Convective-diffusive Transport Research Articles

MODELLING OF MASS TRANSFER IN WASTEWATER FACILITIES

Problem statement. The design of wastewater treatment systems is a complex process and requires the use of special mathematical models. As a rule, empirical models are used at the stage of designing structures of water drainage systems, which allow obtaining only an “integral” characteristic of the efficiency of wastewater treatment. But in a number of cases, it is important to have information about the spatial distribution of the impurity concentration in the structure. To solve this problem, you need to have three-dimensional mathematical models. In the future, there is a shortage of such models, so the creation of three-dimensional multifactorial models for the analysis of the efficiency of drainage system structures is an urgent task. The purpose of the article. Development of a three-dimensional numerical model for the analysis of the mass transfer process to determine the impurity concentration in the clarifier. Methodology. The analysis of impurity concentration fields in the clarifier is carried out by numerical integration of the three-dimensional equation for the velocity potential and the three-dimensional equation of the convective-diffusion transport of the impurity. For the numerical integration of the Laplace equation for the velocity potential, the variable-triangular method and the Liebmann method are used. Finite-difference splitting schemes are used for numerical integration of the three-dimensional equation of convective-diffusion transport of impurities. Scientific novelty. A dynamic multifactorial numerical model was created for the analysis of the process of mass transfer of impurities in a settling tank by conducting a computational experiment. Practical value. The built multifactorial numerical model makes it possible to analyze the efficiency of wastewater treatment in clarifiers that have a complex geometric shape and cannot be calculated on the basis of existing engineering methods. Conclusions. On the basis of the developed three-dimensional numerical model, a computer code was created, which allows you to quickly obtain information about the distribution of the impurity concentration in the settling tank.

ASSESSMENT OF THE ENERGY FACILITY IMPACT ON ENVIRONMENTAL POLLUTION

Problem statement. The task of assessing the influence of the boiler house on atmospheric air pollution is under consideration. Carrying out such an assessment is very important when locating boiler houses near residential areas. Since the weather conditions for each region are characterized by a change in the direction of the wind, the intensity of atmospheric diffusion, the appearance of a calm, it is important to have information about the formation of pollution zones in sedimentary zones. To solve this important problem, it is very important to use mathematical modeling, since it is currently impossible to create a sufficient number of observation posts near the objects of the fuel and energy complex. The purpose of the article. Numerical analysis of the influence of the boiler house on the intensity of atmospheric air pollution under different weather conditions. Methodology. The 3D equation of convective-diffusion transport is used to estimate the pollution zones formed in the atmospheric air when it is emitted from the boiler house pipe. The model takes into account atmospheric stratification, impurity emission intensity, wind profile, wind speed. Numerical integration of the equation of convective-diffusion transport of impurities is carried out using finite-difference schemes. The modeling equation is split into an equation for the convective transport of the pollutant and an equation for the dispersion of the pollutant due to atmospheric diffusion. The equation describing the change in the concentration of the impurity in the atmospheric air as a result of the emission of the pollutant from the pipe is solved separately. At the next stage, finite-difference schemes are built that allow solving the splitting equation. Scientific novelty. On the basis of the constructed numerical model, the zones of atmospheric air pollution during the emission of CO from the pipe of the boiler house are determined. A numerical model is proposed that allows forecasting atmospheric air pollution for different weather conditions within the framework of one program package. Practical significance. On the basis of the proposed numerical model, the forecasting of the zones of chemical pollution of the atmospheric air in the settlement zone in which the boiler house is located was carried out. The results of the computational experiment are presented.

On the generality of the finite element modeling physical fields in biological systems by the multiscale smeared concept (Kojic transport model)

The biomechanical and biochemical processes in the biological systems of living organisms are extremely complex. Advances in understanding these processes are mainly achieved by laboratory and clinical investigations, but in recent decades they are supported by computational modeling. Besides enormous efforts and achievements in this modeling, there still is a need for new methods that can be used in everyday research and medical practice. In this report, we give a view of the generality of the finite element methodology introduced by the first author and supported by his collaborators. It is based on the multiscale smeared physical fields, termed as Kojic Transport Model (KTM), published in several journal papers and summarized in a recent book (Kojic et al., 2022) [1]. We review relevant literature to demonstrate the distinctions and advantages of our methodology and indicate possible further applications. We refer to our published results by a selection of a few examples which include modeling of partitioning, blood flow, molecular transport within the pancreas, multiscale-multiphysics model of coupling electrical field and ion concentration, and a model of convective-diffusive transport within the lung parenchyma. Two new examples include a model of convective-diffusive transport within a growing tumor, and drug release from nanofibers with fiber degradation.

Dynamics of a silicone oil drop submerged in a stratified ethanol-water bath.

We analyze numerically the Marangoni flow around an immiscible droplet submerged in a stably stratified mixture of ethanol and water. The linear stability analysis shows that the base flow undergoes a supercritical Hopf bifurcation that leads to oscillations. The theoretical prediction for the critical droplet radius is consistent with previous experimental results. Ethanol diffusion in water is critical in the flow stability for both low and high droplet viscosity. Direct numerical simulations of the nonlinear oscillatory flow show that the frequency of those oscillations approximately equals that of the critical eigenmode. The nonlinear convective term of the ethanol diffusive-convective transport equationfixes the amplitude of the droplet oscillations. The viscous dissipation associated with the Marangoni flow inside the droplet considerably reduces the oscillation.

Lattice Boltzmann simulations for the drying of porous media with gas–side convection–diffusion boundary

One of the most significant challenges in describing the drying of porous materials is the realistic integration of internal transport phenomena into mathematical models, coupled with the external free flow. However, the intricacies of pore-scale geometry make experimentation and observation very difficult in practice, thereby making modeling techniques a useful tool for the analysis of the drying process. Among the many modeling techniques developed for drying, the lattice Boltzmann method (LBM)-based modeling approach has gained favor in recent years due to its ability to incorporate realistic geometry and transport at the pore scale. Our previous works on Shan–Chen LBM for drying of capillary porous media were based on the Bhatnagar–Gross–Krook collision operator and diffusion interface boundary conditions. This study elucidates the drying of a capillary porous medium under the influence of convection–diffusion boundary conditions at the gas side, using Shan–Chen LBM. The pore-scale effects of convection–diffusion conditions during the drying process are presented in relation to the macroscale drying kinetics. Moreover, the differences between the convection–diffusion kinetics and purely diffusion–dominated kinetics of the drying process are also presented here. This work also aims to incorporate the convection–diffusion transport phenomena into the drying process of a porous medium under the influence of an imposed thermal gradient, establishing and studying the phenomena of stabilization and destabilization of the drying front under the influence of a temperature gradient, thereby extending the lattice Boltzmann method of modeling for the simulation of convection–diffusion drying, both for the isothermal case and the imposition of a thermal gradient.

Computational modeling of low-density lipoprotein accumulation at the carotid artery bifurcation after stenting.

Restenosis typically occurs in regions of low and oscillating wall shear stress, which also favor the accumulation of atherogenic macromolecules such as low-density lipoprotein (LDL). This study aims to evaluate LDL transport and accumulation at the carotid artery bifurcation following carotid artery stenting (CAS) by means of computational simulation. The computational model consists of coupled blood flow and LDL transport, with the latter being modeled as a dilute substance dissolved in the blood and transported by the flow through a convection-diffusion transport equation. The endothelial layer was assumed to be permeable to LDL, and the hydraulic conductivity of LDL was shear-dependent. Anatomically realistic geometric models of the carotid bifurcation were built based on pre- and post-stent computed tomography (CT) scans. The influence of stent design was investigated by virtually deploying two different types of stents (open- and closed-cell stents) into the same carotid bifurcation model. Predicted LDL concentrations were compared between the post-stent carotid models and the relatively normal contralateral model reconstructed from patient-specific CT images. Our results show elevated LDL concentration in the distal section of the stent in all post-stent models, where LDL concentration is 20 times higher than that in the contralateral carotid. Compared with the open-cell stents, the closed-cell stents have larger areas exposed to high LDL concentration, suggesting an increased risk of stent restenosis. This computational approach is readily applicable to multiple patient studies and, once fully validated against follow-up data, it can help elucidate the role of stent strut design in the development of in-stent restenosis after CAS.

In silico evaluation of pharmacokinetic parameters, delivery, distribution and anticoagulative effects of new 4,7-dihydroxycoumarin derivative

In this study, pharmacological profiling and investigation of the anticoagulant activity of the newly synthesized coumarin derivative: (E)-3-(1-((4-hydroxy-3-methoxyphenyl)amino)ethylidene)-2,4-dioxochroman-7-yl acetate (L) were performed. The obtained results were compared with the parameters obtained for Warfarin (WF), which is a standard good oral anticoagulant. The estimated high binding affinity of L toward plasma proteins (PPS% value is > 90%) justifies the investigation of binding affinity and comparative analysis of L and WF to Human Serum Albumin (HSA) using the spectrofluorimetric method (296, 303 and 310 K) as well as molecular docking and molecular dynamics simulations. Compound L shows a very good binding affinity especially to the active site of WF (the active site I -subdomain IIA), quenching HSA fluorescence by a static process. Also, the finite element smeared model (Kojic Transport Model, KTM), which includes blood vessels and tissue, was implemented to compute the convective-diffusion transport of L and WF within the liver. Finally, compound L shows a high degree of inhibitory activity toward the VKOR receptor comparable to the inhibitory activity of WF. Stabilization and limited flexibility of amino acid residues in the active site of the VKOR after binding of L and WF indicates a very good inhibitory potential of compound L. The high affinity of the L for the VKOR enzyme (Vitamin K antagonist), as well as the structural similarity to commercial anticoagulants (WF), provide a basis for further studies and potential application in the treatment of venous thrombosis, pulmonary embolism and ischemic heart disease. Communicated by Ramaswamy H. Sarma

Control-Oriented Reduced-Order Modeling of Conversion Efficiency in Dual-Layer Washcoat Catalysts With Accumulation and Oxidation Functions

Abstract This work proposes a model for predicting conversion efficiency in multifunctional catalysts with dual-layer washcoat. The mass transfer is more relevant in these devices than in single-layer washcoats due to additional transport steps between the catalytic layers. In addition, the different reaction mechanisms between layers make the concentration of the chemical species differ in each layer. To deal with this boundary while considering the need for real-time computation, a reduced-order explicit solver for the convective diffusive reactive transport is presented for the case of dual-layer washcoats. Assuming one-dimensional quasi-steady flow, the solution procedure consisted of substituting the diffusive interfacial fluxes in the bulk gas and washcoat conservation equations by expressions that depend explicitly on the average concentration in the gas phase. The solution was then applied to model the performance of dual-layer oxidation catalysts with reductant accumulation in one washcoat layer, such as diesel oxidation catalyst (DOC) and ammonia slip catalyst (ASC) systems, during driving cycles. First, the response of these catalysts was analyzed by comparing them against experimental data and considering additional parameters provided by the model. Next, the importance of the mass transfer limitations was discussed to complete the analysis. The proposed model was compared with a simplified solver where the mass transfer steps were omitted, thus deteriorating the prediction capabilities in some driving cycle phases. Finally, a sensitivity study was performed to assess the impact of the mesh size on the prediction capabilities and computational requirements.

MATHEMATICAL MODELING OF UNSTATIONARY AIR POLLUTION PROCESS

Problem statement. The task of determining the dynamics of air pollution in the working room when air containing a chemically hazardous substance flows into it is considered. The peculiarity of this problem is that the formation of pollution areas in the room is influenced by many factors, especially the internal geometry (the presence of technological equipment in the room, furniture, etc.). Therefore, it is necessary to have specialized mathematical models that allow predicting the level of chemical air pollution in the room for a given type of pollution. The purpose of the article. Development of a three-dimensional numerical model for indoor air flow aerodynamics and mass transfer of a chemically hazardous substance entering the room through the ventilation system to predict the risk of toxic damage to workers. Methodology. A three-dimensional equation of convective-diffusion transport for a chemically hazardous substance is used to model the process of a chemically hazardous substance spread in the working room air. The air flow velocity field in the working room is calculated on the basis of the model for the incompressible fluid potential motion. For the numerical integration of the Laplace equation for the velocity potential, two finite-difference schemes are used. The splitting method and finite-difference schemes are used for the numerical integration of the three-dimensional mass transfer equation of the impurity. At each splitting step, the determination of the unknown concentration of the impurity is carried out according to an explicit formula. A computer code was created to conduct computational experiments based on the developed numerical model. Scientific novelty. A three-dimensional numerical model has been developed to analyse the dynamics of the formation of chemical air pollution areas in workplaces when impurities enter the premises through the ventilation system. A feature of the model is the consideration of the main physical factors affecting the formation of pollution areas and the calculation speed. Practical value. The numerical model and the computer code developed on its basis allow solving specific problems that arise when assessing the risk of toxic damage to workers at chemically hazardous facilities. Conclusions. An effective three-dimensional numerical model and computer code have been created, which allow predicting the level of chemical contamination of working premises when a toxic substance enters the premises through the ventilation system. The results of the computational experiment are presented.

The electrodiffusional theory for the wall shear stress measurement by two-strip probe

This article deals with the derivation of the fundamental theory describing the mass transport on the active surface of a two-strip mass transfer probe for an arbitrary direction of fluid flow. The existence of such a general theory is a critical point for the application of the electrodiffusion method using a two-strip probe. Considering the different possible sizes of the probe segments, the analytical formulas for the average mass transfer coefficients are derived and presented in dimensionless forms for both segments. The correctness of the derived analytical expressions is verified by numerical solution of the convection-diffusion transport equation. A methodology for possible experimental data treatment is also proposed. It is based on the evaluation of two current signals collected from the segments of a two-strip probe. From the derived equations, it is possible to determine the magnitude and direction of the wall shear rate vector for both frontal and reverse flow regimes. From the analysis of the current ratio predictions for different probe geometries, an optimal probe configuration is found with respect to the sensitivity of the flow direction measurement.

A Bayesian-variational cyclic method for solving estimation problems characterized by non-uniqueness (equifinality)

In this paper a new method for solving complex estimation problems for systems governed by partial differential equations and characterized by non-uniqueness (or equifinality) is presented. For such problems, the usefulness of the MAP estimates is doubtful, especially if the available prior information is very limited or not plausible in general. Thus, the posterior mean or median estimates would be more appropriate, which implies that the Bayesian approach has to be preferred. Since the direct use of the Bayesian approach involving computationally expensive models is not feasible a hybrid method which combines the Bayesian and variational elements in a unique way is suggested. The main idea of the method is to find one particular posterior mode out of a possibly infinite set, which would have the global properties (its first moments, for example) consistent with the available prior information and close to those of the posterior mean. The method is implemented in the form of a cyclic algorithm including the Bayesian estimation part for the lumped global (hidden, latent) variables describing the moments of the spatially distributed or time-dependent variables and the variational estimation part for the invariant ‘shape’ functions. The method has been numerically validated for two different applications: one including the Saint-Venant hydraulic model, and another one including the nonlinear convection-diffusion transport model. The results for the former are reported in a separate paper (reference provided), for the latter - in the present paper. These results confirm the expected properties of the suggested algorithm, such as improved robustness and accuracy, in comparison to the MAP estimator represented by the variational estimation algorithm.

Pore-scale study of dynamic adsorption of a water-soluble catalyst during drainage displacement in porous media using lattice Boltzmann simulations

This paper presents the first systematic pore-scale study of the dynamic adsorption of a water-soluble catalyst during two-phase flows of immiscible fluids (water and oil) in porous media. The results of this paper are based on mathematical modeling in two-dimensional synthetic porous structures using the lattice Boltzmann simulations for two-phase flow and convective-diffusive transport of catalyst dissolved in a water that cannot penetrate the oil. The results showed that an increase in oil viscosity tends to a decrease in the maximum adsorbed amount of catalyst measured in a quasi-stationary state. An increase in capillary number, on the contrary, promotes an increase in the adsorbed amount. In this paper, for the first time, we have characterized the dynamic adsorption regimes versus the adsorption rate constant and capillary number. At a low adsorption rate, the adsorbed amount is determined by the duration of the reaction between the catalyst and the adsorbent particles, while at a high adsorption rate, the adsorbed amount is controlled by the maximum adsorption value. In addition, it has been established that a prediction accuracy of the adsorbed amount deteriorates significantly with decreasing capillary number.

Prediction of atmospheric air pollution near a coal stack in adverse weather conditions

Coal piles on the territory of enterprises are long-term sources of dust pollution of atmospheric air. Forecasting the level of dust pollution of the air for such objects is carried out, as a rule, for convection conditions. But during inversion, very high concentrations of dust can occur on industrial sites. The task of assessing the level of dust pollution of atmospheric air at an industrial site during dust emission in conditions of inversion from a coal stack is considered. A three-dimensional equation of convective-diffusion dispersion of contamination in atmospheric air, compatible with the approach of Prof. Berliand M. on determining the value of the vertical diffusion coefficient in the surface layer of the atmosphere for the case of inversion, to model dispersion of dust from a coal stack under inversion conditions is used. Numerical integration of the modeling equation of convective-diffusion transport of contamination is carried out on the basis of the splitting method compatible with the use of a locally one-dimensional finite-difference scheme. The results of a computational experiment to determine dust pollution zones at the Prydniprovsk thermal power station are presented.

Assessment of radioactive contamination level of environment in case of accident at nuclear power plant

The accidents at nuclear power plants pose a particular threat to the population and the environment. Accidental emissions at nuclear power plants can cause long-term radioactive pollution of the environment, and the elimination of such pollution can take years. For practice, it is very important to predict the intensity and size of radioactive contamination zones for various scenarios of extreme situations at the nuclear power plants. Such a forecast will identify the most vulnerable areas and develop a response strategy to the situation that has arisen. A numerical model has been built that allows to quickly predict the scale of radioactive contamination of the territory during an emergency release at a nuclear power plant. The model is based on the application of implicit difference schemes for the numerical integration of the equation of convective-diffusion transport of impurities in the atmosphere. The developed model is characterized by the calculation speed. The results of the computational experiment are presented.

Bridging transport and deposition of colloidal nanoparticles on cylindrical microfibers

Colloidal deposition on fibers is central to industrial applications including fibrous filters and textiles. We propose a self-consistent Eulerian model to bridge the gap between long-range convective-diffusive transport and short-range Derjaguin-Landau-Verwey-Overbeek (DLVO) deposition of colloidal nanoparticles on microfibers. Starting from a single fiber flow cell, our model extends freely to fiber pairs and multi-fiber arrays. For fiber pairs, we found that the deposition efficiency deviates from Péclet number dependence of Pe-2/3, and that the pressure loss is reduced for cross-stream bundles. For multi-fiber arrays, we show how colloidal deposition can be spatially controlled through fiber zeta potentials and how colloids with poly-disperse zeta potentials can be sorted. Interesting deposition hotspots are accessible on surfaces of fibers, such as in compact or composite filters. Together, our work highlights a simple, flexible and scalable approach for modelling colloidal transport phenomena on fibers separated by hydrodynamic length scales.

SIMULATION OF UNSTEADY TRANSPORT PHENOMENA USING NEW FINITE VOLUME METHOD

Based on the finite volume method (FVM), a numerical scheme is constructed to simulate the unsteady convection–diffusion transport problem. New expressions are obtained for interface approximation of the field variable, subsequently, these newly obtained interface expressions are used to develop the numerical scheme. Convection-dominant and diffusion-dominant phenomena are simulated by taking different values of convective velocity [Formula: see text] and diffusion coefficient [Formula: see text]. This newly proposed numerical scheme gives second order of convergence along space and time. Experiments are carried out to test the new proposed upwind approach. Numerical results produced by the proposed approach are compared with the conventional finite volume method, step-wise approach FVM and quadratic upwind interpolation finite volume approach. This comparative study indicates that for different cases for convection-dominant and diffusion-dominant problems, our proposed approach gives highly accurate and stable solution. The conventional finite volume method and other approaches result solution with non-physical oscillations. Our obtained numerical results are consistent and support our theoretical approach.

Numerical Approximation of One‐Dimensional Transport Model Using an Hybrid Approach in Finite Volume Method

A finite volume method is a well‐known and appropriate approach for numerical approximation of governing problems. This article proposes a finite volume approach to simulate the one‐dimensional convection–diffusion transport problem. New expressions for interface approximation are constructed by combining the assumption of step‐wise profile and piece‐wise linear profile. In addition, a new numerical technique is developed based on these new interface approximations. This new numerical algorithm produces consistent results for numerical approximation of the governing problem and gives second‐order accuracy along space and time. In order to justify the effectiveness of our numerical technique, numerical experiments are conducted for various magnitudes of convection and diffusion coefficients. The numerical results of the proposed algorithm are also compared to the finite volume method and the finite difference method. Based on this comparison, our numerical scheme presents stable and highly accurate results compared to the alternatives.

Dimethyl ether low-temperature catalytic oxidation over Rh/Al2O3 in a stagnation-flow reactor

Dimethyl ether (DME) is a promising fuel for use in low-temperature portable hydrogen production, domestic applications, or diesel engines. It burns with less emissions than conventional fuels and has properties similar to LPG in terms of storage and transport, rendering it effective in many strategies for combating climate change. In this study we investigated the partial and total oxidation of DME over 5 wt% Rh/Al2O3 at low temperatures (215 to 320 °C), relevant to portable and domestic energy applications as well as the after-treatment systems of DME-powered engines. We captured the effects of temperature, flow rate, and inlet feed composition on the reactivity. For partial oxidation, we utilized the stagnation-flow reactor geometry to isolate the oxidation zone from the reforming zone. We discuss the reaction order with respect to DME and O2 and provide activation energy values under kinetics control. We also provide data where internal and external mass transfer limitations are present to examine the diffusive-convective transport near the catalyst surface, not easily done in three-dimensional environments such as packed beds. The experimental data we provide here pave the way for accurate kinetic modeling of DME partial and total oxidation on Rh/Al2O3, for reactor design and optimization as well as rational catalyst design.

A mechanistic model of cross-bridge migration in RBC aggregation and disaggregation.

Red blood cells (RBCs) clump together under low flow conditions in a process called RBC aggregation, which can alter RBC perfusion in a microvascular network. As elevated RBC aggregation is commonly associated with cardiovascular and inflammatory diseases, a better understanding of aggregation is essential. Unlike RBC aggregation in polymer solutions which can be well explained by polymer depletion theory, plasma-mediated RBC aggregation has features that best match explanations with cross-bridging mechanisms. Previous studies have demonstrated the dominant role of fibrinogen (Fg) in promoting aggregate formation and recent cell-force spectroscopy (CFS) experiments on interacting RBC doublets in plasma have reported an inverse relationship between disaggregation force and the adhesive contact area between RBCs. This has led investigators to revisit the hypothesis of inter-RBC cross-bridging which involves cross-bridge migration under interfacial tension during the forced disaggregation of RBC aggregates. In this study, we developed the cross-bridge migration model (CBMM) in plasma that mechanistically represents the migrating cross-bridge hypothesis. Transport of mobile Fg cross-bridges (mFg) was calculated using a convection-diffusion transport equation with our novel introduction of convective cross-bridge drift that arises due to intercellular friction. By parametrically transforming the diffusivity of mFg in the CBMM, we were able to match experimental observations of both RBC doublet formation kinematics and RBC doublet disaggregation forces under optical tweezers tension. We found that non-specific cross-bridging promotes spontaneous growth of adhesion area between RBC doublets whereas specific cross-bridging tends to prevent adhesion area growth. Our CBMM was also able to correlate Fg concentration shifts from healthy population blood plasma to SLE (lupus) condition blood plasma with the observed increase in doublet disaggregation forces for the RBC doublets in SLE plasma.

Characterization of dynamic adsorption regimes in synthetic and natural porous structures using lattice Boltzmann simulations

This paper presents the first systematic study on the characterization of dynamic adsorption regimes of gas in porous media using the ratio of inter- to intraparticle diffusion coefficients. The effect of the ratio between the two diffusion coefficients on the adsorption dynamics was investigated in combination with the adsorbent particles size and the disorder parameter, which numerically describes pore space heterogeneity, by mathematical modelling using the lattice Boltzmann simulations for fluid flow and the convective-diffusive transport of an adsorbate dissolved in a fluid. To characterize the dynamic adsorption regimes, for the first time, a relationship between the surface and total adsorption amount was used. The obtained results during simulations in two-dimensional synthetic porous structures showed that the size of the adsorbent particle strongly affects the surface and the total adsorption dynamics. An increase in the particle size promotes an increase in the rate of surface adsorption. Depending on the ratio of inter- to intraparticle diffusion coefficients, increasing particle size promotes either an acceleration or slowdown of the total adsorption dynamics. The results revealed in two-dimensional structures were verified by simulations in three-dimensional digital models of natural sandstones, which were obtained using X-ray computed tomography.