experimental data that we found in the literature. [ABSTRACT FROM AUTHOR]

Gold nanoparticles are commonly manufactured by the citrate reduction method, a synthesis method pioneered by Turkevich et al. (1951). Based on their experimental evidence, Turkevich et al. (1951) advanced the organizer theory, a nucleation-growth synthesis mechanism. Subsequently, Kumar et al. (2007) developed a mathematical model for the description of the synthesis, basing it on such a theory. However, this model has not been thoroughly tested. Recently, contrary to the evidence provided by Turkevich et al. (1951), other mechanistic descriptions of the synthesis, which emphasize the role of the pH of the solution, have been advanced in the literature. In this paper, we investigated the model of Kumar et al. (2007) for different conditions of pH, temperature and initial reactant concentrations. To solve the model, we used the numerical code Parsival, which is used for solving population balance equations. We tested the model for different synthesis conditions studied experimentally by various researchers, for which results are available in the literature. The model poorly predicted the experimental data because the Turkevich organizer theory does not account for the acid-base properties of chloroauric acid and sodium citrate. A new model, with a more accurate mechanistic description of the synthesis and of the chemistry involved, is therefore required. [ABSTRACT FROM AUTHOR]

In this paper a numerical linear stability analysis is performed to a mathematical model for the two-phase flow in a pipeline-riser system. Most of dynamic models and stability criteria are based on a simplified lumped parameter pipeline, where it is assumed that the void fraction variations can be neglected. As a pipeline with a constant void fraction is not able to describe the flow pattern transition or void fraction propagation waves, the choice of pipeline model influences the stability map. Three different models for the pipeline are considered: (a) A lumped parameter model with constant void fraction; (b) A lumped parameter model with time dependent void fraction; (c) A distributed parameter model, with void fraction dependent on time and position. The results show that the constant void fraction model overestimates the unstable region, pushing the near horizontal branch of the stability boundary beyond the stratified-intermittent transition boundary for high buffer lengths and invalidating the model assumptions. The distributed parameter model is capable of describing void fraction waves along the pipeline under the restriction of a stratified flow pattern, with an additional stabilizing effect, being less sensitive to high buffer lengths and not crossing the stratified-intermittent transition in the nearly horizontal branch. The lumped parameter model with variable void fraction behaves close to the distributed model, but predicting bigger unstable regions. The behavior of the different pipeline models is explained based on the basic assumptions that led to many semi-empirical stability criteria. It is concluded that a distributed parameter model is recommended, with a void fraction correlation that includes the transition from stratified to intermittent flow pattern taken into account in the problem statement. [ABSTRACT FROM AUTHOR]

This study makes use of a novel methodology for the synthesis of heat exchanger networks, which is aimed at overcoming the shortcomings associated with the use of shortcut models to represent individual exchangers in the synthesis network. The new approach entails the use of a number of correction factors to get networks which are based on the use of shortcut models, such as the mixed integer non-linear programming (MINLP) stage-wise superstructure (SWS) of Yee and Grossmann (1990) to more closely represent physically achievable heat exchangers and ensure that the MINLP network topology optimisation step of these models converge on a real design, rather than an approximated one. In this paper, the SWS formulation is used for the generation of an initial network after which its objective function is modified to include the correction factors that force its objective function towards the cost of a network whose individual exchangers are designed using methods such as Bell–Delaware and heuristics. The modified objective function includes parameters that modify the areas obtained by the shortcut based MINLP model so as to more closely represent the areas obtained by the detailed models and also includes a novel method for including the number of shells required for each exchanger duty. The correction factors account for pressure drops, F t correction factors, number of shells, TEMA considerations, and changes to the overall heat transfer co-efficient of each stream match. The methodology is applied to two examples and the solutions are comparable with other solutions obtained in literature and were shown to produce good solutions. The reason that the method is effective is because many potential networks are evaluated during the iterative procedure and the best network, based on the detailed exchanger designs, is chosen. In this way it is possible to use the detailed exchanger designs to “guide” the MINLP optimisation towards more realistic networks and also to generate many different potential networks. [ABSTRACT FROM AUTHOR]

Alkaline direct methanol fuel cells (ADMFCs) produce water at the aqueous fed anode. This complicates water management at anode which is analysed in this study by modelling three extreme case scenarios assuming different conditions for water transport or removal. All scenarios include recycling of methanol solution at anode outlet to achieve high methanol efficiencies. One scenario reveals that high operation times and high methanol efficiencies necessitate active stabilisation of anodic water level since both water accumulation and depletion can take place depending on operation conditions. Another scenario shows that water level can be stabilised by adjusting cathodic evaporation and the corresponding water removal from the system. The results indicate that feeding cathode with water-saturated gas is detrimental for stabilising water level. The last scenario suggests the addition of a gas flow to anodic outlet to remove excess water for water level stabilisation. Minimization of additional methanol loss requires to reach high humidities by evaporation. The present paper reveals the impact of processes occurring in ADMFCs on anodic water management and indicates the necessity to quantify water transport through membrane. Knowledge of the influence of operation conditions on water level in the anodic loop are beneficial for design of ADMFC systems. [ABSTRACT FROM AUTHOR]

The modeling of two-phase flows has always been limited to special cases due to the very complex nature of its interface. When considering vertical pipe flows with low gas volume flow rates, bubbly flow occurs. With increasing gas volume flow rates larger bubbles are generated by bubble coalescence, which further leads to transition to slug, churn-turbulent, and annular flow. Considering, as an example, a heated tube producing steam by evaporation, as in the case of a vertical steam generator, all these flow patterns including transitions are expected to occur in the system. Despite extensive attempts, robust and accurate simulations approaches for such conditions are still lacking. This paper summarizes the state-of-the-art on the understanding of the physics behind churn-turbulent flow, and transitions to and from this flow pattern. Both, benefits and limitations of the existent experimental approaches and their usefulness for model development and validation at these high void fraction conditions are discussed. Limitation of both, low-dimensional approaches (0D, 1D, and 2D), and high resolution approaches such as Direct Numerical Simulations (DNS) are analyzed. Averaging procedures, such as the Eulerian–Eulerian approach including the interfacial momentum closures which has been used in the past for simulating churn flow, are review thoroughly. Finally, possible improvements are proposed. [ABSTRACT FROM AUTHOR]

Dynamic optimization solutions largely rely on the accuracy of the underlying mathematical models. However, these models only represent an approximation of the real dynamic process and their predictions are dependent on a set of parameter values. These parameter values can be hard to estimate exactly (e.g., thermal conductivity) or vary over time (e.g., due to fouling) potentially leading to hazardous situations when applying a model based optimal solution. Robust dynamic optimization deals with the uncertainty related to these parameters in order to quantify their effect and deliver safer (i.e., more robust) operating conditions. This paper discusses a computationally efficient robust dynamic optimization approach based on the Sigma Point method and shows how it outperforms a linearization-based method for a nonlinear dynamic chemical vapor deposition reactor case-study with multiple uncertainties. Moreover, by accounting for uncertainty a trade-off between process safety and performance of the reactor is introduced. This aspect is cast in a multi-objective dynamic optimization framework. In particular, it is illustrated how an increasing robustness (i.e., process safety) induces a worsening of other investigated objective functions and results in robustified Pareto sets. [ABSTRACT FROM AUTHOR]

In this paper, an analytical extension of the classical ideal Anderson–Schulz–Flory (ASF) distribution for the products of Fischer–Tropsch reactions is presented. The extension includes a description of enhanced product formation and re-adsorption and is therefore capable of describing real distributions with the known deviations from the ideal ASF distribution for C 1 and C 2 components and, by including the known double-ASF concept, the deviations of longer-chain hydrocarbons (C 10+ ). The model contains five dedicated parameters, each of which is associated with a particular characteristic of the product distribution. The developed equations are analytical solutions for the mole fractions y n and selectivities S n of product components, the average carbon number n ¯ as well as for the sub-totals y n + and S n + . Besides the flexibility and wide range of applicability of the extended ASF model, it allows simple and direct extraction of the relevant parameters from experimental data. These new distribution functions are considered to be valuable as a descriptive model for characterizing experimental data and as a basis for predictive models of product distribution for engineering applications. [ABSTRACT FROM AUTHOR]

This paper presents a study on the fixed-bed pyrolysis of debarking residue obtained from Norway spruce. Analysis is based on the dynamic model of packed bed pyrolysis which was calibrated by determining appropriate reaction rates and enthalpies to match the model predictions with the experimental data. The model comprises mass, energy and momentum equations coupled with a rate equation that describes both the primary and secondary pyrolysis reactions. The experiments used for the model calibration determined the yields of solid, liquid and gaseous pyrolysis products as well as their compositions at three distinct holding temperatures. Subsequently, the dynamic model was used to predict the product yields and to analyze the underlying phenomena controlling the overall pyrolysis reaction in a fixed-bed reactor. [ABSTRACT FROM AUTHOR]

In literature, the diffusion-free residence time distribution (RTD) of laminar flows – the so-called convection model – has been determined for various velocity profiles mostly on a case-by-case basis. In this analytical paper, we derive general mathematical relations which allow computing the diffusion-free differential and cumulative RTD in straight planar, circular and concentric annular channels for arbitrary monotonic and piece-wise monotonic one-dimensional velocity profiles. The theory is used to determine the RTD of plane Couette–Poiseuille flow with non-monotonic velocity profile, and the optimal value of the volumetric flow rate where the RTD becomes most narrow. It is shown that any velocity profile that depends in a sub-layer linearly on the distance from a stationary or moving no-slip wall has a differential RTD which follows a −3 power law as the residence time approaches its maximum. The variance of the RTD is directly associated with the asymptotic behavior of the RTD and can be finite or infinite. [ABSTRACT FROM AUTHOR]

This paper presents a transient model of internal catalytic combustion suitable for isolated channels and monolith reactors. Due to time-scales in the problem, the model considers a quasi-steady gas phase with a transient solid. The gas is described by axially varying bulk temperature and species. The gas includes lateral diffusion via transfer coefficients and the specification of a gas-phase species concentration at the wall; axial diffusion is neglected. The solid phase is a thermally thin shell with axially varying temperature, surface species, and surface species concentrations. The solid includes axial heat conduction and external heat loss by convection and radiation. The combustion process utilizes detailed gas and surface reaction models. The gas-phase model becomes a system of stiff ordinary differential equations with respect to axial position; the upstream (inlet) boundary conditions are specified and the axially varying solid properties are parameters in integration. The solid phase discretizes into a system of stiff ordinary differential-algebraic equations with respect to time. The time evolution of the system comes from alternating integrations of the quasi-steady gas phase and transient solid. The model is compared to two experimental cases using CO fuel: (1) steady-state conversion in an isothermal platinum tube and (2) transient propagation of a catalytic reaction inside a small platinum tube and includes external tube temperature measurements. This work presents sensitivity studies on important parameters including internal transfer coefficients, catalytic surface site density, external heat-loss, and others. Under mass-transfer limited conditions, global transfer coefficients are adequate to predict fuel conversion. Near light-off, the model predictions improve for the first case after adjusting the surface kinetics such that the net rate of CO adsorption increases compared to O 2 . For the second case, predictions of transient propagation speeds are good for equivalence ratios near unity and greater but require adjustment of external heat loss or kinetics to match under lean conditions. [ABSTRACT FROM AUTHOR]

Ice cream crystallization processes can be modeled by some population and energy balance equations. Due to the infinite dimensional and nonlinear characteristics, such models are highly complex, especially when all the phenomena of nucleation, growth and breakage are considered. Depending on the control problem under consideration, such a complexity can be useless and the control law can be designed on the basis of an input–output reduced order model of the process. In the present paper, we first consider a reduced order model of 6 ordinary differential equations obtained by the method of moments. By means of a sensitivity analysis and a parameter identification, it is shown that, to accurately describe the input–output behavior of the system whatever the conditions are, it is sufficient to change the values of only two parameters of this model, which is really interesting from a control point of view. However, when looking at the simulated data, the complexity of this moments model appears useless, from the input–output point of view. A second model reduction is therefore performed, based on physical assumptions. We finally get a new model with 3 ordinary differential equations, which is validated first on experimental data and then by comparison with the initial moments model. [ABSTRACT FROM AUTHOR]

Abstract: The pulsed column is a widely used technology for liquid–liquid extraction processes in various industries. A thorough understanding of the biphasic flow in the column is essential to achieve process optimization and design. This paper is dedicated to the modelling of the single-phase flow which is strongly influencing the transport, breakage and coalescence of droplets in the apparatus. In this aim, a Computational Fluid Dynamics (CFD) model was developed for the simulation of a disc and doughnut pulsed column. To discuss the relevance of the RANS-based CFD model, the simulation results have been compared to Particle Image Velocimetry (PIV) measurements synchronized on the pulsation period. Since the behaviour of the dispersed phase is strongly dependent on the turbulent properties of the flow, such as eddies size and dissipation rate, the discussion is focussed on turbulent quantities. In this aim, 3D simulations were first carried out and compared to 2D axisymmetric ones. Then, different numerical schemes and turbulence models were compared to experimental data to choose the model offering the most accurate modelling of the single-phase flow. [Copyright &y& Elsevier]

Abstract: The comprehensive description of the thermal degradation and combustion of biomass materials is a very challenging problem, as its complexity occurs at several levels: (1) multi-component problem, with an intrinsic variability of biomass composition; (2) multi-phase problem since the biomass reacts both in the condensed and in the gas phase resulting in the formation of a solid bio-char, a liquid bio-oil, and a gas phase; (3) multi-scale problem since the intra and inter-phase transport phenomena need to be considered both at the particle and reactor scale; and (4) multi-dimensional problem since the overall system could evolve along several coordinates such as the particle radius, biomass bed, and time. This complexity is further enhanced by the need of a coupled and comprehensive approach of the transport phenomena and the detailed kinetic schemes both in the solid and gas phase. After a review of the multi-step kinetic model adopted for the pyrolysis of biomass particles, the homogeneous gas phase reactions, and the heterogeneous reactions of the residual char, this paper analyzes the mathematical model at the particle and reactor scale. The mathematical models of a biomass gasifier and a traveling grate combustor constitute two working examples of the different scales from the biomass particle up to whole industrial devices. [Copyright &y& Elsevier]

Abstract: Large drops rising or sinking in an immiscible liquid can develop thin trailing structures commonly referred to as “skirts”. The paper describes a mathematical model for the thickness of these skirts accounting for the viscous boundary layer that develops along the surface of the parent drop and of the skirt itself. Unlike earlier theories, the skirt thickness is found to decrease with distance from the drop rim, which illuminates the mechanism which terminates the skirt at a finite length. A scaling of the skirt length is suggested by an analysis of published data, which also leads to a scaling for the volume of liquid in the skirt. The theoretical predictions are compared with the few experimental results for which sufficiently detailed information is available. [Copyright &y& Elsevier]

Abstract: The general rate model (GRM) is considered to be a comprehensive and reliable mathematical model for describing the separation and mass transfer processes of solutes in chromatographic columns. However, the numerical solution of model equations is complicated and time consuming. This paper presents analytical solutions of the GRM for linear adsorption isotherms and different sets of boundary conditions at the column inlet and outlet. The analytical solutions are obtained by means of the Laplace transformation. Numerical Laplace inversion is used to transform back the solution in the time domain because analytical inversion cannot be obtained. The first four temporal moments are derived analytically using the Laplace domain solutions. The moments of GRM are utilized to analyze the retention times, band broadenings, front asymmetries and kurtosis of the elution profiles. Relationships are derived among the kinetic parameters to match the first four moments of GRM and the simpler lumped kinetic model (LKM). For validation, the analytical solutions are compared with numerical solutions of a second order finite volume scheme. Good agreements in the results verify the correctness of analytical solutions and the accuracy of the numerical scheme. [Copyright &y& Elsevier]

Abstract: Conventional network structure modifications for retrofitting heat exchanger networks (HENs) usually require a large network superstructure, which might lead to very large scale retrofit models, and thus increases the computational difficulties of optimization, especially for industrial applications. This paper presents a novel optimization approach of retrofitting HENs for both small scale and industrial scale problems. To overcome the drawback of the existing retrofit research, a simple but efficient method is proposed to determine the network retrofit superstructure based on the concept of pinching match. Then two optimization stages (network structure optimization and investment optimization) are solved with the MILP-based iteration method that has been developed. The proposed approach has many benefits for solving HEN retrofit problems. First, smaller size of retrofit superstructure is provided based on the pinching match analysis. Second, the MILP-based iteration method developed converts conventional a mixed integer non-linear programming (MINLP) to a mixed integer linear programming (MILP), and significantly reduce the computational difficulties of nonlinear programming associated with configurational changes or structural modifications for existing heat exchanging arrangements, which is upgraded based on the MILP-based iterative method proposed by Pan et al. (2012a) for retrofitting HENs with heat transfer intensifications, as the earlier work was only applicable to the cases without network topology modification. In case studies, the new proposed approach is compared with the existing methods in two literature examples and one industrial problem, demonstrating that the new proposed approach is able to obtain better and more realistic solutions for HEN retrofitting considering the economic trade-offs between energy savings and investments. [Copyright &y& Elsevier]

Abstract: First of all, the aim of this paper is to systematically analyze the metabolism of mammalian cell cultures and reduce the complicated metabolic networks to a manageable macroscopic reaction scheme. Herein, the central carbon metabolism (glycolysis, TCA cycle and glutaminolysis) of glucose and amino acids was investigated whereas the synthetic metabolism of cell and antibody was simply represented with macroscopically balanced reactions. Without losing generality, perfusion and fed-batch cultures of two typical cell lines (hybridoma and GS-CHO) were carried out in bioreactor. With macroscopic balance analysis and metabolic flux analysis (stationary and dynamical), the metabolic networks were rationally reduced thanks to the experimental facts that most of the amino acids (except glutamine, glutamate, and alanine) contributed negligibly to the central carbon metabolism, i.e., they were allocated mainly to the syntheses. Finally, with the aid of analysis of elementary flux mode analysis and extreme pathways, nine macro reactions were derived with physiological definitions. Furthermore, the results from above analyses (MBA, MFA, EFM and EPs) support following conclusions: the respiratory quotient value in mammalian cell culture generally should be near one; several potential metabolic bottlenecks (pyruvate to acetyl-CoA, cytosol NADH translocation into mitochondrion, glutamate dehydrogenation into TCA) may control and regulate cellular metabolism. These results will benefit the future study of dynamic modeling for process monitoring and control. [Copyright &y& Elsevier]

Abstract: Pseudo-two dimensional (pseudo-2D) fluidized beds, for which the thickness of the system is much smaller than the other two dimensions, are widely used to perform fundamental studies on bubble behavior, solids mixing, or clustering phenomenon in different gas–solids fluidization systems. The abundant data from such experimental systems are very useful for numerical model development and validation. However, it has been reported that two-dimensional (2D) computational fluid dynamic (CFD) simulations of pseudo-2D gas–solids fluidized beds usually predict poor quantitative agreement with the experimental data, especially for the solids velocity field. In this paper, a new model is proposed to improve the 2D numerical simulations of pseudo-2D gas–solids fluidized beds by properly accounting for the frictional effect of the front and back walls. Two previously reported pseudo-2D experimental systems were simulated with this model. Compared to the traditional 2D simulations, significant improvements in the numerical predictions have been observed and the predicted results are in better agreement with the available experimental data. [Copyright &y& Elsevier]

Abstract: Special pseudo-components (SPCs) are proposed to be the compositional entities for characterizing the complicated mixtures of stock and product oils involved in fluid catalytic cracking risers. SPCs have invariant and definite physicochemical properties and are defined in pairs of light and heavy oil cuts of narrow boiling range. A narrow cut of true boiling point distillation of a stock or product oil is expressed with a pair of SPCs, which constitutes the basis for the characterization procedure developed in this paper. A steady state model for a prototype riser with a side feed stream is formulated where material and heat balance is strictly observed, the hydraulic behavior is considered, and the kinetic scheme of Gupta et al. (2007) is adopted. Results of tests with production data from three commercial risers show that the kinetic scheme of Gupta et al. (2007) is predictive as coupled with the suggested characterization procedure in the sense that for a given riser and given catalyst, the kinetic parameters are independent of stock oils. [Copyright &y& Elsevier]

Abstract: This paper uses the fractal diffusion–reaction model (OP diffusion–reaction model) to describe the diffusion and reaction of gases in a mesoporous catalyst. We obtain an approximate solution of the OP diffusion–reaction model by using first approximation. Based on the first approximate and multi-step first approximation, we propose two formulas for the effectiveness factor expressed in general form and use them for an nth-order reaction. The catalytic kinetics could be qualitatively and quantitatively analyzed in detail with these two formulas. We determine the pre-exponential factor of the effective diffusivity and the pre-exponential factor of the fractal rate coefficient. We compare experimental data for the kinetics of an ethylene hydrogenation reaction on Ni/Al2O3 with values calculated from the OP diffusion–reaction model and Fick's diffusion–reaction model. The results show quantitative differences between the effectiveness factors obtained with these two models. There are no qualitative differences between them, but the OP diffusion–reaction model gives a more realistic description of heterogeneous catalysis in a porous catalyst because its calculated results fit better to the experimental data. The effective diffusivity is related to the temperature, molecular weight of gases and structure of the porous material, and it describes diffusional behavior in real catalytic porous particles for each particle size more effectively because it does not depend on the tortuosity factor. [Copyright &y& Elsevier]

Abstract: This paper presents a VOF-based numerical method for simulating mass transfer across deformable fluid interfaces. The underlying mathematical model is based on continuum thermo-mechanics and allows for different solubilities of the species in the respective fluid phases, while volume changes due to mass transfer are neglected. The discontinuous changes in species concentrations at the interface are modeled by means of Henry's law which is shown to be a good approximation to the jump conditions at the interface in many cases. Within the numerical approach the concentration of the transfer component is represented by two separate variables, one for each phase. This is crucial in order to avoid artificial mass transfer. The physical mass transfer is modeled by an interfacial exchange term accounting for Henry's law, where two variants are compared. In addition, a subgrid-scale model is introduced for capturing steep concentration gradients appearing at the interface in convection dominated cases. The approach is validated by comparison of 3D numerical results for a spherical bubble rising at small Reynolds number in a glycerol–water mixture with an accurate solution based on the Hadamard–Rybczynski velocity field. Results obtained from 3D simulations for oxygen transfer from bubbles at moderate Reynolds numbers are compared with known Sherwood number correlations, showing good agreement. Finally, the dependence of the local concentration boundary layer thickness on Schmidt number is investigated. [Copyright &y& Elsevier]

Abstract: In order to optimize the design of gas–liquid packed columns used in distillation or in absorption processes, it is of high importance to be able to predict liquid dispersion. Indeed, dispersion phenomena will impact the choice and design of liquid distributing devices and the height of the packed beds. For this, one mainly relies on industrial feedback and on some experimental results obtained at laboratory scale which cannot be directly extrapolated since their geometric characteristics are at least one order of magnitude less than industrial columns in terms of columns diameter and height. To fill this gap CFD simulation tools should be more used since they can apply to any scale. However the latter option requires adequate modeling in particular for dispersion forces which are little studied due to the lack of data for validation. The present paper aims at developing, from original dispersion experimental measurements, closure laws that can be implemented in CFD codes. Liquid spreading from a source point has been investigated for Mellapak 250.X packing via gamma-ray tomography measurements. Closure laws are discussed from a simple 1D model which enables to go further within the Eulerian two-fluid framework with original user-defined functions and associated models that take into account liquid dispersion in the packed bed. The latter is modeled as a porous medium with appropriate closure laws. The comparison between experiments and CFD results shows that the present approach is adequate and should be further developed in order to be more precise and adapted to more packings. [Copyright &y& Elsevier]

Abstract: A one dimensional dewatering model for a thickener consistent with time-dependent densification of aggregates within a sludge suspension has been developed in this paper. The effects of different densification rate parameters and different underflow solids fluxes on the predictions of the sludge rheological properties and thickener performance have been explored. Pre-shearing of aggregates (which leads to the aggregates densifying to some extent before entering the thickener consolidating bed) must occur if a large underflow solids flux is required in a densified thickener. This increases the suspension gel point, and hence the solids volume fraction at the top of the bed. The solids volume fraction at the top of the bed will however be the initial undensified gel point in the case of a small underflow solids flux, where no pre-shearing of aggregates needs to occur. The effects of densification and/or pre-shearing on the sludge rheological properties and thickener performance have been predicted. For a densified thickener, an algorithm has been developed to determine the maximum permitted underflow solids flux, q max , assuming any possible solids volume fraction at the top of the bed and the maximum underflow solids flux, q mu , constraining to the initial undensified gel point at the top of the bed. Regarding the aggregate densification rate parameter, as this parameter was increased, the sludge rheological properties evolved significantly during thickening and thickener performance was substantially enhanced. Moreover, the total solids residence time required to achieve the desired underflow solids volume fraction was significantly reduced both for a higher densification rate parameter and in the presence of pre-shearing in a densified thickener. [Copyright &y& Elsevier]

[Display omitted] • Generalised framework for modelling of swellable microneedles for drug delivery. • Rate of insulin release is faster in initial phase, followed by a steady rate of release. • Insulin diffusion rate from reservoir to skin increases with the increase in the polymer hygroscopic swelling. • Skin viscoelasticity pushes swelled microneedle upward, decreasing insulin diffusion rate. Recently, swellable microneedles (SMNs) have gained significant interest due to their potential applications in transdermal drug delivery (TDD). SMNs swell by absorbing interstitial fluid in the skin, and they facilitate drug transport into the skin without polymer dissolution. To establish the SMNs for practical usages, one requires an accurate understanding of the drug transport mechanisms from these MNs that would allow both controlled TDD as well as optimisation of the MN geometries. In addressing this issue, a mathematical model is formulated which incorporates the key parameters defining the skin properties and physicochemical properties of the MNs, such as the polymer swelling capacity, mechanical deformation, amount of drug loading, and penetration depth in the skin. Numerical simulations are performed using well-defined MN parameters which represent the MN constituent and drug, namely, polyvinyl alcohol and insulin, in this study. The proposed mathematical model predicts that insulin diffuses into the blood to reach a maximum concentration of 11.72 ng/ml in 1.5 h, and ~95% insulin is eliminated from the blood within 11 h. The rate of insulin diffusion to blood increases with an increase in MN swelling. However, not much difference is observed in the insulin profiles when MNs swell more than two times their mass as the skin tends to displace the MN out of the skin, as it increases the length of the diffusion pathway for the drug in the skin layers. The depth of MN penetration affects the overall insulin delivery, with insulin getting eliminated from the body in 8 h when MN is fully inserted into the skin. The rate of change of blood concentration of insulin is found to increase and decrease non-linearly with time for the cases studied in this paper. The developed model provides a platform for optimization of SMNs for the controlled delivery of different drug molecules. [ABSTRACT FROM AUTHOR]