MASS TRANSFER IN AC ELECTROLYSIS: EXTENSION OF A FILM MODEL TO TURBULENT FLOW ON A ROTATING HEMISPHERE

Turbulent mass transfer to a rotating hemisphere during AC electrolysis was examined with a film model. The analytical results for the limiting AC current density were compared to the experimental data obtained with sinusoidal, square and triangular wave AC. The limiting AC current density in turbulent flow was found to depend on both the Reynolds number as a dimensionless AC frequency K = (ω/Ω)Sc^1/3. The prediction by the film model agreed with the experimental data to within ±15%. For a given root-mean-square of applied AC, the periodic concentration overpotential decreased in the order of quare, sinusoidal, and triangular AC. The phase shift between the applied AC and the concentration overpotential wave decreased with increasing Reynolds number in turbulent flow.     

MASS TRANSFER IN AC ELECTROLYSIS: EXTENSION OF A FILM MODEL TO TURBULENT FLOW ON A ROTATING HEMISPHERE

Turbulent mass transfer to a rotating hemisphere during AC electrolysis was examined with a film model. The analytical results for the limiting AC current density were compared to the experimental data obtained with sinusoidal, square and triangular wave AC. The limiting AC current density in turbulent flow was found to depend on both the Reynolds number as a dimensionless AC frequency K = (ω/Ω)Sc^1/3 The prediction by the film model agreed with the experimental data to within ±15%. For a given root-mean-square of applied AC, the periodic concentration overpotential decreased in the order of quare, sinusoidal, and triangular AC. The phase shift between the applied AC and the concentration overpotential wave decreased with increasing Reynolds number in turbulent flow.     

MASS TRANSFER IN AC ELECTROLYSIS: EXTENSION OF A FILM MODEL TO TURBULENT FLOW ON A ROTATING HEMISPHERE

Turbulent mass transfer to a rotating hemisphere during AC electrolysis was examined with a film model. The analytical results for the limiting AC current density were compared to the experimental data obtained with sinusoidal, square and triangular wave AC. The limiting AC current density in turbulent flow was found to depend on both the Reynolds number as a dimensionless AC frequency K = (ω/Ω)Sc^1/3 The prediction by the film model agreed with the experimental data to within ±15%. For a given root-mean-square of applied AC, the periodic concentration overpotential decreased in the order of quare, sinusoidal, and triangular AC. The phase shift between the applied AC and the concentration overpotential wave decreased with increasing Reynolds number in turbulent flow.     

A MODEL FOR PREDICTING HEAT TRANSFER TO A TURBULENT FALLING FILM

A modified form of Carey'ls method for predicting the heat transfer to a turbulent falling film is presented. The new model is successfully tested against experimental data as well as other models. This method utilizes an optimization technique along with the Rombcrg integration to determine two universal constants for the modified turbulent diffusivisity model. The results show that in spite of its relative simplicity, the new model is a fairly accurate one, having an overall average error of less than 9%.     

流态化结晶过程中晶体生长的湍流传质模型

根据流态化结晶过程的流体处于湍流运动的事实,将多相湍流理论应用于晶体的生长过程,建立该过程的湍流传质动力学模型.模型计算与实验数据比较表明,湍流传质模型对扩散传质控制的晶体生长过程是可靠的.     

MASS TRANSFER TO THE FREE INTERFACE IN STIRRED VESSELS

Liquid-phase mass transfer coefficients between gas and a flat liquid interface in a stirred tank are proportional to the average rate of energy dissipation raised to the power of one third for water and one quarter for organic solvents. This discrepancy can be attributed to the presence of surface active contaminants in aqueous systems. The critical value of the Reynolds number for the transition between the regime controlled by the small scale turbulence to that controlled by large scale eddies is about 100. The Levich-Davies model was found inappropriate in this case.     

MASS TRANSFER TO THE FREE INTERFACE IN STIRRED VESSELS

Liquid-phase mass transfer coefficients between gas and a flat liquid interface in a stirred tank are proportional to the average rate of energy dissipation raised to the power of one third for water and one quarter for organic solvents. This discrepancy can be attributed to the presence of surface active contaminants in aqueous systems. The critical value of the Reynolds number for the transition between the regime controlled by the small scale turbulence to that controlled by large scale eddies is about 100. The Levich-Davies model was found inappropriate in this case.     

EFFECT OF INTERPHASE MASS TRANSFER ON UNSTEADY CONVECTIVE DIFFUSION IN A SIMPLIFIED CROSS MODEL FLUID

This article examines the influence of heterogeneous chemical reaction on the exchange coefficient, convective coefficient, and diffusive coefficient arising in the study of dispersion in a simplified Cross model fluid flow. The exchange coefficient emanates exclusively from the incorporation of the catalytic wall reaction. The convective and diffusive coefficients are also influenced by the wall reaction. The results show that the dispersion coefficient asymptotically reaches a stationary state after a critical time. This critical time decreases as the absorption at the walls increases. The problem finds application in biomechanics such as transport across a semipermeable membrane, in industries releasing waste into the environment, in crude oil conveyance, and in chromatography.     

CONJUGATE HEAT TRANSFER WITH TURBULENT FLOW IN A CIRCULAR TUBE

A steady heat transfer problem has been analyzed as a conjugate problem with turbulent flow in a circular tube. The three kinds of thermal boundary conditions considered here are specified as constant temperature, constant heat flux and constant heat transfer coefficient at the outer surface of the wall.

From the results of numerical calculation for Prandtl numbers in the range 0.01 ≤ Pr ≤ 10 and for Reynolds numbers in the range 10⁴ ≤ Re ≤ 10⁵, it was confirmed that the dimensionless parameter R_c could have significant effects on the heat transfer and the temperature field in the fluid adjacent to the wall.     

MASS TRANSFER EFFECTS ON THE ETCH RATE OF GAAS IN FLOW SYSTEMS

In industrial wet etching reactors, the fluid contacts the substrate surface as a spray of flowing stream, thus introducing mass-transfer resistances to the reaction rate. The etching of gallium arsenide in H₂O₂-NH₄OH-H₂O solutions was studied using an open-channel flow reactor to simulate the industrial conditions. The etch rate was always lower than that obtained under kinetic control, and the dependence of etch rate on H₂O₂ concentration shifted closer to first order. From the calculation of the ratio of rate constant to mass-transfer coefficient, the reaction-rate and mass-transfer resistances were both significant in this system. When the mass-transfer coefficient was calculated from equations for flow past a flat plate, the prediction of etch rate was good, particularly when the starting length for velocity boundary layer development ahead of concentration boundary layer development was taken into account. Another approach for the calculation of mass-transfer coefficient, based on the assumptions for flow between parallel plates, best represented the relative insensitivity of etch rate to fluid velocity.     

MASS TRANSFER EFFECTS ON THE ETCH RATE OF GAAS IN FLOW SYSTEMS

In industrial wet etching reactors, the fluid contacts the substrate surface as a spray of flowing stream, thus introducing mass-transfer resistances to the reaction rate. The etching of gallium arsenide in H₂O₂-NH₄OH-H₂O solutions was studied using an open-channel flow reactor to simulate the industrial conditions. The etch rate was always lower than that obtained under kinetic control, and the dependence of etch rate on H₂O₂ concentration shifted closer to first order. From the calculation of the ratio of rate constant to mass-transfer coefficient, the reaction-rate and mass-transfer resistances were both significant in this system. When the mass-transfer coefficient was calculated from equations for flow past a flat plate, the prediction of etch rate was good, particularly when the starting length for velocity boundary layer development ahead of concentration boundary layer development was taken into account. Another approach for the calculation of mass-transfer coefficient, based on the assumptions for flow between parallel plates, best represented the relative insensitivity of etch rate to fluid velocity.     

A NEW METHOD OF CALCULATING TERNARY MASS TRANSFER WITH A NON TRANSFERRING SPECIES BASED ON GILLILAND'S PARAMETRIC SOLUTION OF THE MAXWELL-STEFAN EQUATIONS FOR THE FILM MODEL

This paper presents a solution for the problem of multiple roots in Gilliland's parametric solution of the Maxwell-Stefan equations. Based on it a new algorithm for calculating ternary mass transfer with a non transferring species is obtained. This new algorithm demonstrates rapid and stable convergence. In contrast to the well known calculation of mass transfer in multicomponent mixtures using the matrix solution of the Maxwell-Stefan equations the new algorithm simplifies the calculation by avoiding any matrix operations.     

MASS TRANSFER FROM FLAT PLATES TO POWER-LAW FLUIDS IN LAMINAR FLOW

Mass transfer from vertical flat plates to water and 0.5 to 1.5% aqueous CMC solutions is measured in the Reynolds number range of 10^{- 2}to 6.0 x 10₃. Blasius analysis has been found to be valid only up to a Reynolds number of 100, below which Graetz-Leveque solution is more appropriate.     

A HOMOGENEOUS MODEL FOR MASS TRANSFER ENHANCEMENT IN GAS-LIQUID-LIQUID SYSTEMS

A modified homogeneous mass transfer model based on penetration theory is proposed for the mass transfer enhancement in gas-liquid-liquid systems. The present model assumes the existence of a shuttle mechanism between the organic dispersed phase and the continuous aqueous phase and considers the effect of diffusivity along with the solubility ratio and the dispersed phase holdup. The concept of effective diffusivity for gas in liquid-liquid emulsions has been used to consider the effect of diffusivity on mass transfer enhancement. The proposed model predicts the experimentally obtained enhancement factor with reasonable accuracy and numerical simplicity. Fresh experiments were also conducted to further validate the proposed model.     

A HOMOGENEOUS MODEL FOR MASS TRANSFER ENHANCEMENT IN GAS-LIQUID-LIQUID SYSTEMS

A modified homogeneous mass transfer model based on penetration theory is proposed for the mass transfer enhancement in gas-liquid-liquid systems. The present model assumes the existence of a shuttle mechanism between the organic dispersed phase and the continuous aqueous phase and considers the effect of diffusivity along with the solubility ratio and the dispersed phase holdup. The concept of effective diffusivity for gas in liquid-liquid emulsions has been used to consider the effect of diffusivity on mass transfer enhancement. The proposed model predicts the experimentally obtained enhancement factor with reasonable accuracy and numerical simplicity. Fresh experiments were also conducted to further validate the proposed model.     

THE USE OF FRACTAL DIMENSION TO QUANTIFY THE EFFECT OF SURFACE ROUGHNESS ON FILM MASS TRANSFER ENHANCEMENT

Experimental results from previous work, contained in a companion paper by Van Vliet and Weber (1988), have shown qualitatively that the external film transfer coefficient for adsorption on particulate adsorbents is very dependent on the roughness of the mass transfer surface. Until recently a suitable method to quantify surface roughness was not available. Experimental data of film mass transfer coefficients of various activated carbons, carbonaceous adsorbents, and polymeric adsorbents are investigated. It is shown that film mass transfer is enhanced by the effect of surface roughness. The fractal dimensions of the adsorbent particle surfaces are determined and are shown to be linked to the degree of mass transfer enhancement. This suggests that the external mass and heat transfer enhancement properties of a rough surface are related to its fractal dimension.     

颗粒与液相间的湍流涡旋裂变传质模型

湍流在宏观上处于远程混沌无序状态, 而在介微观上处于近程有序状态。从分析湍流场中局 域中涡旋的串级结构出发,通过对N-S方程的涡旋输运形式进行求解, 导出一个具有分形意 义的涡旋群运动表达式,并得到涡旋掠过颗粒表面花费的时间, 然后同Higbie的传质渗透模型相联系,以涡旋的分布函数为权求其数学期望,得到搅拌湍流场中的传质系数表达式,结果与实验数据吻合较好。     

A MODEL FOR THE MASS TRANSFER COEFFICIENT IN ROTATING PACKED BED

Abstract

Based on the locus of ink on the well-rotating disc, a model for the mean residence time of liquid in a rotating packed bed, t = ?′ ε (ctg(α₂/2) ? ctg (α₁/2))ωu), is proposed. Model predictions agreed with the reported data with relative error within ±15%. A modified surface renewal model based on Danckwerts, is used. For evaluation of the mass transfer coefficient, prediction of surface renewal frequency 5 is assumed as S =?ω(?is a model parameter), and effective contact time t is determined by the residence time model. Model predictions for k_L agreed well with the experimental data with relative error within ±14%     

ON THE MOMENT COEFFICIENT CALCULATION OF A ROTATING DISK IN A TURBULENT FLUID FLOW

Mixing in co-rotating sinusoidal cavity flows is studied with period, T, and phase shift, a, as parameters. Notice that the main obstacle to uniform mixing is the existence of stable :ower periodic orbits, mixing windows, where uniform mixing takes place, are found in the T— a space u:iing bifurcation analysis. The main advantage of this method is a great saving of the computation time.