October 15, 2000 Quiz Question

Dip Coating of a Bingham Fluid

Perspective Meter:

Dip coating of metallic parts is commonly used to apply polymer coatings which protect against corrosion. Consider the dip coating of a large, flat metal sheet, as illustrated in the Figure below. As pulled from the liquid dip coating bath, the sheet has a uniform fluid coating of thickness Ho. Excess fluid simply drains off of the surface due to the effect of gravity.

The metal sheet is tall and wide, L>>W>>H. Assume that the coating maintains a uniform thickness H(t) as the excess fluid drains. This flow is controlled by gravity and viscosity; for this problem, assume that inertial effects and interfacial tension are negligible.

The fluid used for coating is an incompressible Bingham fluid characterized by the following constitutive equation:


What is the velocity distribution in the coating as it drains off of the metal sheet?
What is the thickness of the coating as a function of time, H(t)?
What is the final thickness of the coating?

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