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Thin liquid film formation on hemispherical and conical substrate
Author(s) -
Scholle Markus,
Marner Florian,
Gaskell Philip H.
Publication year - 2019
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201900111
Subject(s) - conical surface , coating , substrate (aquarium) , materials science , thin film , mechanics , work (physics) , deposition (geology) , layer (electronics) , boundary layer , displacement (psychology) , flow (mathematics) , boundary (topology) , optics , composite material , physics , nanotechnology , mathematical analysis , mathematics , thermodynamics , geology , psychology , paleontology , oceanography , sediment , psychotherapist
Abstract The deposition and coating of thin films onto curved rigid substrate, involving displacement of air by a liquid, has numerous applications within the technology sectors but faces two major challenges: (i) control of the local film thickness; (ii) ensuring that the coating remains stable. The work reported here investigates the full coverage of three‐dimensional curved geometries, of hemispherical and conical shape, by a continuously fed, gravity‐driven, thin liquid layer. The modelling approach adopted utilises a first integral formulation [1,2] of the Navier‐Stokes equations leading to a variational formulation in the case of steady flow and an advantageous re‐formulation of the dynamic boundary condition at the free surface [3]. Asymptotic analysis, underpinned by the long‐wave approximation, enables analytic solutions for the local film thickness to be obtained.