Asymptotics of a Pinhole

✍ Scribed by S.B.G. O'brien

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 94 KB
• Volume: 191
• Category: Article
• ISSN: 0021-9797
• DOI: 10.1006/jcis.1997.4982

✦ Synopsis

ARTICLE NO. CS974982 NOTE Asymptotics of a Pinhole z r 0 as r r ϱ, and z r Å 0tan u at z Å 1, for some r Å r u , [2] It is well known that, in a thin liquid film, corresponding to any particular thickness there is precisely one axisymmetric equilibwhere u is the liquid/air contact angle (see Fig. 1). We are interested in rium solution to the Laplace-Young capillary equation; i.e., correfinding how the minimum radius of the pinhole r 0 varies with e.

sponding to each film thickness there is a unique pinhole radius which has been shown to be unstable (1973, Taylor and Michael, J. Fluid Mech. 58, 625-639). We deduce an asymptotic relationship 2. SOLUTIONS between film thickness and pinhole height in the limit of very thin films.