The Minimum Speed for Film Deposition

and Petrov, J. have established that the threshold speed is independent of the capillary diameter and increases with contact angle according to the law 

If there is hysteresis, e must be replaced by the receding angle In total wetting conditions ( e = 0), Kn = 0 and a film is invariably deposited. 

The threshold speed for depositing a film on a plane surface, a fibre, or inside a capillary can be deduced directly from the law of motion of the contact line in partial wetting conditions, as illustrated in Fig. 1.21  

V 6) is zero for 6 = 6e (contact line at rest), but also for 9 = 0, since the frictional force becomes infinite. Between these two values, there thus exists a minimum speed given by dV/d9 = 0, which implies 

When V Vja, there exists a dynamical contact angle and a meniscus (see Fig. 1.22a). When V macroscopic film is drawn along by the plate, or left behind the droplet in the capillary tube (see Fig. 1.22b). 

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