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Asymptotic and numerical analysis of a simple model for blade coating

Quintans Carou, J. and Wilson, S.K. and Mottram, N.J. and Duffy, B.R. (2009) Asymptotic and numerical analysis of a simple model for blade coating. Journal of Engineering Mathematics, 63 (2-4). pp. 155-176. ISSN 0022-0833

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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. Specially, 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.