Abstract
Motivated by the industrial process of blade coating, the two-dimensional flow of a thin film of Newtonian fluid on a horizontal substrate moving parallel to itself with constant speed under a fixed blade of finite length in which the flows upstream and downstream of the blade are coupled via the flow under the blade is analysed. A combination of asymptotic and numerical methods is used to investigate the number and nature of the steady solutions that exist. Specifically, it is found that in the presence of gravity there is always at least one, and (depending on the parameter values) possibly as many as three, steady solutions, and that when multiple solutions occur they are identical under and downstream of the blade, but differ upstream of it. The stability of these solutions is investigated, and their asymptotic behaviour in the limits of large and small flux and weak and strong gravity effects, respectively, determined.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
