Necking in coating flow over periodic substrates

Autor:	Edward R. Johnson, N. R. McDonald
Rok vydání:	2009
Předmět:	Plane (geometry) Dirichlet conditions General Mathematics Mathematical analysis General Engineering Boundary (topology) Conformal map Geometry Viscous liquid Vortex Physics::Fluid Dynamics symbols.namesake Free boundary problem symbols Necking Mathematics
Zdroj:	Journal of Engineering Mathematics. 65:171-178
ISSN:	1573-2703 0022-0833
DOI:	10.1007/s10665-009-9273-3
Popis:	The free-boundary problem determining the shape of a layer of viscous fluid coating a substrate while draining steadily under gravity is solved analytically for substrates taking the form of a periodic array of long plates of arbitrary width and spacing. The mathematical problem involves solving Poisson’s equation with constant forcing term in the fluid layer subject to vanishing Neumann and Dirichlet conditions on the free boundary. By considering the problem in a potential plane and using conformal mapping, a two-parameter family of solutions is obtained in the form of an infinite series. Explicit, closed-form solutions are derived in the limiting cases of a single gap perforating an infinitely wide plate, and for an array of evenly spaced point plates. In these cases explicit expressions are obtained for the thinning, or necking, of the fluid layer in the gap regions between plates.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::949b162e1ab426cc53e13c51e3ea2b12 https://doi.org/10.1007/s10665-009-9273-3 Zobrazit plný text záznamu Full text from SpringerLink