Mass transfer terminal velocities, effect

The surface viscosity effect on terminal velocity results in a calculated drag curve that is closer to the one for rigid spheres (K5). The deep dip exhibited by the drag curve for drops in pure liquid fields is replaced by a smooth transition without a deep valley. The damping of internal circulation reduces the rate of mass transfer. Even a few parts per million of the surfactant are sometimes sufficient to cause a very radical change. 

The role of normal impurities in liquid-liquid systems in the light of surfactants should be clarified and made quantitative. A goal worth attaining would consist of setting up equations which, with use of experimentally determined constants, would permit accurate prediction of terminal velocity, amplitude and frequency of oscillations, and their combined effect on mass transfer. 

Here Kjj is obtained from Fig. 9.5. Equation (9-27) and the equations of Chapter 5 can be used to determine the decrease in Sh for a rigid sphere with fixed settling on the axis of a cylindrical tube. For example, for a settling sphere with 2 = 0.4 and = 200, Uj/Uj = 0.76 and UJUj = 0.85. Since the Sherwood number is roughly proportional to the square root of Re, the Sherwood number for the settling particle is reduced only 8%, while its terminal velocity is reduced 24%. As in creeping flow, the effect of container walls on mass and heat transfer is much smaller than on terminal velocity. 

MASS TRANSFER TO SUSPENDED PARTICLES. When solid particles are suspended in an agitated liquid, as in a stirred tank, a minimum estimate of the transfer coefficient can be obtained by using the terminal velocity of the particle in still liquid to calculate in Eq. (21.59). The effect of particle size and density difference on this minimum coefficient is shown in Fig. 21.6. Over a wide range of sizes, there is little change in the coefficient, because the increase in terminal velocity and Reynolds number makes the Sherwood number nearly proportional to particle diameter. 

The performance of these reactors is greatly influenced by (1) axial, radial, and global distribution of liquid and solids in the bed and (2) changes in bubble size, velocity, breakup, and coalescence. The second set of factors leads to an enhancement in the rates of heat and mass transfer. This happens because each particle (assumed to be spherical) is surrounded by a gas-liquid mixture of low pseudohomogheneous density. Consequently, the particle terminal velocity increases, which in turn has a positive effect on the mass transfer coefficient. A number of papers have been published (e.g., Arters and Fan, 1986, 1990 Fan, 1989 Nikov and Delmas, 1992 Boskovic et al., 1994 Kikuchi et al., 1995) on mass transfer in these reactors. 

The Kolmogoroff theory can account for the increase in mass transfer rate with increasing system turbulence and power input, but it does not take into consideration the important effects of the system physical properties. The weakness of the slip velocity theory is the fact that the relationship between terminal velocity and the actual slip velocity in a turbulent system is really unknown. Nevertheless, on balance, the slip velocity theory appears to be the more successful for solid-liquid mass transfer in agitated vessels. 

During injection, the effectiveness of the spray against elemental iodine vapor is chiefly determined by the rate at which fresh solution surface area is introduced into the containment building atmosphere. The rate of solution surface created per unit gas volume in the containment atmosphere may be estimated as (6F/VD), where F is the volume flow rate of the spray pump, V is the containment building net free volume, and D is the mass-mean diameter of the spray drops. The first-order removal coefficient by spray, A., may be taken to he = 6 T FfV D, where A g is the gas-phase mass-transfer coefficient, and T is the time of fall of the drops, which may be estimated by the ratio of the average fall height to the terminal velocity of the mass-mean drop (Reference...). 

Usually nozzles can be selected that give a certain average drop size. When this is known, the mass transfer rate can be calculated relatively easily. With eqs. (4.40) and (4.41) the terminal velocity can be calculated (assuming the drops are rigid spheres), so that the contact time can be estimated. The mass transfer within the drops can be described in terms of non-steady state diffusion. When contact times are relatively short, which they normally are, the effect of non-steady state diffusion can be expressed as a mass transfer coefficient, that is time dependent ... 

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