A mathematical model is developed for the time-dependent circular tube flow of compressible polymeric liquids subject to pressure-dependent slip at the wall and applied to a poly (dimethyl siloxane) (PDMS). The parameters of pressure-dependent wall slip velocity and shear viscosity of the PDMS were determined using combinations of small-amplitude oscillatory shear, steady torsional and squeeze flows and were employed in the prediction of the time-dependent circular tube flow behavior of the PDMS. The numerical solutions suggest that a steady tube flow is generated 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 hand, when the flow boundary condition changes from stick (or weak slip) to strong slip at any location along the length of the wall, undamped periodic oscillations in pressure and mean velocity are observed. The experimentally characterized and simulated tube flow curves of PDMS are similar and the simulation findings for flow stability are in general consistent with the experimentally observed flow instability behavior of PDMS.

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