Dynamics of Wetting

Viscous-gravity spreading of time-varying liquid drop volumes on solid surfaces

“…In contrast, in the derivation of de Gennes [3], the slope at the common line is assumed small, and the power exponent in the rate of viscous dissipation per unit contact area is found to vary as (x 0 − x) −1 (instead of (x 0 − x) −1/3 ) with the improper integral obviously diverging. In the work on capillary spreading over a smooth solid surface of Chebbi [17], the slope was found not to violate the lubrication theory for thicknesses as small as 1 nm. Even if we argue in the case studied here of viscous gravity spread that the thickness is not expected to reach zero, it is clear that surface tension effects cannot be neglected as mentioned above.…”

“…Extending this approach of de Gennes [3], and a previous work of Chebbi [17] on capillary spreading over smooth solid surfaces, we study viscous dissipation in this case. The velocity profile is known to be parabolic (see [5], for instance): In dimensional variables, the asymptotic solution near the edge, Eq.…”

Thin-Film Flows And High-Order Degenerate Parabolic Equations

“…The consideration of the role of long-range forces in this context, typically leading in the completely-wetting case to evolution equations of the form (17) (often with m = 1, though more general power laws are also frequently considered), goes back at least to Huh and Scriven (1971) and has been the subject of a great deal of recent attention (with regard to how contact-line singularities can be alleviated, for example) -see Kalinin and Starov (1988), Starov et al (1994), Hocking (1995), Chebbi and Selim (1997), Voinov (1997), Trevino et al (1998), Chebbi (2000) and Pismen et al (2000), for instance. We wish to focus here on two aspects, firstly how Tanner's law (cf.…”

Dynamics of Partial Wetting

“…Then we apply the x-momentum balance, while including friction, pressure and interfacial tension forces, and use a similar approach to that in [12,15], while integrating from a point at which the contact angle can be still considered as nearly equal the dynamic contact angle,x − s max up to a point where continuum mechanics breaks,x − s min . This yields for the axisymmetric case:…”

“…The numerical solution given by Chebbi [4] is relatively elaborate, and the reader is referred to the abovementioned paper. As in the case of complete wetting [11,12], the drop profile has an inflection point [4].…”