Solid-liquid mass transfer slip velocity

Solid-Liquid Mass Transfer There is potentially a major effect of both shear rate and circulation time in these processes. The sohds can either be fragile or rugged. We are looking at the slip velocity of the particle and also whether we can break up agglomerates of particles which may enhance the mass transfer. When the particles become small enough, they tend to follow the flow pattern, so the slip velocity necessary to affect the mass transfer becomes less and less available. 

R. P. Fishwick, J.M. Winterbottom, E.H. Stitt, "Effect of gassing rate on solid-liquid mass transfer coefficients and particle slip velocities in stirred tank reactors", Chem. Eng. Sci., 2003, 58, 1087-1093. 

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. 

Also, data on particle-liquid mass transfer from suspended solids in gas-liquid mechanically agitated vessels are practically nonexistent (R18). However, many studies have been published on mass-transfer experiments in the absence of gas, which give an idea of the magnitude of k. Recent reviews by Nienow (N9) and Blasinski and Pyc (B17, B18) indicate two fundamentally different approaches to the prediction of A s the Kol-mogoroff theory, which implies equal at equal power input per unit volume (B17) and the terminal velocity-slip velocity theory which relates ks to the value that would apply if the solid particle moved at its terminal velocity (H2). As explained by Nienow (N9), the resulting values of A s are approximately the same. Use may be made of the graphical correlation given by Brian et al. (B29). 

Solid/llquid mass transfer in both sparged vessels and stirred vessels can be successfully described with the energy input concept. Direct relation with fluid-particle slip velocities could reveal influence of geometrical factors not covered by the energy input concept. Probably, in stirred vessels the influence of the gas phase can not be completely accounted for by the total energy input/m liquid concept. However, data on this aspect are relatively scarce and more work is needed to clarify this aspect. 

What this shows is that, from the definition of off-bottom motion to complete uniformity, the effect of mixer power is much less than from going to on-bottom motion to off-bottom suspension. The initial increase in power causes more and more solids to be in active communication with the liquid and has a much greater mass-transfer rate than that occurring above the power level for off-bottom suspension, in which slip velocity between the particles of fluid is the major contributor (Fig. 18-23). 

Yashitome et al.148 studied the mass transfer from single samples of benzoic acid suspended in an air-water bubble-column. Spherical, cylindrical, and diskshaped samples were used. The diameters of the particles (ranging from 25 through 75 mm) were considerably larger than the catalyst sizes normally used in gas-liquid-solid catalytic slurry operation. The data were correlated using the slip velocity theory. 

As outlined above, steady-state theories for the liquid-solid mass transfer are largely classified into two categories i.e., those based on Kolmogoroff s theory and those based on the terminal velocity-slip velocity approach. 

The model based on terminal and slip velocity approach is rather tenuous. It breaks down as the density difference between liquid and solid approaches zero. Under highly turbulent conditions, an accurate estimation of slip velocity is rather difficult, and there is disagreement on whether or not the relative velocity between the solid and liquid alone is enough to obtain an accurate estimate of the mass-transfer coefficient. 

The just-suspended state is defined as the condition where no particle remains on the bottom of the vessel (or upper surface of the liquid) for longer than 1 to 2 s. At just-suspended conditions, all solids are in motion, but their concentration in the vessel is not uniform. There is no solid buildup in comers or behind baffles. This condition is ideal for many mass- and heat-transfer operations, including chemical reactions and dissolution of solids. At jnst-snspended conditions, the slip velocity is high, and this leads to good mass/heat-transfer rates. The precise definition of the just-suspended condition coupled with the ability to observe movement using glass or transparent tank bottoms has enabled consistent data to be collected. These data have helped with the development of reliable, semi-empirical models for predicting the just-suspended speed. Complete suspension refers to nearly complete nniformity. Power requirement for the just-suspended condition is mnch lower than for complete snspension. 

How then does this influence the flow of catalyst particles in the vessel and the liquid -solid mass transfer Figure 2c shows the particle velocities, for a particle density of 1,500 kg/m under identical conditions to Figure 2b. By subtraction of the temporally averaged liquid and particle velocities, the spatially resolved slip velocities can be obtained. Figure 3. This shows that the relative velocity of the liquid and particle (and hence the mass transfer) also varies considerably over the vessel, with the highest values confined to the impeller discharge region. 

Unlike creeping flow about a solid sphere, the r9 component of the rate-of-strain tensor vanishes at the gas-liquid interface, as expected for zero shear, but the simple velocity gradient (dvg/dr)r R is not zero. The fluid dynamics boundary conditions require that [(Sy/dt)rg]r=R = 0- The leading term in the polynomial expansion for vg, given by (11-126), is most important for flow around a bubble, but this term vanishes for a no-slip interface when the solid sphere is stationary. For creeping flow around a gas bubble, the tangential velocity component within the mass transfer boundary layer is approximated as... 

However, the gas undergoes a solid-body-like rotation and the slip velocity between liquid and gas is in the same range as in a conventional packed bed. Hence, for the cases in which the controlling resistance is on the gas side, the expected size reduction is only about 5-8 times, which is due to the high specific area of the packing. In most distillation columns, the dominant resistance is on the vapor side. To enhance the slip velocity and hence the gas-side mass-transfer coefficient, a rotor with split packing was proposed by Chandra et al. [5]. Its brief description is given below. 

Concerning the liguid/solid mass transfer coefficient ks, two different theories have been used to correlate data from so-lid/liquid suspensions one uses the terminal slip velocity between particles and the liquid. The other approach is based on Kolmogoroff s theory of isotropic turbulence and uses energy dissipation rate C= Go8 correlation. Sanger [30] recommend the equation... 

Fig 6. Slip velocity correlation for the liquid-solid mass-transfer coefficient. 

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