Unsteady circular tube flow of compressible polymeric liquids subject to pressure-dependent wall slip

mathematical model is developed for the time-dependent circular tube flow of compressible olymeric liquids subject to pressure-dependent slip at the wall and applied to a poly dimethyl iloxane PDMS . The parameters of pressure-dependent wall slip velocity and shear viscosity of he PDMS were determined using combinations of small-amplitude oscillatory shear, steady orsional and squeeze flows and were employed in the prediction of the time-dependent circular ube flow behavior of the PDMS. The numerical solutions suggest that a steady tube flow is enerated when the flow boundary condition at the wall is stable, that is, either a contiguous stick or weak slip or a contiguous strong slip condition along the entire length of the wall. On the other and, when the flow boundary condition changes from stick or weak slip to strong slip at any ocation along the length of the wall, undamped periodic oscillations in pressure and mean velocity re observed. The experimentally characterized and simulated tube flow curves of PDMS are imilar and the simulation findings for flow stability are in general consistent with the xperimentally observed flow instability behavior of PDMS. © 2008 The Society of Rheology. DOI: 10.1122/1.2837104