Shallow viscoplastic flow around the inside of a rotating cylinder

Lubrication theory is presented for the flow of a viscoplastic fluid (described by the Herschel-Bulkley law) around the inside surface of a rotating cylinder. The analysis predicts the steady states typically reached after a small mumber of rotations, at speeds for which the fluid largely collects in a prominent pool in the lower part of the cylinder. The analysis also captures the drainage of the film around the inside of a stationary cylinder. Specific consideration is given to the plastic limit, arising for arbitrarily small rotation rates where the fluid behaves like a perfectly plastic material satisfying the von Mises yield condition. Theoretical predictions are compared with experiments using a Carbopol suspension.