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The elastic analogue of the Landau–Levich dip-coating problem, in which a plate is withdrawn from a bath of fluid on whose surface lies a thin elastic sheet, is analysed for angle of withdrawal
to the horizontal. The flow is controlled by the elasticity number,
, which is a measure of the relative importance of viscous and bending stresses, and
. The leading-order solution for small
is a steady profile in which the thickness of the film on the plate is found to vary as
. This prediction is confirmed in the limit
by comparison with numerical simulation. Finally, the circumstances under which the assumption of a steady solution is no longer valid are discussed, and the time-dependent solution is described.
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