Evaporation dimensionless groups

Figure 4.19 illustrates the effect of liquid phase mass transfer, represented by the dimensionless group Kuq (see Eqs. (55) and (57)). If the evaporation velocity is in the same order of magnitude as the liquid phase mass transfer coefficient, then the selectivity of the evaporation process vanishes though the relative volatility as well as the gas phase mass transfer coefficients remain unchanged. 

Mixers. See also Agitation blend time, 290 dimensionless groups, 290 gas dispersion, 296-301 in line type, 300,301 liquids, power and speed need, 293,295 powders and pastes, 301,303,304 power number, 290-292 quality characterization, 290-292 suspension of solids, 295-299 tank desien. 287.288 Moisture c tent, critical, 237 Molecular distillation, 425-427 equipment sketches, 427 Hickman still, 427 operating conditions, rate of evaporation. 

This relation is analogous to the expression for the heat transfer by forced convection given earlier. The dimensionless group kd/D corresponds to the Nusselt group in heat transfer. The parameter rj/pD is known as the Schmidt number and is the mass-transfer counterpart of the Prandtl number. For example, the evaporation of a thin liquid film at the wall of a pipe into a turbulent gas is described by the equation... 

Wilhelm Nusselt (1882-1957) was nominated Professor of Theoretical Mechanical Engineering at the Technische Hochschule, Karlsruhe in 1920. Between 1925 and 1952 he taught at the Technische Hochschule, Munich. In 1915 he published his fundamental work The Fundamental Laws of Heat Transfer , in which he introduced dimensionless groups for the first time. Further important investigations included heat transfer in film condensation, cross current heat transfer and the analogy between heat and mass transfer in evaporation. 

Predicted Deformation Mechanisms. Recent work has developed maps of the deformation mechanisms expected in films with different properties. Two dimensionless groups were found to determine which of the deformation mechanism occurs. The first is the time for particle deformation compared to the time for evaporation, captured in 1 = ERt]o/yH, where E is the evaporation rate, t]o is the polymer viscosity, and y is the water-air surface tension. The second dimensionless group is the Peclet number, which determines the vertical homogeneity in the film, Pe = 6nt] R H E/kT. The deformation regimes are shown in Fig. 9. 

In the 1904 edition there is, for example, a sample calculation of the heat balance on a Glover tower treated as an evaporator, which shows how inefficient it was then ( what a heat waster it is (23)), There is also a discussion on the efficiency of various packings, explaining in terms of surface areas why coke is 1.5 to 2 times more efiBcient than bricks (23, 26), But in general, Davis approach was still empirical the operations are described as procedures of practical utility, and are not based on fundamental physics. Neither the work of Osborne Reynolds nor dimensionless group theory had been assimilated yet into the profession. 

Within the bubble boiling regime, thermal induced disintegration occurs when the vapor pressure unbalances the equilibrium between surface tension, viscous forces and inertial forces. The nature of this mechanism is different from those observed onto cold surfaces, as it is triggered by combined effects induced by the liquid surface tensirm and the latent heat of evaporation, /ifg, and the analysis requires the use of dimensionless groups complementary to those in Table 8.1. The most important is the Jakob number, defined as/a = Cp(Tw — 7 sat)//tfg where Cp is the specific heat of the liquid. 

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