June 17th, 2012

(no subject)

Читаю статью, где эпюра силы капиллярного натяжения, действующая на подложку, выводится из дерягинского расклинивающего давления:


"Other way to rationalize the deformation of the substrate is to associate it with the action of surface forces of the second kind. As it was shown in Ref. [18], the local stress experienced by the substrate can be computed as

f = Pcapb−Π(h) (12)

where Pcapb is the capillary pressure of the drop, and Π(h) is a local value of disjoining pressure dependent on the local thickness of a liquid layer above the given point of the substrate. The normal stress is illustrated in Fig. 7. In the equilibrium wetting film Π(h0)=Pcapb, and thus, according to Eq. (12), the substrate under the film is not stressed. Under the bulk part of the drop where h>h, the substrate is uniformly stressed by the pressure |Pcapb| (we recall here that Pcapb<0 for drops and other convex menisci). However, much larger stresses may be observed under the transition zone between the drop and the wetting films. In this region, the local thickness of liquid layer above the substrate varies in the range h0 < h < h, and, depending on the shape of the disjoining pressure isotherm, the substrate experiences alternating stresses, the intensity of which may well exceed the plastic yield stress. These local stresses may develop a significant deformation at the wetting rim. Attempts to move the three phase contact line over deformed ridge will meet detectable resistance. As a result, the deformed substrate will demonstrate advancing and receding contact angle hysteresis. In addition, as the moving menisci have the curvature (and, consequently, the capillary pressure) different from that of the steady drop, the deformation of the substrate will be different at the advancing and receding edges, thus affecting the hysteresis as well."

(L. Boinovich, A. Emelyanenko "Wetting and surface forces" Advances in Colloid and Interface Science 165 (2011) 60–69)

PS. Скажем так, из этого совсем не очевидно, что баланс сил равен нулю (что есть следствие третьего закона Ньютона). Более того, на первый взгляд ничто не мешает подобрать капиллярное давление Pcapb (оно определяется радиусом капли) так, что оно близко к минимуму Π(h), и тогда растягивающего давления почти и не будет.