Two-phase flow—IV. Gas and liquid side mass transfer coefficients

Mass transfer coefficients in gas and liquid have been obtained for the case of cocurrent gas—liquid flow through a vertical tube 6 mm i.d. by absorbing sulphur dioxide into sodium hydroxide solution and carbon dioxide into sodium carbonate—sodium bicarbonate solution respectively. The liquid side mass transfer coefficient was found to increase with the gas velocity but showed a maximum when plotted against the liquid velocity. A model based on the analogy between momentum and mass transfer has been proposed for the rate of mass transfer in the liquid phase. The mass transfer coefficient in the gas phase increases with the gas velocity but the liquid velocity has an opposite effect. A correlation in terms of dimensionless groups is presented for the gas side mass transfer coefficient.     

伴有二级不可逆反应的非牛顿幂律流体薄膜流中化学吸收的研究

本文对伴有二级不可逆反应的非牛顿幂律流体降膜流中的吸收过程进行了研究,提出扩散反应方程和它的解,并得到实验验证.     

Analytical approximate solution of competitive facilitated transport of acid gases through liquid membranes

An analytical approximate solution for the competitive facilitation factor of components A and E across a liquid membrane is developed in the case of instantaneous reactions inside the liquid membranes. This analytical solution solves the dimensionless, nonlinear diffusion-reaction transport problem governing the competitive facilitated transport of two gaseous components through liquid membranes. Prediction of the facilitation factors has been obtained for the equilibrium chemical reaction regime, considering the unequal complexes diffusivities and cases of zero and nonzero permeate side solute concentrations. This mathematical solution leads to analytical expressions for the concentration profiles of the species across the liquid membrane. In comparison with the present numerical solution and also numerical calculations and experimental data from the open literature, the difference between the analytical predictions and those obtained from the numerical solution were found to be in well agreement.     

A study of the contribution of solvent transport to liquid junction potentials between electrolytes in different solvents

Measurements have been made on cells which contain liquid junctions between two solutions containing different solvents. By employing cells in which the two solutions are saturated with the same salt, it has been possible to directly measure the contribution to the liquid junction potential of the transfer of solvent species across the solution—solution interface. This solvent—solvent junction potential has been measured for junctions between water and methanol, ethanol, acetone, acetonitrile, and propylene carbonate solutions and for some junctions between pairs of these nonaqueous solutions. The values obtained for the solvent contributions to the liquid junction potentials were somewhat smaller than the corresponding values obtained indirectly by other workers using cells with junctions between salt solutions in different solvents. The potentials were found to depend greatly on the particular salt employed, but to be independent of the method of forming the liquid junction. A possible explanation of the mechanism giving rise to these potentials is given. The possible formation of solid solvates of lithium, potassium, thallium, and mercurous chlorides in these solvents was also investigated.     

Mathematical model of the liquid flow pattern in an aerotank-sedimentation tank system

An analytical solution has been obtained for the mathematical model of the liquid flow pattern in an aerotank-sedimentation tank system with recycling in the form of a dispersion dependence on the model parameters: the Peclet number and recycling stream fraction. A technique is offered to determine the model parameters.     

Chemical absorption of mercaptan in an aerosol operated loop reactor

A mechanistic mathematical model for the chemical absorption of mercaptan in sodium hypochlorite solution has been derived. In order to describe the process adequately, a semi-verified complex scheme of the involved kinetic reactions based on stopped-flow measurements with UV-detection has been implemented. The overall system of differential equations has been solved numerically. For some asymptotic cases, approximation formulae are given. The process has been carried out in an aerosol operated jet loop reactor which is characterized by high interfacial areas at low liquid flow rates. Fitting the model solution to the experimentally obtained conversion data enabled determination of the unknown hydrodynamic parameters. By means of a sensitivity analysis, the influences of the different parameters are discussed.     

Ascending cocurrent flows in an inclined flat channel

A conjugate solution has been obtained for ascending cocurrent turbulent gas flow and laminar liquid wavy film flow in an inclined flat channel without drop entrainment. The waves have been represented as surface roughness features. Experimental studies have been conducted for air-water, air-diethylene glycol, and air-aqueous sucrose systems, and the results have been compared with the calculated data.     

Unsteady mass transfer around axisymmetric drops of revolution in variable diffusion coefficient liquids

Unsteady mass transfer in the continuous phase around axisymmetric drops of revolution at high Peclet numbers has been theoretically studied. The liquid is a binary system, having a variable diffusion coefficient, which depends on the solute concentration. The solution to the problem was obtained by extending the theory of Favelukis and Mudunuri, developed for a constant diffusion coefficient liquid. The procedure consists of transforming the differential mass balance, for a binary system, into a partial differential equation which has an analytical solution, and an ordinary differential equation that needs to be solved numerically. Solutions to a large number of problems can be immediately obtained with the only requirements being the shape of the drop, the tangential velocity at the surface of the drop and an expression for the variable diffusion coefficient liquid. An approximate analytical solution is also suggested which is in excellent agreement with the numerical results.     

Simultaneous absorption of two gases which react between themselves in a liquid medium: An approximate solution

An approximate solution for the simultaneous absorption and reaction of two gases in a liquid has been presented based on the film theory, assuming a nonlinear (exponential) profile for the concentration of each of the gaseous species in the film. The solution obtained has been compared with the numerical solution of Roper, Hatch and Pigford and found to be in good agreement, thus proving the validity of the approximations.     

Modelization of matter transfers between plasticized PVC and liquids in case of a maximum for liquid-time curves

When plasticized PVC and liquids are contacted with each other, as in liquid and packaging, some matter transfer may occur. The phenomenon is complicated, and no analytic solution can be found. A simultaneous transfer of the liquid into and plasticizer out from the PVC mass takes place with concentration-dependent diffusivities. Very often, liquid concentrationtime curves have a maximum, when the rate of transfer is higher for the liquid than for the plasticizer at the beginning of the contact. Another application of short tests has been obtained with success in this hard case. A new model using short test data has been developed. It takes into account not only the diffusion of both liquids through the PVC, but also matter transfers through the liquid—PVC interface with a coefficient of matter transfer, as well as the data corresponding to the equilibrium. Some information of interest is given by way of the materials transferred through PVC faces, and the profile of concentration through the PVC for the liquid and plasticizer.     

On boundary conditions to the film model of mass transfer in chemical absorption

The problem of appropriate boundary conditions for mass transfer within the liquid film in chemical absorption ih reconsidered. It has been shown that the most general solution to the problem of mass transfer in the liquid film can be obtained if a fixed bulk composition is taken as a film-bulk boundary condition to the differential balance equations of the film. This method leads to solutions which can be incorporated into absorber balance equations of any type. As an illustrative example, the simultaneous absorption of two gases which react together in a semi-batch absorber is discussed. A new, approximate but very simple and accurate solution to this problem is proposed.     

Velocity profiles at the exit of circular tubes

An investigation has been carried out on velocity profiles of Newtonian liquids at the exit of circular tubes for Reynolds numbers from about 50 to 1000. A simple expression which asymptotically approaches a Poiseuille parabolic distribution for higher Reynolds numbers is obtained. Experimental measurements of extrudate swell ratios were used as criteria for convergence to the solution. Comparison with jet shapes from previous experimental and theoretical studies supports the obtained results. The work also illustrates a straightforward method for simplifying and solving the governing equations for laminar flows of thin liquid layers.     

Reduction of concentration polarization at feeding interphase of a hollow fiber supported liquid membrane by using periodic operation

An experimental investigation was carried out to reduce the concentration polarization at feeding interphase between feed solution and liquid membrane imposing flow instabilities. The periodic operation of the hollow fiber supported liquid membrane for separation of lanthanide metal by using D2EHPA as extractant dissolved in kerosene. The operating flow rate of the feed solution was varied according to a symmetric square wave function around time-average values of 200, 300 and 400 ml/min. Time periods ranging from 18 to 3 minutes and amplitudes of 50 and 100 ml/min were investigated. The results of these periodic tests were compared with results obtained from the conventional steadystate mode of operation. It has been found that the periodic operation leads to higher stripping concentration or higher ion flux than that obtained from the corresponding steady state operating conditions. This is because periodic operation disturbs concentration polarization in the boundary layer between the feed solution and liquid membrane. It has also been found that the ion flux increases with increasing amplitudes and decreasing time periods of the forcing function. However, when the period is less than 3 minutes the flux decreases because the liquid membrane is peeled out from the pores of hollow fiber.     

Enhancement Factor for Gas Absorption in a Finite Liquid Layer. Part 2: First‐ and Second‐Order Reactions in a Liquid in Plug Flow

Gas absorption accompanied by an irreversible chemical reaction of first‐order or second‐order in a liquid layer of finite thickness in plug flow has been investigated. The analytical solution to the enhancement factor has been derived for the case of a first‐order reaction, and the exact solution to the enhancement factor has been obtained via numerical simulation for the case of a second‐order reaction. The enhancement factor in both cases is presented as a function of the Fourier number and tends to deviate from the prediction of the existing enhancement factor expressions based on the penetration theory at Fourier numbers above 0.1 due to the absence of a well‐mixed bulk region in the liquid layer. Approximate enhancement factor expressions that describe the analytical and exact solutions with an accuracy of 5 % and 9 %, respectively, have been proposed.     

Liquid membrane separation: Modelling and development of a continuous counter-current pilot scale contactor

Analogy of liquid membrane permeation (LMP) with liquid—liquid extraction has led the authors to study a counter current device for LMP separation. A model has been carried out giving the “ideal” performances of a plug flow continuous counter current contactor. Results of such a model have been compared with those obtained with two kinds of pilot scale contactors: a pulsed column and a spray one.     

An analysis of simultaneous absorption of two gases reacting between themselves in a semi-batch reactor

The problem of simultaneous absorption of two gases reacting between themselves in a semi-batch reactor has been analysed. An exact analytical solution for the enhancement factor has been obtained which requires neither a prior knowledge of the regime of absorption nor arbitrary choice of bulk liquid phase concentrations of gaseous reactants. The methodology developed here can easily be extended to a continuous flow reactor.     

液体非电解质水溶液粘度的预测

在Teju-Rice液体混合物粘度模型的基础上,对常用的液体混合物粘度关联式进行了分析和比较;导出了适用于二元和多元非电解质水溶液的粘度模型;结合实际数据导出的水溶液二元作用参数的估算式可进行水溶液粘度的预测。用该模型计算了7个体系398个不同温度和组成的二元水溶液和4个体系189个不同温度和组成的三元水溶液的粘度,结果表明,计算值对实验数据的总平均相对偏差分别为6.848%和5.043%,本文水溶液粘度估算式的计算准确性优于Teju-Rice法。     

Separation of Nickel(II) and Cadmium(II) with Ion-Exchange Process

Separation of nickel(II) and cadmium(II) ions from sulphate solution has been studied. The solutions of Ni(II) and Cd(II) have been treated with different exchange resins: Lewatit OC-1026, Lewatit TP-207, and Lewatit MonoPlus SP 112. Data obtained from the ion-exchange process was compared with data from the supported liquid membrane experiment. It was shown that the use of the supported liquid membrane process enables separation of investigated ions. In this process the highest recovery factor was obtained. The best separation of metal ions was obtained for the ion-exchange process with Lewatit OC 1026.     

Unsteady mass transfer between a slender bubble and a viscous liquid in a simple extensional flow

Unsteady mass transfer between a slender bubble and a viscous Newtonian liquid in a simple extensional and creeping flow has been studied. The exact analytical solution, at large Peclet numbers, has been obtained using similarity transformations and by the method of characteristics. It was determined that when a dimensionless time (the strength of the flow multiplied by the time) is greater than 2, then steady state is, in practice, obtained.