Mass transfer transitional flow

Let us begin with the system of mass transfer for flow in a conduit Figure 11-2 illustrates the correlation for heat and mass transfer. Note that the additional parameter as L/D is used in the regimes of laminar and transition flow. Also note that the heat and mass transfer can be described by one correlation at high Reynolds numbers (i.e., 5000 or more). This means that the turbulent mass transfer Nusselt number (by analogy) to equation (6-21) is... 

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In turbulent flow, the edge effect due to the shape of the support rod is quite significant as shown in Fig. 6. The data obtained with a support rod of equal radius agree with the theoretical prediction of Eq. (52). The point of transition with this geometry occurs at Re = 40000. However, the use of a larger radius support rod arbitrarily introduces an outflowing radial stream at the equator. The radial stream reduces the stability of the boundary layer, and the transition from laminar to turbulent flow occurs earlier at Re = 15000. Thus, the turbulent mass transfer data with the larger radius support rod deviate considerably from the theoretical prediction of Eq. (52) a least square fit of the data results in a 0.092 Re0 67 dependence for... 

Table IV includes theoretical transition times (C2, R14, SI7c) in laminar flow between parallel plates, following a concentration step at the wall (Leveque mass transfer). Clearly, in laminar flow (Re 100 or lower), transition times are comparable to those in laminar free convection. Here, however, the dependence on concentration (through the diffusivity) is weak. The dimensionless time variable in unsteady-state mass transfer of the Leveque type is...

Overall mass-transfer rates at a sphere in forced flow, and mass-transfer rate distribution over a sphere as a function of the polar angle have been measured by Gibert, Angelino, and co-workers (G2, G4a) for a wide range of Reynolds numbers. The overall rate dependence on Re exhibited two distinct regimes with a sharp transition at Re = 1250. Local mass-transfer rates were deduced from measurements in which the sphere was progressively coated by an insulator, starting from the rear. 

It is generally agreed that mass transfer coefficients are only correlated for negligibly small convectional motion of the transitional component, which is vertical to the interface. However, when the mass transfer is mutual and equimolar, no such convections normal to the interface result otherwise the transfer coefficient and the driving force must be corrected with the aid of theories of mass transfer [18]. The transitional rates and, accordingly, convectional flow rates normal to the interface are only low for the extraction process, so that the uncorrected Eq. (9.31) may be used. 

For simplicity, this section discusses only the mass transfer of one component in a liquid-liquid system with negligible miscibility of both liquids and with one transitional component. On the other hand, calculations must consider mass transfer rates of several components and more or less strong variation in the mass flows along the column, where both complicate the equation considerably [21-23]. Chemical reactions may cause further complications. Their kinetics can enhance the mass transfer coefficients and, therefore, the reaction equations have to be part of the mathematical model of the extractor [24,25]. 

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