Abstract
The problem of capillary-driven flow in a V-shaped surface groove is addressed. A nonlinear diffusion equation for the liquid shape is derived from mass conservation and Poiseuille flow conditions. A similarity transformation for this nonlinear equation is obtained and the resulting ordinary differential equation is solved numerically for appropriate boundary conditions. It is shown that the position of the wetting front is proportional to (Dt)½ where D is a diffusion coefficient proportional to the ratio of the liquid-vapour surface tension to viscosity and the groove depth, and a function of the contact angle and the groove angle. For flow into the groove from a sessile drop source it is shown that the groove angle must be greater than the contact angle. Certain arbitrarily shaped grooves are also addressed.
Publisher
Cambridge University Press (CUP)
Subject
Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics
Reference10 articles.
1. Shepard, J. W. & Bartell, F. E. 1953 Surface roughness as related to hysterisis of contact angles. III.J. Phys. Chem. 57,458.
2. Bascom, W. D. , Cottington, R. L. & Singleterry, C. R. 1964 Dynamic surface phenomena in the spontaneous spreading of oils on solids. In Contact Angle, Wettability, and Adhesion (ed. R. F. Gould ),p. 355.American Chemical Society.
3. Cottington, R. L. , Murphy, C. M. & Singleterry, C. R. 1964 Effect of polar-nonpolar additives on oil spreading on solids, with applications to nonspreading oils. In Contact Angle, Wettability, and Adhesion (ed. R. F. Gould ),p. 341.American Chemical Society.
4. Parker, E. R. & Smoluchowski, R. 1944 Capillarity of metallic surfaces.Trans. ASME 35,362.
5. Adams, C. M. 1966 Spreading, penetration, and capillary flow in metallic systems. In Fundamental Phenomena in the Materials Sciences , Vol. 2 (ed. L. J. Bonis & H. H. Hausner ),p. 175.Plenum.
Cited by
143 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献