Liquid film region

Figure 8.13 Conceptual concentration profiles and particle distribution in the liquid film region (Wachi and Jones, 199 la)...

Similar to the two previous cases (see Sections 9.5.2 and 9.5.3), the problem is solved numerically, whereas the liquid film region is discretized in a spatially uniform grid. The process is considered as an isothermal operation, assuming plug flow of both phases and constant flow rate values of both gas and liquid phases due to low solute concentrations [70]. In the bulk liquid, reaction equilibrium condition is used as a boundary condition for the film region. In order to describe film diffusion, the simple Fick s law is applied. 

Liquid-Film Region. The single-phase flow and heat transfer in this region can be described by the continuity equation, the momentum equation in Eqs. 9.76 and 9.77, and the energy equation (Eq. 9.80). We deal only with the volume-averaged velocities, such as (ue) = U(, therefore, we drop the averaging symbol from the superficial (or Darcean) velocities. For the two-dimensional steady-state boundary-layer flow and heat transfer, we have (the coordinates are those shown in Fig. 9.18) the following ... 

The convection heat transfer in the liquid-film region is generally negligible [113], therefore, Eq. 9.95 can be written as... 

In Figure 5.3.2, we observe two distinct regions in the liquid film region I, where there is no C due to instantaneous reaction of H2S, and region II, where C reacts only with CO2 species A (species B, H2S, being nonexistent). The governing diffusion equations in region... 

Region I, P > 2. Reaction is fast and occurs mainly in the liquid film so C L 0- The rate of reaction = kj aEC i will be large when a is large, but hquid holdup is not important. Packed towers or stirred tanks will be suitable. 

Figure 8.14 Predicted (a) concentration profiles in the film region, and (h) mean particle sizes during gas-liquid precipitation of CaC03 (Wachi and Jones, 1991a). Ga.s-liquid precipitation cell...

The general features of two-dimensional flow with evaporating liquid-vapor meniscus in a capillary slot were studied by Khrustalev and Faghri (1996). Following this work we present the main results mentioned in their research. The model of flow in a narrow slot is presented in Fig. 10.16. Within a capillary slot two characteristic regions can be selected, where two-dimensional or quasi-one-dimensional flow occurs. Two-dimensional flow is realized in the major part of the liquid domain, whereas the quasi-one-dimensional flow is observed in the micro-film region, located near the wall. 

The relationship of isoviscosity calculated by Eq (5) and a distance apart from the solid surface is shown in Fig. 7. For different kinds of solid materials with different surface energy, the isoviscosity becomes very large as the film thickness becomes thinner. It increases about several to more than ten times that of bulk fluid when it is close to the solid surface. In the thick film region, the isoviscosity remains a constant, which is approximately equal to the dynamic viscosity of bulk liquid. Therefore, the isoviscosity of lubricant smoothly... 

Fig. 48 —Interference patterns of the film of glycerin under a load of 4 N. The film thickness in the central region was 10 nm, 105 nm in the first dark ring, and about 315 nm in the second dark ring, (a) External voltage was 0 V, which means no EEF was applied to the liquid film, (b)-(f) The external voltage was kept constant (6 V) for a time of "t," and (b) f=0 s, (c) t=0.5 s, (d) t=1.0 s, (e) t=5.0 s, (f) t=100 s.

Fig. 55—Temperature calculation for different liquid films (glycerin and hexadecane) at different locations in the contact region Area A is the central area in the inset photo and area B is the edge area. The filled histogram represents the positive EEF intensity of 518.6 kV/cm, and the empty one of 667.7 V/cm. The solid (glycerin) and dotted (hexadecane) lines are variation curves of the boiling point along the radial direction in the contact region.

Film Boiling and Heat Transfer in Liquid-Deficient Regions 274... 

Brown (1967) noted that a vapor bubble in a temperature gradient is subjected to a variation of surface tension which tends to move the interfacial liquid film. This motion, in turn, drags with it adjacent warm liquid so as to produce a net flow around the bubble from the hot to the cold region, which is released as a jet in the wake of the bubble (Fig. 4.10). Brown suggested that this mechanism, called thermocapillarity, can transfer a considerable fraction of the heat flux, and it appears to explain a number of observations about the bubble boundary layer, including the fact that the mean temperature in the boundary layer is lower than saturation (Jiji and Clark, 1964). 

FILM BOILING AND HEAT TRANSFER IN LIQUID-DEFICIENT REGIONS... 

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