Start-up plane Poiseuille flow of a Bingham fluid.

Highlights • The start-up plane Poiseuille flow of a Bingham fluid is considered. • The analytical expression for the velocity in the core is given. • The analytical solution is extended to include the velocity in the yielded zone. • Strict bounds on the validity of the analytical solution are provided. Abstract The start-up flow of a Bingham plastic in a channel is considered and Safronchik's solution [1] for the initial evolution of the yield surface and the core velocity is revisited. Stricter time bounds for the validity of the above solution are derived and the solution is extended to include the velocity profile in the evolving yielded zone. Comparisons are made with another approximate solution derived under the assumption that the velocity in the yielded zone is parabolic adjusting with the evolving yield surface. This approximation performs well for small values of the yield stress, or, equivalently, for large values of the imposed pressure gradient. [ABSTRACT FROM AUTHOR]