Mass transfer translational flow

Volumes 1, 2 and 3 form an integrated series with the fundamentals of fluid flow, heat transfer and mass transfer in the first volume, the physical operations of chemical engineering in this, the second volume, and in the third volume, the basis of chemical and biochemical reactor design, some of the physical operations which are now gaining in importance and the underlying theory of both process control and computation. The solutions to the problems listed in Volumes 1 and 2 are now available as Volumes 4 and 5 respectively. Furthermore, an additional volume in the series is in course of preparation and will provide an introduction to chemical engineering design and indicate how the principles enunciated in the earlier volumes can be translated into chemical plant. 

In this study, the effects of cosolvent (EtOH) addition on the solubilization and recovery of PCE by a nonionic surfactant (Tween 80) was evaluated using a combination of batch, column and 2-D box studies. Batch results demonstrated that the addition of 5% and 10% EtOH increased the solubilization capacity of Tween 80 from 0.69 g PCE/g surfactant to 1.09 g PCE/g surfactant. For a 4% Tween 80 solution, this translates into a solubility enhancement of more than 50%, from 26,900 mg/L to 42,300. mg/L. When the surfactant formulations were flushed through soil columns containing residual PCE, effluent concentration data clearly showed that PCE solubilization was rate-limited, regardless of the EtOH concentration. Using analytical solutions to the 1-D ADR equation, effective mass transfer coefficients (Ke) were obtained from the effluent concentration data for both steady-state (A e ) and no flow conditions The addition of EtOH had... 

Looking at the schematic representation of the flow profile within the fiber shown in Fig. 3-39, it becomes apparent that a further sensitivity increase can be accomplished by changing the parabolic flow profile. When the fiber is packed with inert Nafion beads, the translational diffusion of ions is favored over longitudinal diffusion. This, in turn, improves the mass-transfer across the membrane which leads to a further increase in sensitivity, particularly pronounced in the case of orthophosphate as the salt of a weak acid. 

Levich. V. G. (1962) Physicochemical Hydrodynamics (English translation), Prentice-Hall. Englewood Cliffs, NJ, pp. 80-85. This reference contains much information on diffusion in aqueous solutions. Included are derivations of expressions for mass transfer coeflicienis for different flow regimes with thin concentration boundar layers. 

Note that in some problems of heat and mass transfer and chemical hydrodynamics, the velocity fields near the body can be determined by the flow laws of ideal nonviscous fluid. This situation is typical of flows in a porous medium [75, 153, 346] and of interaction between bodies and liquid metals (see Section 4.11, where the solution of heat problem for a translational ideal flow past an elliptical cylinder is given). 

Mass Transfer in Translational Flow at Low Peclet Numbers... 

Mass transfer to a particle in a translational flow, considered in Section 4.4, is a good model for many actual processes in disperse systems in which the velocity of the translational motion of particles relative to fluid plays the main role in convective transfer and the gradient of the nonperturbed velocity field can be neglected. 

Spherical particle as Re —> 0, 0 < Pe < oo. The problem of mass transfer to a solid spherical particle in a translational Stokes flow (Re -f 0) was studied in the entire range of Peclet numbers by finite-difference methods in [1, 60, 281], To find the mean Sherwood number for a spherical particle, it is convenient to use the following approximate formula [94] ... 

The analysis of available experimental data on heat and mass transfer to a solid sphere in a translational flow results in the following correlations [94]. Heat exchange with air at Pr = 0.7 ... 

Spherical drop at high Peclet numbers for Re > 35. For high Re, the fluid velocity distribution in the boundary layer near the drop surface was obtained in [180]. These results were used in [504], where mass transfer to a spherical drop in a translational flow was investigated. The results for the mean Sherwood number are well approximated by the formula [94]... 

Mass Transfer in a Translational-Shear Flow and in a Flow With Parabolic Profile... 

Let us consider mass transfer for a translational flow past a solid spherical particle, where the flow field remote from the particle is the superposition of a translational flow with velocity U and an axisymmetric straining shear flow, the translational flow being directed along the axis of the straining flow. The dimensional fluid velocity components in the Cartesian coordinates relative to the center of the particle have the form... 

Mass Transfer Between Cylinders and Translational or Shear Flow 191... 

Transient Mass Transfer in Steady-State Translational and Shear Flows... 

In the case of nonstationary mass transfer in a steady-state translational Stokes flow past a spherical drop with limiting resistance of the continuous phase, the steady-state value Shst is presented in the first row of Table 4.7. By substituting this value into (4.12.3), we obtain... 

In this chapter, some problems of mass and heat transfer with various complicating factors are discussed. The effect of surface and volume chemical reactions of any order on the convective mass exchange between particles or drops and a translational or shear flow is investigated. Linear and nonlinear nonstationary problems of mass transfer with volume chemical reaction are studied. Universal formulas are given which can be used for estimating the intensity of the mass transfer process for arbitrary kinetics of the surface or volume reaction and various types of flow. 

Flat plate. Let us investigate convective diffusion to the surface of a flat plate in a longitudinal translational flow of a viscous incompressible fluid at high Reynolds numbers. The velocity field of the fluid near a flat plate is presented in Subsection 1.7-2. We assume that mass transfer is accompanied by a surface reaction. 

Mass Transfer to a Flat Plate in a Translational Flow... 

One should realize that these calculations are based on an expression for Vr which corresponds to potential flow past a stationary nonde-formable bubble, as seen by an observer in a stationary reference frame. However, this analysis rigorously requires the radial velocity profile for potential flow in the Uquid phase as a nondeformable bubble rises through an incompressible liquid that is stationary far from the bubble. When submerged objects are in motion, it is important to use liquid-phase velocity components that are referenced to the motion of the interface for boundary layer mass transfer analysis. This is accomplished best by solving the flow problem in a body-fixed reference frame which translates and, if necessary, rotates with the bubble such that the center of the bubble and the origin of the coordinate system are coincident. Now the problem is equivalent to one where an ideal fluid impinges on a stationary nondeformable gas bubble of radius R. As illustrated above, results for the latter problem have been employed to estimate the maximum error associated with the neglect of curvature in the radial term of the equation of continuity. 

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