Mass Transfer Model Research Articles

Physics-informed neural network integrate with unclosed mechanism model for turbulent mass transfer

Turbulent mass transfer is widespread in chemical engineering processes including separation, reaction, and others. Traditionally, turbulent mass transfer processes can be simulated by computational fluid dynamics (CFD) methods. However, CFD methods require adequate turbulent models for the fluid flow and mass (and heat) transfer, which are normally difficult to develop for reliable solutions. Moreover, the CFD simulation is computationally intensive and hard to use in the cases like process optimization or analysis where the simulation needs to be called repeatedly. In this paper, physics-informed neural network (PINN) is developed and trained by unclosed mechanism model and sparse observation data of turbulent mass transfer process. The PINN method shows stronger generalization ability in solving the velocity, pressure and concentration fields in a turbulent mass transfer process than traditional deep neural network (DNN) method and turbulent Schmidt model. Under different boundary conditions, the PINN developed in the present paper can instantly predict the concentration distributions with sufficient accuracy and be used for inverse computation for estimating the turbulent viscosity and mass diffusivity as output results. The PINN is also capable of handling data noise by adjusting parameters, suggesting its potential in integrating experimental data.

Measurement of interfacial mass transfer of single bubbles rising in homogeneous turbulence

Accurate quantification of the mass transfer coefficient kl of bubbles under high Reynolds number conditions has been in desperate need for decades to provide insights into its fundamental physics and reach a general mass transfer model. In this paper, a state-of-the-art SI-LIF technique is developed to quantify kl indirectly based on the law of conservation of mass. The reconstruction algorithms of the required physical quantities are validated numerically, suggesting an overall uncertainty of less than ± 5 % in the estimation of kl. We perform mass transfer experiments of single oxygen bubbles with deq = 1.5 mm rising in both quiescent water and homogeneous turbulence, with turbulent Reynolds number ReT ranging from 0 to 1114. The measured kl under turbulent conditions are independent of ReT, and all collapse to the analytical solution of potential flow approximation, revealing that the flow in the immediate vicinity of the bubble interface remains undisturbed by the fluctuating liquid motions across all the turbulence settings examined in this paper.

Experimental and numerical study on thermal protective performance of weft-knitted spacer fabric system against hot pressurized steam

Hot pressurized steam is a dangerous environment threatening the safety of workers. Developing steam protective clothing with excellent thermal protective performance (TPP) and clarifying its design mechanism are essential to protecting workers. This study totally developed eleven spacer fabric systems (SFSs) and investigated the effects of four design factors of spacer fabrics (SFs) on TPP, including heat setting, spacer yarn fineness, feeding structure, and top layer structure. Additionally, a heat and mass transfer model was established to analyze the steam protective mechanism of SFSs. The results demonstrated that SF heat setting had a negligible effect on TPP of SFSs. As the spacer yarn thickened to 80 D, the TPP of SFSs improved and the positive effect of feeding structure II on TPP increased. Conversely, dense mesh on the SF top layer had a negative effect on TPP. The model predicted that skin burn times of SFSs decreased with the increasing of pressure. When the pressure was 2.5 kPa, the relative errors between experimental and predicted skin burn times were the smallest (0∼12 %), which could more accurately simulate the steam protective mechanism of SFSs. These findings provide a theoretical basis for the development of high performance steam protective clothing.

Valorization of wild thyme (Thymus serpyllum L.) herbal dust by supercritical fluid extraction – Experiments and modeling

The aim of this study was to develop five empirical and three mass-transfer based models for fitting the T. serpyllum SFE process. Additionally, the determination of the effect of SFE parameters (pressure, temperature, CO2 flow rate and mean particle size) on kinetic curves and model parameters was investigated. Among the selected models, all empirical and mass-transfer models provided adequate fit with experimental data. However, mass-transfer model VIII has proved to fit the experimental results accordingly and has shown that the most influential parameters were pressure and CO2 flow rate. The pressure and CO2 flow rate exhibited positive effect, while the temperature had rather negative impact on Y. In addition, the initial slopes of Model VIII were calculated in order to increase the efficiency and reduce unnecessary process costs.

A conjugated heat and mass transfer model to implement reaction in particle-resolved CFD simulations of catalytic fixed bed reactors

Modelling catalytic fixed bed reactors with a small tube-to-particle diameter ratio requires a detailed description of the interactions between fluid flow, intra-particle transport, and the chemical reaction(s) within the catalyst. Particle-resolved computational fluid dynamics (PRCFD) simulations are the most promising approach to predict the behaviour of these reactors accurately, since they take into account the local packed bed structure explicitly. In this work, a conjugated heat and mass transfer model for use in PRCFD simulations is presented in order to couple the fluid flow through the fixed bed with transport and reaction in the porous catalyst, while guaranteeing the no-slip boundary condition at the fluid–solid interface. For this purpose, the solutions of the solid and fluid domain are computed separately and are coupled by calculation and updating the boundary condition at the particle surface. Owing to the consideration of secondary gradients, the developed transfer model is also valid for unstructured calculation meshes containing non-orthogonal cells at the fluid–solid interface. Such meshes are often used to resolve complex geometries, such as a packed bed, in a computationally efficient manner. The coupling approach is validated using cases for which an analytical solution or literature correlations derived from experimental data are available. The simulation results of a short catalytic packed bed with rings catalysing the partial oxidation of n-butane to maleic anhydride exemplify the potential of PRCFD involving reactions to analyse the catalyst performance in great detail.

Evaporation and sublimation measurement and modeling of an alpine saline lake influenced by freeze–thaw on the Qinghai–Tibet Plateau

Abstract. Saline lakes on the Qinghai–Tibet Plateau (QTP) affect the regional climate and water cycle through water loss (E, evaporation under ice-free conditions and sublimation under ice-covered conditions). Due to the observational difficulty over lakes, E and its underlying driving forces are seldom studied when targeting saline lakes on the QTP, particularly during ice-covered periods (ICP). In this study, the E of Qinghai Lake (QHL) and its influencing factors during ice-free periods (IFP) and ICP were first quantified based on 6 years of observations. Subsequently, three models were calibrated and compared in simulating E during the IFP and ICP from 2003 to 2017. The annual E sum of QHL is 768.58±28.73 mm, and the E sum during the ICP reaches 175.22±45.98 mm, accounting for 23 % of the annual E sum. E is mainly controlled by the wind speed, vapor pressure difference, and air pressure during the IFP but is driven by the net radiation, the difference between the air and lake surface temperatures, the wind speed, and the ice coverage during the ICP. The mass transfer model simulates lake E well during the IFP, and the model based on energy achieves a good simulation during the ICP. Moreover, wind speed weakening resulted in an 7.56 % decrease in E during the ICP of 2003–2017. Our results highlight the importance of E in ICP, provide new insights into saline lake E in alpine regions, and can be used as a reference to further improve hydrological models of alpine lakes.

Reaction path model of the formation of abiotic immiscible hydrocarbon fluids in subducted carbonated serpentinites, Lanzo Massif (Western Italian Alps)

Fluids generated from subducted slabs participate in the cycling of deep carbon in the crust and upper mantle. In these fluids, aqueous carbon species vary in oxidation state between +IV and -IV depending on whether the fluids are oxidizing or reducing, respectively. Most studies of subduction-zone fluids have focused on oxidized carbon species. However, recent studies of natural samples have demonstrated the occurrence of deep, reducing fluids, generated in both subducted oceanic upper mantle and crustal rocks. CH4-H2-rich fluid inclusions in subducted carbonated serpentinites have demonstrated the existence of abiotic, immiscible, hydrocarbon fluids at upper mantle conditions. To investigate the formation of such immiscible hydrocarbon fluids during the evolution of subducted carbonated serpentinites, we used equilibrium constants from the Deep Earth Water model to carry out predictive chemical mass transfer modeling to simulate the alteration reactions. A novel feature of the models was the inclusion of an immiscible hydrocarbon fluid containing six components (CH4,f,C2H6,f,C3H8,f,isoC4H10,f,CO2,f,H2,f). This feature enabled prediction of the formation of a separate immiscible fluid in equilibrium with aqueous species and minerals.We developed a predictive reaction path model of invasive H2,f reacting with carbonated serpentinites and interstitial aqueous fluids for comparison with the natural samples from the Lanzo Massif, western Italian Alps. Over a range of temperatures and pressures, immiscible hydrocarbon fluids formed in association with altered mineral assemblages. Reaction progress caused the transformation of carbonated serpentinites and the formation of clinopyroxene, brucite, graphite, and hydrocarbon fluids, along with changes of pH, logfO2, and aqueous species. CH4,f was the most abundant hydrocarbon species in all the models. The overall results at 2.0 GPa and 400 to 450 °C were consistent with the natural samples from the Lanzo Massif. Interestingly, large amounts of H2O formed due to oxidation of H2. More hydrocarbons and H2O formed in models with lower fluid/rock mass ratios or with more reactant H2. Models at different pressure and temperature conditions showed similar results with some variation in the relative stabilities of aragonite, graphite and olivine solid solution, and associated differences in mineral sequences, hydrocarbon fluids, values of aqueous species, and the final logfO2 and pH. Our models strongly support the laboratory and field evidence that reduction of carbonated serpentinites by infiltrating H2 fluids can cause the formation of immiscible, abiotic hydrocarbon fluids in subduction zones.

Experimental investigation and modeling of mass transport properties of O2 in biomass chars

This study presents two sets of kinetic adsorption data for O2 on two different biomass chars at temperatures from (298 to 373) K and pressures from (26 to 300) kPa. Thereon, incorporating data of 21 adsorption kinetic curves on a hydrochar and 24 adsorption kinetic curves on a torrefied beechwood char, a parameterization of the pore-structure dependent kinetic adsorption (PSK) model is obtained for the two investigated chars. Extensive possibilities to predict time- and pore-structure-resolved mass transport properties using the PSK model are discussed. The mass transfer coefficient and the adsorption flow rate are direct outcomes and derivatives of the PSK model and hold for a physically sound description of the time-resolved mass transport of gaseous species in the porous structure of particles. The physical and extrapolative behavior of the modeled mass transfer coefficients and adsorption flow rates are discussed for temperatures up to 1100 K, allowing for new insights into the mass transfer.

Effect of a traveling magnetic field on cadmium zinc telluride growth by the traveling heater method

The growth of high-quality cadmium zinc telluride (CZT) crystals using the traveling heater method (THM) is strongly influenced by the morphology of growth interface. Here, we investigate the effect of a traveling magnetic field (TMF) on the growth of CZT single crystals by the THM using the multi-physics numerical simulation method. When no magnetic field is applied, the concave morphology of the growth interface caused by the gravity-driven natural convection is confirmed using a multi-component mass transfer model based on the Maxwell-Stefan equations. In contrast, the application of an upward TMF accelerates the flow near the crucible wall and hence the lateral flow along the growth interface, finally leading to a relatively flat growth interface. Conversely, the increase of a downward TMF intensity significantly weakens natural convection in the central melt region; particularly, when the magnetic induction strength is increased to 300 mT at a frequency of 50 Hz, the desired convex-shaped growth interface can be achieved with the appearance of strong vortices at the dissolution interface. Therefore, we conclude that both the upward and downward TMF can improve the growth interface and thereby facilitates the growth of high-quality single crystals.

Calibrating a Heat Transfer Model for Baled Switchgrass Using Heat Generation

HighlightsHeat and mass transfer in baled switchgrass was modeled based on thermal conductivity and internal heat generation.Model calibration was performed through a 60-day storage evaluation of baled switchgrass in an environmental chamber.Empirical models of heat generation and DML were developed based on thermal conductivity and aerobic respiration.Model validation was performed based on an energy balance and the aerobic respiration rate of switchgrass.Abstract. This study characterizes heat transfer within baled switchgrass through the development of a two-dimensional heat conduction model and an exponential drying approach to predict moisture content. The model was simulated using the finite difference method while accounting for the effect of internal heat generation to improve prediction accuracy. Model calibration was performed using rectangular bales of switchgrass (102 x 46 x 36 cm) stored in a controlled environmental chamber for 60 days at a fixed temperature and relative humidity. The heat and mass transfer model was implemented as an inverse model to empirically estimate heat generation and dry matter loss (DML). Internal heat generation and dry matter losses were also assessed using previously published models describing the aerobic respiration rate of switchgrass. Both heat generation models were in close agreement at a nominal moisture content of 10% w.b. (R2 = 0.9542) but deviated at nominal moisture contents of 20% to 40% w.b. (R2 < 0.7543). DML simulated using the numerical model closely agreed with the DML measured in the storage evaluation (R2 > 0.9060), indicating sufficient DML estimates through the conduction model and exponential drying approach. DML simulated through the published aerobic respiration model deviated to a greater extent, particularly at the highest moisture treatment (R2 = 0.4340), indicating an insufficient consideration of the various biochemical processes occurring at elevated levels of moisture and density. The results of this study provide a framework for the development of post-harvest quality models to optimize the storage, drying, and bioconversion of baled biomass feedstocks. Keywords: Bales, Heat and mass transfer, Heat transfer model, Storage losses, Switchgrass.

Understanding the rate-limiting step adsorption kinetics onto biomaterials for mechanism adsorption control

Biomaterials are a class of porous materials that have been widely exploited over the past two decades. However, the implications of controlling adsorption by rate-limiting steps are still not adequately established. Identifying the rate-limiting step is a promising approach for the design of adsorption systems. In this review, we study in detail the rate-limiting step of the adsorption of dyes in aqueous media on biomaterials to rationalize the factors governing the rate-limiting step involved in the adsorption process using empirical kinetics and mass transfer models. This knowledge is then applied to identify the best fit of these models to study the rate-controlling step involved in the adsorption process, which is crucial for the design of the adsorption system. This review first studies the limiting step of adsorption of dyes in an aqueous medium on biomaterials. Kinetic modeling is used to better understand the rate control step involved in biosorption. Generally, the equations used are empirical models of kinetics and mass transfer and the biomaterials come from the following categories: agricultural and industrial waste, algae, fungi, bacteria, and plants. In most adsorption studies reported in this review, the pseudo second-order model was found to be best suited for fitting the kinetic data of dyes on biomaterials, indicating that chemisorption is the rate-limiting step that controls adsorption. Concerning the diffusion effects of mass transfer, intraparticle diffusion is among the most often used models to examine the rate-limiting step which is controlled by both film diffusion and intraparticle diffusion. The first takes place when the external transfer is greater than the internal transfer while the opposite occurs in the case of porous diffusion. However, the majority of works do not study the real step of controlling the overall adsorption kinetics, namely, film diffusion or intraparticle diffusion.

Research on the distribution of heat fluxes during infrared drying of grain material

Purpose. To develop mathematical models of unsteady heat and mass transfer during the infrared (IR) drying process, and to create an algorithm for calculating the variable power of IR energy input to ensure quality drying of thermolabile material. Methods. The methods of mathematical modeling used to describe the unsteady drying process of thermolabile material in a dryer are based on the formalized description in the form of nonlinear inhomogeneous differential equations, taking into account the change in the power of IR energy input during the drying process. Results. A dependency for calculating the perceivable power of the IR source by the grain, based on the given process mode parameters, has been obtained. The drying kinetics of the grain, derived from formula (10), more accurately characterizes the process from a physical point of view than the drying equation (8) with a constant coefficient kck. It was established that three characteristic periods of the drying process can be traced in the graphical dependencies: I – heating; II – constant drying rate; III – falling drying rate. The calculation of heat fluxes for downward cross-ventilation of the grain layer, where air washes over IR heaters and reflectors and heats up to 35 °C, is presented. It was found that in the implementation of the process with a downward airflow, it is necessary to supply 20–25 % less radiant energy to the material at the same drying exposures according to the graphical dependencies. Conclusions. A mathematical description of the unsteady drying process of thermolabile material in a dryer, considering the change in the power of IR energy input during drying, has been formulated. An algorithm for calculating parameters that can be used for process identification and optimization of the operating parameters of existing grain dryers has been developed. Keywords: drying, grain material, mathematical model, diffusive transfer, moisture content, temperature, speed.

МАТЕМАТИЧЕСКОЕ МОДЕЛИРОВАНИЕ РАСПРОСТРАНЕНИЯ ЗАГРЯЗНЯЮЩИХ ВЕЩЕСТВ В ВОЗДУШНОЙ СРЕДЕ ПРОИЗВОДСТВЕННЫХ ПОМЕЩЕНИЙ

The mathematical model of pollutants diffusion in the air environment of industrial premises is considered, which is based on the classical model of continuous medium on the basis of the system of Navier-Stokes equations using the standard k - ε turbulence model, which takes into account the degree of air flow vortexing in the room. The developed mathematical model of heat and mass transfer of pollutants in the room, unlike existing models, allows to take into account the movement of a person and to estimate the concentration fields in different rooms in the building. The mathematical model is implemented on a computer in the problem-oriented environment SolidWorks 2020. The results of experimental studies and computational experiment on the spread of butyl acetate in the air environment of the room are presented. The received values of concentrations of butyl acetate satisfactorily agree with each other. Results of researches confirm possibility of use of the developed mathematical model in the software environment SolidWorks 2020 for carrying out computational experiments. The results of numerical modelling of butyl acetate distribution in air environment of premises at different location of a source are presented. It is shown, that moving of the person has essential influence on distribution of concentration field of butyl acetate in air environment of industrial premises.

Numerical Modelling of Coupled Heat and Mass Transfer in Porous Materials: Application to Cinder Block Bricks

Numerical Modelling of Coupled Heat and Mass Transfer in Porous Materials: Application to Cinder Block Bricks

РАЗРАБОТКА ПРОГРАММНОГО ОБЕСПЕЧЕНИЯ МОДЕЛИРОВАНИЯ ПРОЦЕССОВ ТЕПЛОМАССОПЕРЕНОСА ПРИ МНОГОФАЗНОМ ПОТОКЕ

Mathematical models simulating the process of heat and mass transfer in a multiphase flow and taking into account the thermal conductivity of the working fluid, taking into account its location in space, physical properties and other characteristics, are difficult to implement in the form of software. Usually such models are represented by nonlinear equations, which makes it difficult to implement them correctly using numerical methods. When developing such mathematical models, hydrodynamics, heat transfer of a moving working fluid and the dependence of viscosity on temperature and velocity gradient are not taken into account. (Research purpose) The research purpose is developing a mathematical model of the functioning of the heat supply system as a set of cylindrical pipelines with a heat source through which the working fluid moves. Additional conditions are introduced to achieve high accuracy of calculations at boundary points. The possibility of using analytical equations to calculate the internal heat dissipation during the transportation of the working fluid inside the pipeline is studied. (Materials and methods) Using the two-phase delay theory (DPL-model) and the finite element method (FEM) as flow balancing methods, we obtain a model of the heat exchange of the working fluid motion in the pipeline with the possibility of taking into account relaxation properties. (Results and discussion) The developed algorithm is implemented using the high-level interpreted programming language MATLAB and its simulation environment for complex technical systems Simulink. (Conclusions) Equations modeling the real motion of a multiphase working fluid in locally nonequilibrium systems, including heat supply systems, are obtained. The results obtained make it possible to compile an algorithm and implement it using the high-level interpreted programming language MATLAB, defining a working version of the software for modeling heat and mass transfer processes in a multiphase flow.

Adsorption of cationic/anionic dyes and endocrine disruptors by yeast/cyclodextrin polymer composites.

Factory and natural wastewaters contain a wide range of organic pollutants. Therefore, multifunctional adsorbents must be developed that can purify wastewater. Phytic acid-cross-linked Baker's yeast cyclodextrin polymer composites (IBY-PA-CDP) were prepared using a one-pot method. IBY-PA-CDP was used to adsorb methylene blue (MB), bisphenol A (BPA), and methyl orange (MO). Studies on the ionic strength and strongly acidic ion salts confirmed that IBY-PA-CDP adsorbs MO through hydrophobic interactions. This also shows that Na+ was the direct cause of the increased MO removal. Adsorption studies on binary systems showed that MB/MO inhibited the adsorption of BPA by IBY-PA-CDP. The presence of MB increased the removal rate of MO by IBY-PA-CDP due to the bridging effect. The Langmuir isotherm model calculated the maximum adsorption capacities for MB and BPA to be 630.96 and 83.31 mg g-1, respectively. However, the Freundlich model is more suitable for fitting the experimental data for MO adsorption. To understand the rate-limiting stage of adsorption, a mass-transfer mechanism model was employed. The fitting results show that adsorption onto the active sites is the rate-determining step. After five regeneration cycles, IBY-PA-CDP could be reused with good stability and recyclability.

Numerical Modeling of Mass Transfer in the Interaction between River Biofilm and a Turbulent Boundary Layer

Numerical Modeling of Mass Transfer in the Interaction between River Biofilm and a Turbulent Boundary Layer

3D cell aggregates amplify diffusion signals.

Biophysical models can predict the behavior of cell cultures including 3D cell aggregates (3DCAs), thereby reducing the need for costly and time-consuming experiments. Specifically, mass transfer models enable studying the transport of nutrients, oxygen, signaling molecules, and drugs in 3DCA. These models require the defining of boundary conditions (BC) between the 3DCA and surrounding medium. However, accurately modeling the BC that relates the inner and outer boundary concentrations at the border between the 3DCA and the medium remains a challenge that this paper addresses using both theoretical and experimental methods. The provided biophysical analysis indicates that the concentration of molecules inside boundary is higher than that at the outer boundary, revealing an amplification factor that is confirmed by a particle-based simulator (PBS). Due to the amplification factor, the PBS confirms that when a 3DCA with a low concentration of target molecules is introduced to a culture medium with a higher concentration, the molecule concentration in the medium rapidly decreases. The theoretical model and PBS simulations were used to design a pilot experiment with liver spheroids as the 3DCA and glucose as the target molecule. Experimental results agree with the proposed theory and derived properties.

Microfluidic extensional flow device to study mass transfer dynamics in the polymer microparticle formation process.

Polymer microparticles are often used to encapsulate drugs for sustained drug-release treatments. One of the ways they are manufactured is by using a solvent extraction process, in which the polymer solution is emulsified into an aqueous bulk phase using a surfactant as a stabilizing agent, followed by the removal of the solvent. The radius of a polymer drop decreases as a function of time until the polymer reaches the gelling point, after which it is separated and dried. Among the various operating parameters, the rate of solvent extraction is a critical step that affects the morphology and porosity, and consequently, the kinetics of drug release. But a fundamental mechanistic understanding of the solvent extraction dynamics as a function of shear is still unexplored. In this study, we have developed an experimental mass transfer model to predict the extraction by using the microfluidic extensional flow device (MEFD) to probe the shear and extraction dynamics at the level of a single drop in a linear extensional flow field. We used a computer-controlled feedback algorithm to manipulate the flow field and hydrodynamically trap a Hele-Shaw drop and observe the extraction process. For the polymer solution, we used a biocompatible polymer, poly-lactic-co-glycolic acid (PLGA) with ethyl acetate (EtOAc) as the solvent. Our experiments were conducted by varying the extensional rate (G) in the channel from ∼0.1 s-1 to ∼10 s-1, and using an analytical solution of the flow field, we captured the dissolution process and measured the change in drop radius (R) with time (t). Interestingly, we initially observed a short-time asymptote R ∼ t, and later the long-time asymptote of R = constant; both trends were physically explained. The transport model developed in this work can be used to predict extraction rates and polymer microparticle composition for any polymer-solvent system. This work is also an important contribution to the literature on convective mass transfer in partially miscible emulsions.

Modeling heat and mass transfer in grain drying processes under the influence of electromagnetic field

Drying of grain materials by traditional convective methods typically involves significant energy consumption, primarily due to unproductive losses of thermal energy with the exhausted drying agent. Optimizing this process entails reducing the volume of drying agent used and compensating for reduced thermal energy through non-contact heat transfer methods such as microwave (MW) or infrared (IR) irradiation. However, mathematical modeling of these processes requires refinement as they differ from traditional convective heat drying processes. Grain drying is a complex thermophysical process, with heat and moisture transfer occurring within the capillary-porous material in a mutually dependent manner. To better understand these processes, it is necessary to establish mathematical models that account for the influence of the electromagnetic field. This article aims to theoretically investigate the drying process of plant raw materials under the influence of MW and IR electromagnetic fields based on analytical mathematical models. The conducted research indicates the potential of using electromagnetic fields to intensify the drying of plant raw materials, particularly through MW and IR irradiation, which allows for targeted heating of the moist zones of the material. The obtained analytical dependencies enable the calculation of temperature and moisture content fields in materials and determine the degree of influence of electromagnetic field parameters on heating and drying processes. These dependencies also help to more accurately identify heat and mass transfer model coefficients based on experiments. Such an analytical-empirical approach can be utilized to calculate rational processing regimes for grain raw materials under the influence of electromagnetic fields.