CIRCULATION,DIFFUSION, AND REACTION WITHIN A LIQUID TRAPPED IN A CAVITY

The problem of convective diffusion from and reaction within the circulating flow inside a two-dimensional rectangular cavity is studied. The circulation is of the type induced by an external flow. Mass transfer occurs across the interface between the cavity and the external flow. A reactant may diffuse into the cavity from the external flow. The equations of steady motion and transient convective diffusion and chemical reaction are solved numerically. An enhancement factor is defined which quantifies the effectiveness of internal circulation in promoting diffusion and reaction. The dependence of this enhancement factor on geometry (cavity aspect ratio), Peclet number, and kinetic parameters is displayed.     

Mass transfer with mth order chemical reaction for multi-particle systems

The steady-state diffusion equation with convective term and mth order chemical reaction term was numerically solved by the finite difference method. The penetration theory agreed only with the numerical solution around single spheres in an infinite potential flow field. The enhancement factor varies with the values of the Reynolds number, void fraction and contamination factor.     

Gas diffusion in polymer solutions: A double-cone flow technique

A new double-cone flow technique for an experimental investigation of gas diffusion in polymer solutions is described. A theoretical development of the pertinent convective diffusion problem for the flow of a non-Newtonian fluid over the double cone is presented. Experimental investigation of diffusion of carbon dioxide in aqueous solutions of certain polymers was carried out. The diffusion coefficient deduced from this work shows a marginal enhancement over its value in pure solvent. Possible mechanistic explanations for this phenomenon are explored.     

Effect of Convective Flow across a Film on Facilitated Transport

Abstract

An analytical expression is derived for the facilitation factor in facilitated transport across a liquid film. This solution is an extension of previous results in that it accounts for convective flow across the film. In addition, the expression accounts for external mass-transfer resistances as well as diffusion and reaction within the liquid film. A solution procedure to evaluate the important system parameters is described.     

Computational analysis of convective diffusion with chemical reaction in a cavity

Unsteady convective diffusion problems involving chemical reaction in a rectangular are numerically examined. The effect of various factors affecting the removal of the contaminant in the cavity has been analyzed systematically. The vorlicity and streamfunction are used for numerical computations. For low Reynolds number cases, the rate of removal of the contaminant increases as the Grashof number becomes larger. For high Reynolds number, the secondary flow hinders the rate of removal of the contaminant as the Grashof number becomes larger.     

两相流载气蒸发研究和传热数据关联

两相流载气蒸发是在蒸发器的垂直加热管中引入一种惰性气体,使液体的蒸发在气液两相界面上进行的过程.本文研究了载气蒸发的流型区域和传热规律,对载气蒸发的特性进行了机理分析,并以叠加模型关联了实验数据,获得了准数方程式.     

长链烯烃与苯烷基化外扩散影响的数学模拟

在一定粒度的固体酸催化剂上进行不同反应原料质量流速的烷基化反应实验,通过模型参数估值及模型预测分析,建立评价外扩散阻力影响程度的外扩散有效因子数学模型。在此基础上考察外扩散阻力对烷基化反应的影响规律,确定消除外扩散阻力影响的实验条件。模型预测结果表明,计算值与实验值吻合较好。在一定的反应条件下,随着流体质量流速的增大,外扩散有效因子先快速增大然后缓慢趋于1;随着烷基化反应时间的延长,外扩散有效因子持续增大;随着烷基化反应速率的提高,消除外扩散阻力影响的流体质量流速相应有所增大。当流体质量流速达到4.0g.cm-2.h-1时可消除外扩散阻力影响。     

Pressure changes during diffusion with chemical reaction in a porous pellet

A method is proposed for evaluation of the pressure change in an isothermal porous pellet within which a single chemical reaction takes place, accompanied by mass transfer by Knudsen diffusion, bulk diffusion and viscous convective flow of the reacting mixture. The dimensionless pressure is expressed as a function of two dimensionless parameters which characterize transport mechanism and mixture properties respectively. The pressure change also depends on the reaction and on the mixture composition on the pellet surface. The method requires numerical integration of an initial-value problem.A simple analytical method is also proposed for estimation of the maximum possible pressure changes in the system, both for the Knudsen diffusion control regime and for the bulk diffusion with viscous convective flow control regime.Both methods are illustrated by the computed results for a general two-molecule reaction and for the ammonia synthesis reaction.     

Simultaneous intraparticle forced convection,diffusion and reaction in a porous catalyst

The effect of intraparticle forced convection on a heterogeneous reaction within a porous catalytic pellet is examined. It is found that an appreciable enhancement of the catalyst performance can be expected for liquid-phase reactions on coarse-grained particles. Quantitative results are obtained for an irreversible isothermal first-order reaction in flat, spherical and cylindrical geometries with uniform internal flow. A maximum increase in the effectiveness factor is observed in the region where the kinetics just becomes diffusion controlled.     

EFFECT OF INTERPHASE MASS TRANSFER ON UNSTEADY CONVECTIVE DIFFUSION:PART I, PLANE-POISEUELLE FLOW OF A POWER-LAW FLUID IN A CHANNEL

The paper presents an all-time analysis of unsteady convective diffusion of solute undergoing an irreversible first-order chemical reaction at the bounding walls of a parallel-plate channel. The heterogeneous chemical reaction significantly influences the convective and diffusive coefficients. A new coefficient arises exclusively due to the incorporation of wall reaction. The effects of wall-catalysed reaction and power-law index 'N' on dispersion are investigated against the background of the no-reaction problem. The analytical result on dispersion of solute with wall catalysed reaction at long times is compared with the analytical solution when.reaction is absent. The Taylor [1 ] and Ans [2] regimes of dispersion for the present problem are obtained as limiting cases from the study. The graphical results of the study serve as a jury on any numerical study that might be undertaken considering non-asymptotic all-time analysis.     

微小通道内流动沸腾换热的预测新模型

为了得到适用于微小通道内流动沸腾换热的预测方法,本文以近些年发表的9篇文献中的2924个实验数据点组成数据库,考虑到随着通道直径减小,表面张力对微小通道内两相流动和换热的影响起到主要作用,将Chen形式的换热模型中的核态沸腾和对流换热两部分的修正系数进行了优化。沸腾抑制系数和对流增强系数由气相韦伯数、两相雷诺数、沸腾数、气泡抑制数等量纲为1数组成,反映出了表面张力、水力直径、流动条件、热力条件对于换热的综合影响。结果表明,拟合出的微小通道中沸腾换热的新模型,适于预测水力直径3 mm以下的细管道中CHF（临界热流密度）点以前的换热系数。与实验数据比较,新模型预测的平均绝对误差为19.0%。     

微通道内醇胺/离子液体复配水溶液吸收CO2的传质特性

研究了微通道内醇胺[单乙醇胺(MEA)和甲基二乙醇胺(MDEA)]与离子液体[1-丁基-3-甲基咪唑四氟硼酸([Bmim][BF₄])和1-羟乙基-3-甲基咪唑甘氨酸([C₂OHmim][GLY])]复配水溶液吸收CO₂的传质特性。考察了醇胺/离子液体浓度比(c_AA∶c_IL)对液相体积传质系数(k_La)的影响,发现k_La随反应速率的增大而增大。为进一步阐释复配水溶液吸收CO₂的传质机理,分析了比表面积、扩散速率、增强因子和液弹循环对传质速率的影响。结果表明,四种复配溶液中,反应速率和循环频率(f_cir)分别在低流率和高流率下对传质速率起主导作用。k_La可表示为f_cir的函数,低气相流率下k_La与f_cir呈线性关系,斜率与反应速率成正相关,高气相流率下,液弹循环因膜弹传递困难而对整体传质速率的影响减弱,k_La与f_cir呈指数关系,幂律指数小于1。     

Inspiratory Deposition Efficiency of Ultrafine Particles in a Human Airway Bifurcation Model

The inspiratory deposition efficiency of ultrafine particles in a physiologically realistic bronchial airway bifurcation model, approximating the airway generation 3-4 juncture, was computed for different particle sizes, ranging from 1 to 500 nm, under three different flow conditions, representing resting to heavy exercise breathing conditions. For the smallest particle sizes, say between 1 and 10 nm, molecular diffusion is the primary deposition mechanism, as indicated by the inverse relationship with flow rate, except for the highest flow rate where the additional effect of convective diffusion has to be considered as well. For the larger particle sizes, say above 20 nm, the independence from particle size and dependence on flow rate suggests that convective diffusion plays the major role for ultrafine particle deposition in bifurcations. A semiempirical equation for the inspiratory deposition efficiency, m (D, Q), as a function of diffusion coefficient D and flow rate Q, due to the combined effect of molecular and convective diffusion was derived by fitting the numerical data. The very existence of a mixed term demonstrates that molecular and convective diffusion are not statistically independent from each other.     

Particle collision behavior and heat transfer performance in a Na2SO4 circulating fluidized bed evaporator

The particle collision behavior and heat transfer performance are investigated to reveal the heat transfer enhancement and fouling prevention mechanism in a Na₂SO₄ circulating fluidized bed evaporator. The particle collision signals are analyzed with standard deviation by varying the amount of added particles ε (1%–3%), circulation flow velocity u (0.37–1.78 m·s^-1), and heat flux q (7.29–12.14 kW·m^-2). The results show that the enhancement factor reach up to 14.6% by adding polytetrafluoroethylene particles at ε = 3%, u = 1.78 m·s^-1, and q = 7.29 kW·m^-2. Both the standard deviation of the particle collision signal and enhancement factor increase with the increase in the amount of added particles. The standard deviation increases with the increase in circulation flow velocity; however, the enhancement factor initially decreases and then increases. The standard deviation slightly decreases with the increase in heat flux at low circulation flow velocity, but initially increases and then decreases at high circulation flow velocity. The enhancement factor decreases with the increase in heat flux. The enhancement factor in Na₂SO₄ solution is superior to that in water at high amount of added particles. The empirical correlation for heat transfer is established, and the model results agree well with the experimental data.     

Investigations in mass transfer enhancement in textiles with ultrasound

A novel application of ultrasound is for the intensification of wet textile treatments, in which mass transfer in the inter- and intra-yarn pores of the textile is the basic physical mechanism. This paper describes a simple methodology for the estimation of mass transfer enhancement in ultrasonic textile treatments. For this study, washing of EMPA 101 fabric, soiled with carbon soot and olive oil, is selected as a model process. In the absence of precise knowledge of the convection velocity resulting due to transient cavitation, a semi-empirical method is used to estimate mass transfer enhancement. The experimental soil removal rate during model process is determined by precise time-controlled ultrasonic treatment of the textile, with the source of cavitation nuclei located close to the textile surface. The mass transfer in the textile during the model process is found to occur in two distinct steps, characterized by two different convective diffusion coefficients. This effect is explained in terms of uneven soil distribution in the inter- and intra-yarn region. The mass transfer enhancement factor, defined as ratio of convective diffusion coefficient to molecular diffusion coefficient of soil particles, is found to be in the range 1000-2000. In addition, it is found that the mass transfer enhancement increases with acoustic pressure amplitude during textile treatment. A qualitative estimate of the convection velocities generated in the vicinity of the bubble is provided using numerical simulations of bubble dynamics equation.     

An analytical model for real gas flow in shale nanopores with non‐circular cross‐section

An analytical model for gas transport in shale media is proposed on the basis of the linear superposition of convective flow and Knudsen diffusion, which is free of tangential momentum accommodation coefficient. The present model takes into the effect of pore shape and real gas, and is successfully validated against experimental data and Lattice–Boltzmann simulation results. Gas flow in noncircular nanopores can be accounted by a dimensionless geometry correction factor. In continuum‐flow regime, pore shape has a relatively minor impact on gas transport capacity; the effect of pore shape on gas transport capacity enhances significantly with increasing rarefaction. Additionally, gas transport capacity is strongly dependent of average pore size and streamline tortuosity. We also show that the present model without using weighted factor can describe the variable contribution of convective flow and Knudsen diffusion to the total flow. As pressure and pore radius decrease, the number of molecule‐wall collisions gradually predominates over the number of intermolecule collisions, and thus Knudsen diffusion contributes more to the total flow. The parameters in the present model can be determined from independent laboratory experiments. We have the confidence that the present model can provide some theoretical support in numerical simulation of shale gas production. © 2016 American Institute of Chemical Engineers AIChE J, 62: 2893–2901, 2016     

Prediction of rates of heat or mass transfer in complex situations by interpolating between simpler limiting cases

This paper emphasizes the generality of a simple algebraic procedure suggested in 1962 by the author to predict the rate of heat or mass transfer in complex situations. It consists in replacing the terms in the convective diffusion equation by expressions involving scaling quantities multiplied by constants. Thus the convective-diffusion equation is replaced by an algebraic equation for the mass transfer coefficient containing a number of constants. The constants are determined from the solutions available for some simpler limiting cases. To illustrate the procedure a variety of examples are given which include: penetration theory for diffusion with chemical reaction, laminar flow along a plate accompanied by a chemical reaction, diffusion with chemical reaction in a turbulent liquid, mass transfer from a drop to a continuous phase, unsteady heat transfer to a liquid in steady laminar flow along a plate and free convection superimposed on forced convection. Numerous other complex situations have been or can be treated by interpolation between some simpler limiting cases.     

A mathematical model of multiple ion transport across an ion-selective membrane under current load conditions

A macrohomogeneous mathematical model of the simultaneous transport of multiple ions across an ion exchange membrane based on the Nernst–Planck equation was developed. Schlögl's equation of motion was used to evaluate the convective term of the mass-transfer inside the membrane. The model accounts for the external diffusion of the ions through the Nernst diffusion layer to the phase boundary on both sides of the membrane. Donnan equilibrium is used to describe the potential and the concentration discontinuity on the membrane-solution interface. The results document the importance of the external diffusion layers for ion transport across the membrane.     

RELATIVE IMPORTANCE OF VAPOUR DIFFUSION AND CONVECTTVE FLOW IN MODELLING OF SOFTWOOD DRYING

The influence of vapour diffusion on the drying rate of a softwood board has been examined for drying temperatures varying from 60°C to 140°C. It is found that for very low temperature drying a model which considers both vapour convective and diffusion in wood predicts dry-rate curves matching the experimental data closely. For high temperature drying, both of the above drying model and a drying model which considers only vapour convective flow give predictions in agreement with the observed data. This illustrates that the diffusion of vapour and air is important in low temperature drying panicularly during the late stages of drying. However, for high temperature drying, the convective flow of moisture vapour is dominant and the diffusion component is negligible. The observation provides evidence for simplifying a drying model for high temperature drying without reducing its credibility in predicting drying rate curves.     

A novel technique for local mass transfer measurements

A novel electrodeposition technique is developed to estimate time‐averaged convective local mass transfer coefficients. This method is based on the diffusion‐controlled deposition rate of copper. With an electrolyte solution consisting of H2SO₄ and CuSO₄, copper is dissolved at the anode and deposited onto the nickel cathode. The thickness of the copper, measured with an optical microscope, provides an estimate of the time‐averaged local mass transfer coefficient for the given location, and by depositing multiple layers, the coefficients under different flow conditions can be obtained from one cathode. The results for laminar flow in a smooth, round pipe showed good agreement with those calculated from the analytical Leveque solution. Results were also obtained for turbulent flow and demonstrate the potential for acquiring convective local mass transfer coefficients for various flow configurations.