Cessation Flows of Bingham Plastics With Slip At the Wall

Abstract eng:
We use finite elements in space and a fully implicit scheme in time in order to solve the cessation of axisymmetric Poiseuille flow of a Bingham plastic under the assumption that slip occurs along the wall. The Papanastasiou regularization of the constitutive equation is employed and a power-law expression is used to relate the wall shear stress to the slip velocity. The numerical results show that the velocity becomes and remains uniform before complete cessation and that the stopping time is finite only when the exponent s<1. In the case of Navier slip (s=1), the stopping time is infinite for any non-zero Bingham number and the volumetric flow rate decays exponentially. When s>1, the decay is much slower, i.e. polynomial. The asymptotic expressions for the volumetric flow rate in the case of full-slip are also derived.

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