Mass Diffusion Model Research Articles

Numerical study on the impact of variable diffusion co-efficients and chemical reaction on transport phenomenon in nonlinear axisymmetric flow

In this article, conservation laws, temperature dependent viscosity, thermal conductivity and mass diffusion models are used for mathematical modeling of flow of Casson fluid induced by nonlinear axisymmetric stretching sheet exposed to non-uniform magnetic field. Mathematical models are solved by finite element method. Convergence is ensured and grid independent analysis is performed. Several numerical simulations are executed to investigate the behavior of velocity, temperature and concentration under the variation of parameters. The impact of viscous dissipation, Joule heating, variation of viscosity and thermal conductivity is investigated through numerical simulations. The developed computer program is tested by comparing with computed results. The intensity of applied magnetic field and Joule heating are directly proportional to each other and an increase in the intensity of magnetic field causes an increase in the temperature. A rise in viscosity due to a rise in temperature has remarkable impact on both velocity and temperature. However, an increase in thermal conductivity (due to rise in temperature) results a significant increase in the temperature as conduction of heat from hot surface into the fluid speeds up. The wall heat flux increases when intensity of the magnetic field is increased.

Moisture absorption in thick composite plates: modelling and experiments

Purpose When a thick structure is, on the contrary, subjected to moisture absorption, a fairly long time may be needed to reach full saturation. It is, therefore, important to understand and predict the areas of complex composite structures that are more prone to saturation. The material knock-down factors (proportional to the moisture content) may be applied only to these zones, in order to obtain a less pessimistic structural response prediction. The purpose of this paper is to investigate an FE diffusion model that was used to validate the absorption testing results of thick carbon epoxy laminates. Design/methodology/approach The experimental results were validated by using a diffusion model in Abaqus FE code. Findings The absorption results of three 15 mm thick carbon epoxy laminates are presented and reproduced via a mass diffusion model. The laminates were conditioned at 70°C and 85 per cent relative humidity in a moisture chamber. Areas more prone to saturation have been predicted by the FE model and the moisture content in the non-saturated areas has been calculated. Practical implications The practical implications of the absorption model are discussed on an example of an aero-engine fan blade-like structure. Originality/value Validation of thick panels’ absorption data is an important point of novelty of this paper, given the lack of experimental and modelling validation in the open literature.

Application of double diffusion theories to Maxwell nanofluid under the appliance of thermal radiation and gyrotactic microorganism

PurposeThe purpose of this paper is to address the entropy analysis of the 3D flow of Maxwell nanofluid containing gyrotactic microorganism in the presence of homogeneous–heterogeneous reactions with improved heat conduction and mass diffusion models over a stretched surface. Improved models are supported out by utilizing Cattaneo–Christov heat flux and generalized Fick’s law, respectively.Design/methodology/approachGoverning equations which present the given flow phenomenon are modeled in the form of PDEs by applying boundary layer analysis and then suitable makeovers are engaged to transfigure prevailing partial differential equations into a set of ordinary differential equations. Transformed equations are handled via optimal homotopy analysis process in computational tool Mathematica and also a special case of already published work is substantiated and found to be in excellent settlement.FindingsThe bearing of innumerable convoluted physical parameters on velocity, temperature, concentration, reaction rate, the concentration of motile microorganism and entropy generation are presented and deliberated through graphs. Moreover, the convergence of the homotopic solution is presented in tabular form which confirms the reliability of the proposed scheme. It is perceived that mounting values of the magnetic parameter and Brinkman number boosts the irreversibility analysis and Bejan number diminishes for these parameters. Moreover, the growing values of Prandtl and Schmidt numbers reduce the temperature and concentration fields, respectively.Practical implicationsThe work contained in this paper has applications in a different industry.Originality/valueThe work contained in this paper is original work and it is good for the researcher in the field of applied mathematics.

Molecular diffusion and phase stability in high-pressure combustion

The increased modeling complexity needed to simulate high-pressure combustion in rocket engines results in significant computational costs–costs which are not always justified for engineering applications. Multicomponent diffusion computations are at least 40% more expensive than the constant Lewis number diffusion assumption for the simplest hydrogen/oxygen combustion; the computational penalty increases rapidly with the number of species under consideration. The higher-fidelity diffusion modeling is justified in cryogenic fuel combustion if it affects the phase-stability of the propellants. We investigate the impact of the mixture averaged, multicomponent, and constant Lewis number diffusion models of a laminar counterflow flame at trans- and supercritical conditions for typical rocket propellants, namely: hydrogen, methane, and kerosene. Using vapor liquid equilibrium (VLE) theory, we show that, even in the limit cases, the mass diffusion model has a limited effect on the phase stability and pseudo-phase change of the propellants; the majority of the differential diffusion errors are located in the high temperature/ideal gas regions of the flame. The differential diffusion error due to real fluid thermodynamics is at most about 20% of the differential diffusion error which occurs in the ideal gas region of the flame. As a result, the impact of the differential diffusion remains similar to low-pressure combustion conditions, thus supporting the use of engineering-level simplifications for the simulation of these complex high-pressure reactive flows.

Simulation of mass and heat transfer in liquid hydrogen tanks during pressurizing

In order to accurately predict the heat and mass transfer behaviors and analyze key factors affecting pressurization process in the hydrogen tank, a comprehensive 2D axial symmetry Volume-Of-Fluid (VOF) model is established by Computational Fluid Dynamics (CFD) method. The effects of phase change, turbulence and mass diffusion are included in the model and relationships between physical properties and temperature are also comprehensively considered. The phase change model is based on Hertz-Knudsen equation and the mass transfer time relaxation factor is determined by the NASA’s experimental data. The mass diffusion model is included in gaseous helium pressurizing. The key factors including the inlet temperature, inlet mass flow rate, injector types and pressurizing gas kinds are quantitatively analyzed. Compared with the experiment, the simulation results show that the deviation of pressurizing gas mass consumption, condensing mass and ullage temperature are 3.0%, 7.5% and 4.0% respectively. The temperature stratification is existed along the axial direction in the surface liquid region and the ullage region, and the bulk liquid is in subcooled state during pressurizing. The location of phase change mainly appears near the vapor–liquid interface, and the mass transfer expressing as condensation or vaporization is mainly determined by the heat convection and molecular concentration near the vapor–liquid interface. The key factors show that increasing the inlet temperature and inlet mass flow rate could shorten the pressurizing time interval and save the pressurizing gas mass. The proportion of the total energy addition of the tank absorbed by the ullage region, the liquid region and the tank wall respectively is greatly influenced by the injector types and more heat transferred into the ullage would result in a faster pressure rising rate. Gaseous hydrogen pressurization has a higher efficiency than gaseous helium pressurization. The simulation results presented in this paper can be used as a reference for design optimization of the pressurization systems of cryogenic liquid launch vehicles so as to save the mass of pressurizing gases and shorten the pressurizing time interval.

Information filtering based on eliminating redundant diffusion and compensating balance

In statistical physics, researchers concentrate on mass diffusion and heat conduction-based information filtering models, which effectively facilitate recommendation accuracy and diversity. There are many improved methods combining mass diffusion with heat conduction theories. Research results show that the best results are achieved when the combination of mass diffusion and heat conduction reaches equilibrium. With elaborative analysis, we find that similarity redundancies derive from the attribute correlations of objects, and deduce the similarity estimation deviation. Considering the former deficiencies, we propose a novel model through eliminating redundant diffusion and compensating balance (shortly ERD-CB), which symmetrically combines mass diffusion with heat conduction process through balance compensation. Three benchmark datasets from Movielens, Amazon and Netflix are used in our extensive experiments. Experiment results show that the ERD-CB model outperforms the benchmarkbaselines for accuracy, diversity and novelty.

Non-Fourier's and Fick's laws applications in the flow of temperature dependent thermal conductivity generalized Newtonian liquids: A 3D computational study

The current article presents a numerical study for local solutions of Sisko liquid flow by bidirectional stretched surface. Additionally, the analysis of relaxation times for the heat and mass transfer mechanisms are made by utilizing modified heat flux and mass diffusion models. These improved relations are the generalized form of Fourier's and Fick's laws in which the time space upper-convected derivative are employed to portray the heat conduction and mass diffusion mechanisms. Appropriate transformations lead to a strongly nonlinear differential system of equations which is then solved numerically by employing the applications of bvp4c package in Matlab software. Another numerical method namely shooting technique with RK45 Fehlberg and Newton-Raphson method is utilized to authenticate the results. Graphical illustrations demonstrating the impacts of sundry physical parameters with required discussion highlighting their physical effect are also a part of this exploration. It is perceived that the temperature and concentration of Sisko liquid are diminishing functions of relaxation times for the heat and mass transfer mechanisms. It is also fascinating to perceive that the temperature and concentration of Sisko liquid are higher in case of classical form in comparison with an improved constitutive relations.

Prediction of species concentration distribution using a rigorous turbulent mass diffusivity model for bubble column reactor simulation part II: Analogy between turbulent mass and momentum transfer in toluene emissions biodegradation process

Toluene is a kind of volatile organic compounds usually present in industrial emissions. In this work, the rigorous model for species concentration distribution prediction proposed in part I was applied in simulating the biological degradation process of toluene in a bubble column (BC) reactor. We show in the present paper that the species concentration, turbulent mass diffusivity and velocity distributions in the bubble column bioreactor can be obtained simultaneously by applying the proposed model. On the basis of the simulations, the analogy between the turbulent mass diffusivity and turbulent viscosity for the bubble column reactor was investigated. The results showed that this analogy may depend on the rate of chemical or bio-chemical reaction in the bubble columns and remain for the case with a lower reaction rate.

Modelling mass diffusion for a multi-layer sphere immersed in a semi-infinite medium: application to drug delivery

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

Prediction of species concentration distribution using a rigorous turbulent mass diffusivity model for bubble column reactor simulation part I: Application to chemisorption process of CO2 into NaOH solution

Rigorous prediction of species concentration distribution has been challenging in the simulation of bubble column reactors. In the present manuscript, a theoretical model of turbulent mass transfer is introduced to the numerical simulation of the process of chemisorption of CO2 into NaOH aqueous solution in a bubble column reactor. In this model the turbulent mass diffusivity was expressed as a function of the concentration variance c2‾ and its dissipation rate εc, which were modeled to close the turbulent mass transfer differential equation system. As a result, along with the fluid velocity distribution, the species concentration distribution in the bubble column can be rigorously predicted simultaneously. By using the present model, the experience relying assumption of a constant turbulent Schmidt, which has been usually adopted in a traditional species concentration simulation, can be avoided. An RNG k-ε method combined with a population balance model for predicting the bubble size distribution was used to predict the gas–liquid velocity in the turbulent flow. The simulated pH values and carbonate concentration were shown to be in satisfactory agreement with the experimental data in literature. The simulations showed that the turbulent mass diffusivity varied along axial and radial directions in the bubble column and the calculated turbulent Schmidt number was not a constant. The proposed approach can be especially useful when empirical turbulent mass diffusivity is not available for simulating a similar process in a bubble column reactor.

Three-dimensional flow of Prandtl fluid with Cattaneo-Christov double diffusion

Abstract This research paper intends to investigate the 3D flow of Prandtl liquid in the existence of improved heat conduction and mass diffusion models. Flow is created by considering linearly bidirectional stretchable sheet. Thermal and concentration diffusions are considered by employing Cattaneo-Christov double diffusion models. Boundary layer approach has been used to simplify the governing PDEs. Suitable nondimensional similarity variables correspond to strong nonlinear ODEs. Optimal homotopy analysis method (OHAM) is employed for solutions development. The role of various pertinent variables on temperature and concentration are analyzed through graphs. The physical quantities such as surface drag coefficients and heat and mass transfer rates at the wall are also plotted and discussed. Our results indicate that the temperature and concentration are decreasing functions of thermal and concentration relaxation parameters respectively.

A Mass Diffusion Model for Dry Snow Utilizing a Fabric Tensor to Characterize Anisotropy

AbstractA homogenization algorithm for randomly distributed microstructures is applied to develop a mass diffusion model for dry snow. Homogenization is a multiscale approach linking constituent behavior at the microscopic level—among ice and air—to the macroscopic material—snow. Principles of continuum mechanics at the microscopic scale describe water vapor diffusion across an ice grain's surface to the air‐filled pore space. Volume averaging and a localization assumption scale up and down, respectively, between microscopic and macroscopic scales. The model yields a mass diffusivity expression at the macroscopic scale that is, in general, a second‐order tensor parameterized by both bulk and microstructural variables. The model predicts a mass diffusivity of water vapor through snow that is less than that through air. Mass diffusivity is expected to decrease linearly with ice volume fraction. Potential anisotropy in snow's mass diffusivity is captured due to the tensor representation. The tensor is built from directional data assigned to specific, idealized microstructural features. Such anisotropy has been observed in the field and laboratories in snow morphologies of interest such as weak layers of depth hoar and near‐surface facets.

Synaptic neuron-astrocyte communication is supported by an order of magnitude analysis of inositol tris-phosphate diffusion at the nanoscale in a model of peri-synaptic astrocyte projection

BackgroundAstrocytes were conceived for decades only as supporting cells of the brain. However, the observation of Ca2+ waves in astrocyte synctitia, their neurotransmitter receptor expression and gliotransmitter secretion suggested a role in information handling, conception that has some controversies. Synaptic Neuron-Astrocyte metabotropic communication mediated by Inositol tris-phosphate (SN-AmcIP3) is supported by different reports. However, some models contradict this idea and Ca2+ stores are 1000 ± 325 nm apart from the Postsynaptic Density in the Perisynaptic Astrocyte Projections (PAP’s), suggesting that SN-AmcIP3 is extrasynaptic. However, this assumption does not consider IP3 Diffusion Coefficient (Dab), that activates IP3 Receptor (IP3R) releasing Ca2+ from intracellular stores.ResultsIn this work we idealized a model of a PAP (PAPm) to perform an order of magnitude analysis of IP3 diffusion using a transient mass diffusion model. This model shows that IP3 forms a concentration gradient along the PAPm that reaches the steady state in milliseconds, three orders of magnitude before IP3 degradation. The model predicts that IP3 concentration near the Ca2+ stores may activate IP3R, depending upon Phospholipase C (PLC) number and activity. Moreover, the PAPm supports that IP3 and extracellular Ca2+ entry synergize to promote global Ca2+ transients.ConclusionThe model presented here indicates that Ca2+ stores position in PAP’s does not limit SN-AmcIP3.

Study on mechanism of bubble growth within a water droplet under rapid depressurization

This paper reports an experimental and numerical study on mechanism of bubble growth within a water droplet under rapid depressurization. During the experiments, a distilled water droplet was suspended on a thermocouple, which was also used to measure the droplet temperature. A high speed camera was applied to record the bubble expansion. Two mathematical models were developed to describe the bubble growth process. The mass diffusion model considered the bubble growth related to the mass diffusion of nitrogen dissolved in the droplet during pressure drop, and the model was based on the momentum equation of bubble growth coupling with the diffusion equation within the liquid phase. The heat transfer model considered that the droplet superheating resulted in bubble growth. Both of the models considered the influence of thermocouple suspension mode on bubble growth, and a simplified treatment was applied by introducing a friction coefficient. During our experiments, the duration times for bubble growth were mostly 4–8 ms. The verification of mathematical models was achieved by comparing the numerical results with the experimental data. The result shows that the numerical bubble radii calculated by the heat transfer model agree well with the experimental measurement. Through numerical calculations, the factors of pressure difference, droplet diameter and thermocouple suspension mode on bubble growth were analyzed. The results provide insight into the dynamic of bubble growth within a water droplet under rapid depressurization.

Experimental and simulation study of nylon 6 solid–liquid extraction process

Abstract The solid–liquid extraction process of nylon 6 to eliminate small molecules, i.e., caprolactam (CL), cyclic dimers (CD) and cyclic trimers (CT), is investigated in detail by both batch extraction experiments and numerical simulations. In the batch extraction experiments, due to the small molecules attaching to the polymeric surface, the basic physical mechanism shifts from surface diffusion to internal diffusion as the extraction proceeded. The experimental data are well reproduced by a diffusion model consisting of two distinct steps, characterized as surface diffusion and internal diffusion. Furthermore, based on the established mass transfer mechanism and diffusion model of the two distinct steps, the equilibrium constants and internal diffusion coefficients of CL, CD and CT are acquired. An industrial countercurrent extraction tower is further simulated. It is found that the extraction efficiency of CL can be significantly improved by increasing the temperature at the bottom portion of the tower. The elimination of CD, which can be greatly promoted by a high-concentration CL-water solution, is controlled by mass transfer resistance, whereas the removal of CL is mainly affected by the equilibrium.

Simulation of Oxygen Transport Membranes for CPO Reactors in Small-scale Hydrogen or Syngas Production Applications

The proposed work aims at presenting a 1D finite volume steady state simulation model of an Oxygen Transport Membrane for Catalytic Partial Oxidation (OTM-CPO) reactor developed at the Group of Energy COnversion Systems (GECOS) at Politecnico di Milano. The model is able to simulate supported and unsupported perovskite-based reactive membranes by means of a lumped mass and energy transport method; the active ceramic layer is modelled throughout a generalised O2 permeation equation, which depends on the micro-structure characteristics and mixed-ion conduction properties of the material. The supporting porous structure is represented by a mass diffusion model dominated by gas-gas, porous and surface exchange transport processes. The model also includes a global chemical reaction kinetic mechanism of CPO on Rh-based catalysts. The model is applied to simulate the behaviour of a membrane reactor operated upstream the Hydrogen Transport Membrane for Methane Steam Reforming (HTM-MSR) installed at the Laboratory of Micro-Cogeneration (LMC) at Politecnico di Milano. The test bench is focused on testing fuel pre-processing systems for low temperature fuel cells (PEM) applications. The simulation object of this work would allow obtaining a feasibility assessment of the system and a preliminary design of the OTM-CPO reactor.

Cattaneo-Christov heat and mass flux model for 3D hydrodynamic flow of chemically reactive Maxwell liquid

This research focuses on the Cattaneo-Christov theory of heat and mass flux for a three-dimensional Maxwell liquid towards a moving surface. An incompressible laminar flow with variable thermal conductivity is considered. The flow generation is due to the bidirectional stretching of sheet. The combined phenomenon of heat and mass transport is accounted. The Cattaneo-Christov model of heat and mass diffusion is used to develop the expressions of energy and mass species. The first-order chemical reaction term in the mass species equation is considered. The boundary layer assumptions lead to the governing mathematical model. The homotopic simulation is adopted to visualize the results of the dimensionless flow equations. The graphs of velocities, temperature, and concentration show the effects of different arising parameters. A numerical benchmark is presented to visualize the convergent values of the computed results. The results show that the concentration and temperature fields are decayed for the Cattaneo-Christov theory of heat and mass diffusion.

An improved heat conduction and mass diffusion models for rotating flow of an Oldroyd-B fluid

An analysis is presented to inspect the steady three-dimensional boundary layer flow of an Oldroyd-B fluid over a stretching surface. Heat and mass transfer analysis are scrutinized by utilizing the non-Fourier’s and non-Fick’s models in rotating frame. The expressions of heat and mass fluxes are based upon the Cattaneo-Christov theory. The Cattaneo-Christov heat and mass flux models are used for the development of energy and concentration equations which account the contribution of thermal and concentration relaxation times. Additionally, temperature dependent thermal conductivity is also considered here. Apposite transformations are betrothed to obtain the ordinary differential equations with high nonlinearity. The analytical solutions are established for the resulting ordinary differential system by utilizing the homotopy analysis method (HAM). Our observations reveal that the rotation parameter serves to diminish the primary velocity f′(η) and associated momentum boundary layer thickness and similar trend is observed for the secondary velocity g(η). It is also observed that the thermal and concentration relaxation time parameters reduce the temperature and concentration profiles. For endorsement of the current relation, the attained consequences are eminent with former exploration in precise cases and splendid agreement has been distinguished.

Controllable preparation of 1-D and dendritic ZnO nanowires and their large area field-emission properties

Large-scale one-dimensional (1-D) and dendritic ZnO nanowires were synthesized on Si substrates using a catalyst-free thermal oxidation technique. By adjusting the stress of the starting Zn thin film for the growth using an Ar ion bombardment process, controllable syntheses of samples composed of only one or a mixture of these two morphologies were achieved. Different nucleation mechanisms were proposed by detailed observations of nucleation and growth process of 1-D and dendritic ZnO nanowires. The strain-induced mass diffusion model and self-catalytic gas-liquid-solid model were used to explain the growth of 1-D and dendritic ZnO nanowires, respectively. In addition, the field-emission characteristics of ZnO nanowires were measured, which showed that dendritic ZnO nanowires have stable emission current.

Parametric optimization and modeling of batch extraction process for extraction of betulinic acid from leaves of Vitex Negundo Linn

ABSTRACTExtraction of betulinic acid from leaves of Vitex Negundo Linn was carried out in a series of solvents (methanol, ethanol, isopropyl alcohol, and water). Methanol gave maximum yield of extraction and therefore was used to investigate influence of particle size, speed of agitation, solid loading, and temperature, etc., on the rate and recovery in a stirred batch reactor. Effective intra-particle diffusivity of the acid in each solvent at different temperatures was estimated using an unsteady state mass diffusion model. The diffusivity of betulinic acid through the cellulose matrix of leaves is in the range 1.7 x 10−13 to 9.23 x 10−11 m2/sec and is strongly influenced by the temperature of the extraction. The Response Surface Methodology was used to estimate optimal conditions for betulinic acid extraction.