Mass transfer with fast chemical reaction in drops

Mass transfer with a fast second-order chemical reaction inside a drop has been studied photographically. Measured flow patterns and the reaction surface position have been compared with predictions of solutions of transport equations. The agreement is within experimental error.     

A kinetic study on the mass transfer with chemical reaction in the AUC precipitation process

The theoretical analysis of mass transfer with chemical reaction kinetics is developed for AUC precipitation process using the penetration theory and computed numerically on an VAX 11/780. The nonlinear partial differential equations were solved by a finite difference method of Crank-Nicolson. Approximate solutions can be used to study experimental parameters and to interpret the experimental results in AUC precipitation process.     

A study of mass transfer from single large oscillating drops

A study was made of mass trasfer rates from single large oscillating drops of pure liquid-liquid systems, in the size range of 5 to 10 mm. A thrermostatically-controlled, 50 mm in diameter, 1000 mm long, rising drop column was used, in which mirrors in the jacket enabled front and side views of drops to be photographed simultaneously. The systems studied were (1) toluene and acetone (dispersed)-water (continuous), and (2) n-heptane and acetone (dispersed)-water (continuous). High concentrations of acetone (up to 3.75 kmol/m³) were used to examine the effect of different parameters on the mass transfer rate, frequency and amplitude of oscillation in countercurrent operation. Previous theories and empirical correlations [2–6, 12, 13, 15] for the prediction of overall mass transfer coefficients showed large deviations from measured values. These may have aarisen because the models do not represent droplet oscillation accurately, and/or apply only to oscillations of small droplets. Fair agreement was obtained for small oscillating droplets as low solute concentrations. The oscillations of a travelling drop were asymmetrical; the period of oscillation was uniform for mutually-saturated systems but changed when mass transfer was taking place. The periods were longer than those predicted by the Lamb [7] and Shroeder and Kintner [37] correlations. Terminal velocities predicted from literature correlations [32, 34] did not give reasonable agreement with experimental data when there was mass transfer of solute. The drag coefficient increased with increasing mass transfer rate from the drop. Correlation of the results and the dispersed phase mass trasfer coefficients by dimensional analysis resulted in the correlation

1 List of symbols at the end of the paper.

with a mean deviation of ±23%, by insertion of experimental oscillation frequency data. This will facilitate more accurate prediction of the dispersed phase mass transfer coefficients relating to equipment containing droplets in the oscillating regime, e.g. pulsed columns or agitated tanks.     

An experimental study of mass transfer with chemical reaction from single gast bubbles

Rates of forced convection mass transfer from single bubbles of carbon dioxide reacting in aqueous ethanolamine solutions have been determined experimentally for intermediate babble Reynolds numbers. A water tunnel apparatus, and technique for measuring mass transfer rates are described. The results of the experimental study are compared with a mathematical model describing mass transfer with an accompanying second order reaction; the hydrodynamic condition of the model is described using Kawaguti type velocity profiles. The experimental data appear to confirm the model satisfactorily.     

A finite element solution of coupled heat and mass transfer with chemical reaction

A finite element method is presented for solving the coupled non-linear parabolic differential equations describing transient transport of heat and mass in chemically reacting systems. The method appears to be a useful approximation for a wide variety of problems. Typical numerical results are reported for non isothermal catalytic solid—fluid reactions. Applications to other fields such as absorption accompanied by reaction and non-catalytic solid—fluid reaction models are also formulated.     

Mass transfer with chemical reaction from spherical one or two component bubbles or drops

Unsteady state mass transfer between a one or two component bubble (or drop) and the continuous phase with a chemical reaction occuring either in the continuous or in the dispersed phase is examined. The main assumption for binary bubbles is that the rate determining step is diffusion in the continuous phase. Two limiting velocity fields. Hadamard flow (Re?:1) and potential flow (Re?:1) are used in the calculations.     

Numerical simulation of mass transfer in circulating drops

Numerical simulations of mass transfer are performed for a circulating liquid drop with applications in liquid–liquid extraction. Simulation parameters are chosen for a multi-component ternary system acetone–methanol–benzene. The drop circulation pattern is estimated via a truncated Galerkin representation of the drop streamfunction. Fickian diffusivities for multi-component mass transfer are obtained via Maxwell–Stefan theory with thermodynamic corrections. The advection–diffusion equations governing mass transfer are solved via two distinct numerical methods: a finite difference scheme (using the alternating direction implicit method) and a finite element scheme. Good agreement was obtained between both schemes. Simulation results are presented for a Reynolds number (Re=30) and for a selection of Peclet numbers (Pe=100, 1000 and 10 000, thereby giving insight into the effects of increasing Peclet number). The numerical simulations of the full advection–diffusion equations are compared against predictions of a rigid drop model (i.e. without circulation) and also against predictions of a semi-analytical boundary layer model developed by Uribe-Ramirez and Korchinsky. Results for bulk mass fractions reveal that the rigid drop model predictions evolve too slowly, while the boundary layer model predictions evolve much more quickly than the numerical simulations. Advection–diffusion simulation results for the evolution of mass fractions at selected individual locations in the drop show that points on streamlines nearest to the drop surface and/or drop axis evolve fastest, while those closest to the drop internal stagnation point evolve slowest. Corroborated by contour plots of component concentrations throughout the drop at selected times, this supports a picture whereby mass fractions become roughly uniform along individual streamlines, but mass is transferred diffusively from streamline to streamline.     

Simultaneous effects of chemical reaction and Ohmic heating with heat and mass transfer over a stretching surface: A numerical study

In this article,we have considered the simultaneous influence of ohmic heating and chemical reaction on heat and mass transfer over a stretching sheet.The effects of applied magnetic field are also taken into consideration while the induced magnetic field is not considered due to very small magnetics Reynolds number.The governing flow problem comprises of momentum,continuity,thermal energy and concentration equation which are transformed into highly nonlinear coupled ordinary differential equations by means of similarity transforms,which are then,solved numerically with the help of Successive Linearization method (SLM) and Chebyshev Spectral collocation method.Numerical values of skin friction coefficient,local Nusselt number,and Sherwood number are also taken into account with the help of tables.The physical influence of the involved parameters of flow velocity,temperature and concentration distribution is discussed and demonstrated graphically.The numerical comparison is also presented with the existing published results and found that the present results are in excellent agreement which also confirms the validity of the present methodology.     

A gradientless contactor for experimental study of interphase mass transfer with/without reaction

The proposed experimental contactor features uniformity of composition of both gas and liquid phases with independent control of individual film resistances and interfacial area. Tracer experiments showed a reasonable approach to phase uniformity, and experiments with four systems gave reliable, consistent mass transfer coefficients.This device which we call the double mixed contactor is especially suited for kinetic studies. It overcomes the shortcomings of present contactors and it extends the concept of gradientless reactors, so popular today for heterogeneous catalysis, to two fluid systems.     

Modeling liquid-phase chemical reaction and interphase mass transfer in churn-turbulent bubble columns

The slug and cell model of liquid-phase mixing has been extended to consider the effects of interphase mass transfer and liquid-phase chemical reaction in isothermal churn-turbulent bubble columns. Inclusion of the effects of the gas phase is straightforward since the gas phase has previously been considered as it strongly affects the mixing of the liquid phase. The computational simplicity of the slug and cell model has been retained with the species conservation equations being reduced to a system of algebraic equations. The behavior of the model has been examined for two cases: (1) liquid-phase chemical reaction in the absence of interphase mass transfer and (2) in the presence of interphase mass transfer without liquid-phase chemical reaction. In the second case the model behavior has been compared to available literature data for the absorption of oxygen into water.     

Effects of surfactants on mass transfer outside drops

A study was made of the effect of a surface-active agent, on mass transfer of Iodine from an aqueous phase to a falling drop of carbon tetrachloride. The size of drops was varied from 0.2 to 0.4 cm equivalent spherical diameters and the concentrations of Teepol ranged from 0 to 0.5 cm³/l. The experimental falling velocities have been compared with various correlations proposed by several workers. It has been found that the experimental results for the pure or slightly contaminated system (0.05 cm³/l) agree well with Vignes' correlation. In case of mass transfer, a maximum reduction in the mass transfer coefficient of 58% due to the presence of Teepol has been observed. Results have been expressed in dimensionless form using the Galileo and Sherwood numbers.     

Direct formation of particles from drops by chemical reaction with gases

The factors which influence the direct formation of solid particles by reaction of sprays with gaseous media were investigated by studying the reaction of single macro-drops of orthophosphoric acid with gaseous ammonia. The composition, temperature and physical nature of the drops were measured or recorded as the reaction proceeded. The controlling resistance for mass-transfer was found to exist within the drop and a diffusion model adequately described the uptake of ammonia for the conditions studied. The maximum uptake of ammonia increased with delay in formation of a permanent solid phase. This delay was increased or altered by (i) reduction in acid concentration, (ii) addition of sulfuric acid, (iii) cyclic exposure of the drop to the gas, and (iv) humidification of the gas.     

An analytical solution for mass transfer in turbulent falling films with or without chemical reaction

A simple analytical solution is presented for mass transfer in an isothermal turbulent falling liquid film with or without chemical reaction. The exact solutions are compared with previous work for the cases of physical absorption and first-order reaction. New solutions are presented for a zero-order reaction, and generalized results are presented for first and pseudo nth-order reactions. The method of superposition is used to generate the first ten eigenvalues and corresponding values of the Sherwood number for several limiting situations. The analytical solution offers substantial advantages over previous finite-difference numerical solutions both in computation time and in describing the effects of operating variables.     

Unsteady mass transfer around spheroidal drops in potential flow

Unsteady mass transfer in the continuous phase around spheroidal drops in potential flow and at high Peclet numbers has been theoretically studied. Analytical solutions for the concentration profile, the molar flux, the concentration boundary layer thickness, and the time to reach steady state are presented. The solution to the problem was obtained by the useful equations derived by Favelukis and Mudunuri for axisymmetric drops of revolution, with the only requirements being the shape of the drop and the tangential velocity at the surface of the drop. The solution suggests that, as the eccentricity increases, the total quantity of material transferred to or from the drop decreases (for prolate spheroids) and increases (for oblate spheroids). It was also determined that when the dimensionless time is greater than 2, then steady state is in practice obtained, with prolate drops attain steady-state conditions faster than oblate drops.     

A contactor for studying mass transfer with reaction in liquid-liquid systems

A contactor has been developed which is especially suitable for experimental investigations of mass transfer with chemical reaction in liquid-liquid systems. Its function has been tested with the reaction between tetrachlorohydroquinone (dissolved in a mixture of 2-octanone and carbon tetrachloride) and ceric sulfate (in 0.5M sulfuric acid). In the contactor described in this work the kinetics of this reaction can be investigated in the very slow reaction regime (kinetic regime). It is also possible easily to determine whether a reaction takes place to an appreciable extent in only one or both phases.