Rupture of Ultra-Viscous Films

We consider films that arc cither suspended in air or depo.sited on a low-viscosity substrate. The only difference between these two situations is the nature of the driving force Fa/ responsible for opening up the hole. Fm = 27 for a suspended film, whereas Fm = S for a film on a liquid substrate, the only purpost of which is to control the wettability and to provide an opportunity to create thicker films. 

W herc V = i/v- The velocity V is quite small ( 20 iin/s). but the factor R/c itself can become oxtr(uncly large for very thin films (/ = 1 cm aiul 0=1 pm gives R/c = lO ). 

These three results are entirely consistent with one another. Radial velocities indeed do lead to a uniform thickness. From the velocity field expressed in equation (7.61), we can calculate the energy dissipation. In a cylindrical coordinate system, we get 

Yet another hydrodynamic model of the bursting of a purely viscous film leads to a similar exponential growth, although for long times the velocity keeps on increasing up to the limit of inertial bursting V — 2 y jpe beyond 

In general, foams may appear even in the absence of surfactants when we inject air in a liquid paste. They play an important role in various areas of organic and mineral chemistry. To better understand them, we proceed next to examine viscous bubbles. 

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