# zbMATH — the first resource for mathematics

On the ability of drops or bubbles to stick to non-horizontal surfaces of solids. (English) Zbl 0543.76140
Summary: It is common knowledge that relatively small drops or bubbles have a tendency to stick to the surfaces of solids. Two specific problems are investigated: the shape of the largest drop or bubble that can remain attached to an inclined solid surface; and the shape and speed at which it moves along the surface when these conditions are exceeded. The slope of the fluid-fluid interface relative to the surface of the solid is assumed to be small, making it possible to obtain results using analytic techniques. It is shown that from both a physical and mathematical point of view contact-angle hysteresis, i.e. the ability of the position of the contact line to remain fixed as long as the value of the contact angle $$\theta$$ lies within the interval $$\theta_ R\leq \theta \leq \theta_ A$$, where $$\theta_ A\not\equiv \theta_ R$$, emerges as the single most important characteristic of the system.

##### MSC:
 76T99 Multiphase and multicomponent flows
Full Text:
##### References:
 [1] DOI: 10.1016/0021-9797(80)90124-1 [2] DOI: 10.1016/0021-9797(69)90411-1 [3] DOI: 10.1016/0095-8522(50)90059-6 [4] Sadhal, Trans. ASME 101 pp 48– (1979) [6] DOI: 10.1016/0017-9310(78)90186-2 [7] Macdougall, Proc. R. Soc. Lond. 180 pp 151– (1942) [10] Hocking, Q. J. Mech. Appl. Maths 34 pp 37– (1981) [11] DOI: 10.1017/S0022112077002134 [12] DOI: 10.1016/0021-9797(71)90280-3 [13] DOI: 10.1017/S0022112078000075 · Zbl 0373.76040 [14] DOI: 10.1016/0095-8522(62)90011-9 [15] DOI: 10.1017/S0022112076002838 · Zbl 0341.76010
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.