Inertial Dewetting

Wc now consider the case of dewetting at high velocity, when the dynamics is controlled by the rate at which surface energy is being converted to kinetic energy of the liquid, 

As it happens, the simplest material combination available for studying the inertial regime is water on highly hydrophobic surfaces, in which case dewetting can proceed at ultra-fast rates, with velocities approaching 10 

FIGURE 7.13. Inertial dewetting on hydrophobic glass. Ripples are emitted around the hole. (From F. Brochard, E. Raphel, and L. Vbvelle, in Comptes Rendus de VAcademie des Sciences, 321, p. 367 (1995) Reproduced by permission.) 

Andrieu was the first to examine the dewetting of water on plastic. One conclusion of this study was that, upon decreasing the thickness e, the velocity diverges as 1/y/e instead of approaching a limiting value independent of e as would happen in a viscous regime. 

Buguin conducted the first quantitative study of the dewetting of water on highly hydrophobic silanized glass. ° With the help of a very simple optical setup, he was able to follow the time evolution of the profile of a water film. He identified several distinct regimes, which we proceed to describe in the next section. 

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In the intermediate case (ii) corresponding to classic dewetting on a solid substrate (Poiseuille flow), we find that viscous dissipation generally predominates. In contrast, for low-viscosity liquids, such as water, dewetting very hydrophobic surfaces (large angles 6 ), rapid inertial dewetting can be achieved... 

Two dimensionless numbers play a key role in inertial dewetting phenomena ... 

The previous discussion can be extended to the case of a liquid film on a liquid substrate. X. Noblin has studied the inertial dewetting of a film of water deposited on carbon tetrachloride, which is a highly hydrophobic surface, as evidenced by the large thickness of the puddles Cc = 7 mm. " The dewetting velocity is extremely high, of the order of a m/s for thin films. Since a liquid substrate constitutes an ideal surface, one can create much thinner metastable films than is possible on a solid and, therefore, attain larger velocities. Under such conditions, Culick s law is perfectly verified. 

FIGURE 7.17. Inertial dewetting of water floating on a pool of carbon tetrachloride (CCI4) for three different thicknesses. Left picture e = 0.73 mm, with no ripples and no shock middle picture e = 0.61 mm, with ripples toward center and shock waves directed downstream right picture e = 0.43 mm, with ripples toward the center and the outside, shock waves upstream and downstream (courtesy X. Noblin). 

When i e 1, dewetting is viscous and we then have Fm = Fy. This limit corresponds to the analysis in section 7.2 where we have neglected the inertial term d MV)/dt. When > 1, dewetting is inertial and Fy is negligible. The second term in equation (7.48) no longer depends on V. The ridge of mass M(t) = peR advances at a constant velocity V that is the solution of equation (7.48). That velocity is... 

Using the laser beam deflection technique, A. Buguin was able to measure the film s profile during the dewetting process (Figure 7.16) in the inertial regime Re 1), both in the presence and in the absence of shock waves. 

In summary, Culick s law V = / Sd /ep accurately describes dewetting in the inertial regime, but the dynamical spreading parameter Sd is less than the value 5 measured under static conditions. When V > which corresponds to > 1, a shock wave is observed with the telltale appearance of capillary waves moving in phase with the liquid front, which itself advances at a velocity Vp on a film at rest Vp = c). 

Redon and coworkers were the first to study the dewetting process of macroscopic films deposited on planar and horizontal surfaces. They used different alkanes and poly (dimethylsiloxane) (PDMS) on sUanized silicon wafers. In all their studies, inertial effects were negligible against viscous ones. The film is extended on a circular surface and fixed in a perimetral wetting ring. Dewetting is initiated by producing a hole at the center of the film with a jet of ait. 

When dewetting occurs at velocities so high that inertial effects cannot be neglected, viscous effects are negligible and a simple analysis on the balance of capillary and inertial forces gives the relation between the dewetting velocity and the film thickness ... 

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