×

zbMATH — the first resource for mathematics

The spreading of drops with intermolecular forces. (English) Zbl 0842.76019
The author studies the spreading of a thin drop of fluid that partially wets a plane surface. The model includes capillarity, slip, and intermolecular forces. It is shown that a complete solution is possible without having to exclude the vicinity of the contact line and without having to assume the dynamic behaviour of the contact angle. An equation is found for the evolution of the drop radius; when the drop is not close to its equilibrium radius, the spreading law has the expected one-tenth power dependence on the radius, with a coefficient which is determined as a function of the intermolecular forces and the slip coefficient. The calculation is performed for small static contact angles and also for the limit when this angle tends to zero.
Reviewer: J.Prakash (Bombay)

MSC:
76D08 Lubrication theory
76D45 Capillarity (surface tension) for incompressible viscous fluids
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Hocking L. M., Q. J. Mech. Appl. Math. 36 pp 55– (1983) · Zbl 0507.76100
[2] Hocking L. M., J. Fluid Mech. 239 pp 671– (1992) · Zbl 0754.76022
[3] de Gennes P. G., Rev. Mod. Phys. 57 pp 827– (1985)
[4] Miller C. A., J. Colloid Interface Sci. 48 pp 368– (1974)
[5] Hocking L. M., Phys. Fluids A 5 pp 793– (1993)
[6] Koplik J., Phys. Rev. Lett. 60 pp 1282– (1988)
[7] Thompson P. A., Phys. Rev. Lett. 63 pp 766– (1989)
[8] Sheludko A., Adv. Colloid Interface Sci. 1 pp 391– (1967)
[9] Hocking L. M., J. Fluid Mech. 121 pp 425– (1982) · Zbl 0492.76101
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.