Renewal frequency

Both the mass transfer kinetic parameters (diffusion in the phases, D, D j, surface renewal frequency, s) and chemical reaction rate constants (kg, kj) strongly influence enhancement of the absorption rate. The particle size, dp, the dispersed liquid holdup, e and the partition coefficient, H can also strongly alter the absorption rate [42-44,46,48]. Similarly, the distance of the first particle from the gas-liquid interface, 6q is an essential factor. Because the diffusion conditions are much better in the dispersed phase (larger solubility and, in most cases, larger diffusivity, as well) the absorption rate should increase with the decrease of the (5g value. 

Considering that the renewal frequency A 1 is given by the renewal frequency of the bubbles in a given point in the vicinity of the wall, one can write... 

The main result obtained by Danckwerts, especially when absorption is accompanied by a chemical reaction, was a clear separation of the physicochemical parameters from the hydrodynamic ones. No explicit expressions have been, however, proposed for the renewal frequency s. While this problem will be examined later, for the moment various questions that can be raised concerning the two basic assumptions will be emphasized. 

In contrast to Section IV,M, where the turbulent diffusivity was employed to derive an expression for the mass transfer coefficient, in this section expression (401), which is based on a physical model, constitutes the starting point. Concerning the renewal frequency s, the following dimensional considerations can lead to useful expressions. The state of turbulence near the interface can be characterized by a characteristic velocity ua = (gSf)i/2, the dynamic viscosity rj, the surface tension a, and the density p. Therefore... 

Smaller bubbles and higher gas-liquid interface renewal frequency are beneficial to improving mass transfer. 

Intensified turbulence can destroy the stability of large bubbles, which leads to smaller bubbles, and increase the frequency of bubble coalescence and breakup, which improves the surface renewal frequency of bubbles [17,18]. Intensified turbulence can be achieved by changing the gas sparger to decrease the initial bubble size and improve its radial distribution, but the effective region of the gas sparger is only limited to a certain height above the distributor [19]. 

Mass transfer is essential in EL-ALRs. Smaller bubbles and a uniform gas holdup radial distribution increase the interfacial area and improve mass transfer. Intensified turbulence increases the surface renewal frequency and decreases bubble size. A novel internal to improve mass transfer and the hydrodynamic behavior in a gas-liquid system is reported. Experiments were carried out to study the effect of the internal on the bubble behavior and liquid velocity in an EL-ALR. 

F, and the volume of the contacting solution, V, i.e., the leachant renewal frequency ... 

Figure 2 shows the predicted, normalized cumulative mass losses based on the behaviors of silicon and sodium for three different values of the leachant renewal frequency. The physical parameters used refer to the leaching of PNL 76 68 borosilicate glass in deionized water at 90°C, (4) and reference is made to the geometric surface area, SA, of the sample. In particular, the curves corresponding to silicon and sodium tend to have the same, constant slope with increasing flow rate. In particular, the curves corresponding to = 1 day 1 practically coincide, indicative of network dissolution control. 

Figure 3 shows the predicted behavior of the pH of the solution as a function of leachant renewal frequency for the same system parameters. As can be seen, the higher the flow rate, the sooner steady state is achieved, and the closer the leachant composition to that of the original solution. In particular, the pH curve for the static case ( = 0) shows that the solution pH has not reached steady state yet after 28-days leaching. Approach to steady state under the static leaching conditions can be a very lengthy process. However, an equilibrium pH value can be estimated by use of the solution electroneutrality condition as applied to the reactions modeled. Indeed, at all times ... 

Equation (7) shows that the local heat transfer coefficient is a function of the thickness and the renewal frequency of the cluster layer. If the gas-solids flow is fully developed and rb dp, Eq. (7) can be simplified to... 

The renewal frequency of the cluster layer at the heat transfer surface is mainly dependent on the solids exchange rate between the layer and the other suspension, and usually assumed to be proportional to the ratio of the characteristic velocity to the characteristic length. Here we define... 

The calculation of k using Eqs. 9.2.11 and 9.2.12 requires a priori estimation of the exposure time or the surface renewal rate s. In some cases this is possible. For bubbles rising in a liquid the exposure time is the time the bubble takes to rise its own diameter. In other words, the jacket of the bubble is renewed every time it moves a diameter. If we consider the flow of a liquid over a packing, when the liquid film is mixed at the junction between the packing elements, then is the time for the liquid to flow over a packing element. For flow of liquid in laminar jets and in thin films, the exposure time is known but in these cases it may be important to take into account the distribution of velocities along the interface. In the penetration model, this velocity profile is assumed to be flat (i.e., plug flow). For gas-liquid mass transfer in stirred vessels, the renewal frequency in the Danckwerts model s may be related to the speed of rotation (see Sherwood et al. 1975). 

The contactor is a stirred cell and was depicted in Figure 5.9. The stirrer is rotated at such a speed that the surface renewal frequency of the phase under consideration is... 

This is the value used by Krishna (1981a) in his simulations of Modine s experiments. This value is consistent with a penetration model of mass transfer in the liquid phase with a contact time of 0.065 s or a surface renewal frequency of 0.25 s The molar density of the liquid phase has been estimated as... 

Mass transfer rate equation Surface renewal frequency [s ]... 

Measurements of heat transfer in circulating fluidized beds require use of very small heat transfer probes in order to reduce the interference to the flow field. The dimensions of the heat transfer surface may significantly affect the heat transfer coefficient at any radial position in the riser. All the treatment of circulating fluidized bed heat transfer described above is based on a small dimension for the heat transfer surface. The heat transfer coefficient decreases asymptotically with an increase in the vertical dimension of the heat transfer surface [81]. It can be stated that the large dimensions of the heat transfer surface can prolong the residence time of particles or particle clusters on the surface, resulting in lower renewal frequency and hence a low apparent heat transfer coefficient. 

As the renewal frequency of bubbles is already fairly large in a turbulent fluidized bed, introducing internals into such a bed is mainly not for breaking bubbles,... 

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