Region internal wake

In the internal wake region W(2), one can neglect molecular mass transfer in the radial direction. 

Internal flows arc dominated by the influence of viscosity throughout the flow field. In external flows the viscous effects are limited to boundary layers near solid surfaces and to wake regions downstream of bodies. 

The performance equation for the model is obtained from the continuity (material-balanoe) equations for A over the three main regions (bubble, cloud + wake, and emulsion), as illustrated schematically in Figure 23.7. Since the bed is isothermal, we need use only the continuity equation, which is then uncoupled from the energy equation. The latter is required only to establish the heat transfer aspects (internally and externally) to achieve the desired value of T. 

Flow separation in the case of a drop is delayed compared with the case of a solid particle, and the vorticity region (wake) is considerably narrower. While in the case of a solid sphere, the flow separates and the rear wake occurs at Re 10 (the number Re is determined by the sphere radius), in the case of a drop there may be no separation until Re = 50. For 1 < Re < 50, numerical methods are widely used. The results of numerical calculations are discussed in [94], For these Reynolds numbers, the internal circulation is more intensive than is predicted by the Hadamard-Rybczynski solution. The velocity at the drop boundary increases rapidly with the Reynolds number even for highly viscous drops, In the limit case of small viscosity of the disperse phase, /3 —> 0 (this corresponds to the case of a gas bubble), one can use the approximation of ideal fluid for the outer flow at Re > 1. 

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