Coating flow dynamics

In the simplest case the stationary film thickness is a function of the withdrawal speed Vyj, the dynamic viscosity ri, specific gravity pg and the surface tension y. So, 

To express these five variables only three fundamental units are needed. According to Buckingham s it theorem these variables can be combined in 5-3 = 2 dimensionless parameters (see for example Ref. [61]) as follows 

At high withdrawal speed Ca 1) the coating film is independent from the nature of the static meniscus, hence 

Derjaguin showed the constant to be unity. For an arbitrary withdrawal speed expression (6.46) can be rewritten [62] as 

The function f can be obtained by a detailed analysis of the fluid dynamics of the coating flow. 

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Chemical vapor deposition is a very complex process. There are numerous factors such as type, shape, and size of reactor, gas flow rate and arrangement that can affect the properties of the coating. Therefore, it is necessary to review briefly the process itself which includes reactor, reaction zones, temperature, pressure, precursors, and gas flow dynamics before discussing the thermodynamics and kinetics of the CVD. 

Many attempts have been made to obtain (semi-)analytical descriptions for non-Newtonian coating flows. These are necessarily approximate and the approximations made to obtain tractable mathematics are sometimes non-physical [58]. These models do not predict the coating behaviour very well from the rheological parameters. The thickness is usually considerably overestimated. It seems more advantageous to simulate non-Newtonian coating flows by computational fluid dynamic methods (see also Ref. [58]). 

The force driving the coating flow is usually gravity and/or an externally applied pressure. One boundary surface of the liquid layer is its interface with the supporting fluid, the other a fluid interface. If the ambient fluid is a dynamically passive gas, the film has a free surface as it flows down inclined planes. Coating flows are free-surface flows and as such are difficult be solved mathematically. The free surface is an integral part of the solution. In the solution scheme, it must be guessed... 

Physics mathematics engineering chemistry suspension mechanics hydrodynamics computational fluid dynamics microfluidic systems coating flows multiphase flows viscous flows. 

FIGURE 5. Adhesion of BL6 cells to mouse ECs is based on interaction of GM3 (expressed on BL6 cells) with Gg3 or LacCer (expressed on ECs). (A, B) Laminar flow dynamic adhesion system. Wall shear stress was calculated as described by Lawrence et al. (1990). One of the parallel plates was coated with Gg3-liposome, LacCer-liposome, FN, or laminin (LN), and BL6 cells suspended in medium were passed through the laminar flow chamber. See Kojima etal. (1992c) for experimental details. Adhesion based on Gg3 or LacCer predominated over that based on FN or LN, regardless of shear stress. (C) Static adhesion system. FN- or LN-dependent adhesion became obvious only after 30 min of incubation. In contrast, Gg3- or LacCer-dependent adhesion were obvious at 20 min. These results suggest that there is a longer lag time for integrin-based cell adhesion compared to adhesion based on carbohydrate-carbohydrate interaction, in a static system. 

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