Flow pattern, contacting dynamic solids

Petrov and Petrov (1998) developed a molecular hydrodynamic theory of film deposition during removal. Their theory correctly assumes a flow pattern - which we identified as a split streamline - between the solid substrate and the monolayer in Figure 10.5 (c). This pattern is indeed the necessary pattern for successful deposition during removal, but it is not the only flow pattern for solid removal at all dynamic contact angles. Petrov and Petrov (1998) address the kinetics of water removal between the solid and the monolayer and the formation of wet or dry monolayers depending on the amount of water entrained. 

Region IV is the window of operation for successful deposition of Y-type films. The flow pattern in this region is typical during removal of solids with dynamic contact angles 0 < < 90°. The split-ejection streamline is in the liquid phase and the interface... 

For very small dynamic contact angles, the liquid is not completely removed by the split streamline and it is entrained between the film and the solid surface, creating what is known as a wet LB film. Water trapped between the solid surface and the LB monolayer prevents adhesion and is a leading cause of monolayer instability. Petrov etal. (1980) sketched the flow pattern near the moving contact line. The flow pattern is the one described here for region IV. The authors, however, reference Huh and Scriven (1971)... 

The Gibbs elasticity characterizes the lateral fluidity of the surfactant adsorption monolayer. For high values of the Gibbs elasticity the adsorption monolayer at a fluid interface behaves as tangentially immobile. Then, if two oil drops approach each other, the hydro-dynamic flow pattern, and the hydrodynamic interaction as well, is the same as if the drops were solid particles, with the only differenee that under some conditions they could deform in the zone of contact. For lower values of the Gibbs elastieity the... 

Most of the fluid dynamic studies of gas-flowing solids-fixed bed contactors were devoted to countercurrent flow systems, because of the higher efficiency of countercurrent operations for most of the processes when compared with cocurrent operations. However, there is an upper limit for gas flow rate in countercurrent systems, due to flooding. Hence, the cocurrent operation system is an interesting alternative for higher gas flow rates, particularly for very small particles. Further, in some of the proposed applications, cocurrent contacting is a desirable flow pattern [22]. 

Extrapolating continuous description of fluid motion to a molecular scale might be conceptually difficult but unavoidable as far as interfacial dynamics is concerned. Long-range intermolec-ular interactions, such as London-van der Waals forces, still operate on a mesoscopic scale where continuous theory is justified, but they should be bounded by an inner cut-off d of atomic dimensions. Thus, distinguishing the first molecular layer from the bulk fluid becomes necessary even in equilibrium theory. In dynamic theory, the transport in the first molecular layer can be described by Eq. (60), whereas the bulk fluid obeys hydrodynamic equations supplemented by the action of intermolecular forces. Equation (61) serves then as the boundary condition at the solid surface. Moreover, at the contact line, where the bulk fluid layer either terminates altogether or gives way to a monomolecular precursor film, the same slip condition defines the slip component of the flow pattern. 

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