Limiting flow in a pre-metered coating device

A limiting case of flow in a pre-metered coating device is analyzed using a singular perturbation method. The ability of this device to coat a range of film thicknesses at the same coating speed is traced to the freedom of the two free surfaces to adopt any curvature within certain limits. The observed limitations on operating conditions for this coater are explained by the failure of the desired steady-state to exist for all values of the operating parameters. The parameter bounds within which the device can coat a uniform liquid layer are predicted quantitatively. Some analyses of dip coating are reviewed in the light of the present work.