Inclination angles of the boundary in moving liquid layers

Wetting: Inverse Dynamic Problem and Equations for Microscopic Parameters

“…In particular, experimental data analyses in (1,9) reveal that wetting hydrodynamics can be affected by molecular size. The same conclusion is drawn from the precursor film theory (2,3,14,15). The maximum precursor film thickness exceeds the molecular size, so the film only exists when the dynamic contact angle (and the capillary number) is low.…”

“…This is because we are interested in the value of inclination angle α only at distances rather large as compared with the microdistance (h h m ). In this case the condition α = α m at h = h m (1,3) incorporates the microscopic angle α m . The inclination angle α is approximately described by the asymptotic equation provided in (1):…”

“…The inverse problem in wetting dynamics is to determine the constant inherent in the asymptotic solution [3] (or in a more accurate solution) on the basis of macroscopic measurements. When formulating the inverse problems, one should bear in mind that (1,9) demonstrate the agreement of dynamic angle theory with experiment in the case of using the simplified condition α = α m for h = h m , where h m is comparable with the liquid molecule dimension.…”

“…We are interested in developing the respective theories-including the behavior at speeds close to the critical value in the system with a meniscus. The hydrodynamic effect of the existence of a critical (or maximum) speed of a contact line receding from a dry surface is known from (1,3,9), for example. However, the dynamics of wetting at near-critical speeds has been studied inadequately.…”

Closed-form solution of a thermocapillary free-film problem due to Pukhnachev

“…It is worth noting that the ordinary differential equation in (1.7) arises in many other contexts involving thin films, and so has been studied extensively; see, for example, the papers by Voinov [18] [9], Janeček et al [7] and Snoeijer & Andreotti [16]. In particular, Duffy & Wilson [4] discussed the general solution of this differential equation in some detail.…”