Viscous film flow in the stagnation region of the jet impinging on planar surface

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Abstract
A capillary jet of liquid impinges on a planar surface that is normally oriented to the axis of the jet. The surface is initially covered with a thin uniform film of a viscous liquid. The impact and radial spreading of the liquid from the jet cause the underlying viscous film to be removed from the surface. An approximate analysis predicts the thinning rate of the film in the stagnation region of the jet. It uses the shear stress and pressure distribution of the classical Homann flow as boundary conditions for an analytical solution of the Reynolds lubrication equations in this underlying viscous film. A more exact analysis modifies the Homann flow to account for the mobility of the liquid film beneath the spreading jet and sheds light on the limitations of the analytical lubrication analysis. Data presented are in excellent agreement with the theory, subject only to the choice of a value for the hydrodynamic constant that appears in the Homann analysis.

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