Flow of viscoplastic liquids through axisymmetric expansions–contractions

We examine the internal flow of viscoplastic liquids through ducts consisting of an abrupt axisymmetric expansion followed by an abrupt contraction. Steady, inertialess numerical solutions were obtained by solving the conservation equations of mass and momentum via the finite volume method. The viscoplastic behavior of the liquid was modeled by the generalized Newtonian liquid model with a recently proposed viscosity function. Flow visualization experiments were also conducted with Carbopol aqueous solutions at different concentrations. Yield surfaces delimiting yielded and unyielded regions were observed for different combinations of the governing parameters. The unyielded region is located in the large-diameter portion of the channel, near the wall. The size of the unyielded region is shown to be a strong function of the geometrical, rheological, and flow parameters.