Axisymmetric extrusion of a shear-thinning fluid in unconfined and confined geometries

We consider the axisymmetric, radial extrusion of Newtonian and shear-thinning, power-law fluids from a cylindrical source, which displace an ambient inviscid fluid of equal density. In unconfined geometries, the upper and lower fluid interfaces are stress free, and the flow is dominated by extensional stresses everywhere. In a layer of extruded shear-thinning fluid, a radially growing viscosity field, associated with a radially decaying velocity field, causes the current to bulge near the cylindrical source, with the thickness of the layer growing without bound over time. In contrast, with a Newtonian fluid, the thickness of the fluid layer never exceeds the height of the cylindrical source. We compute numerical solutions to this system, and find similarity solutions describing its late-time behaviour for values of the rheological power-law exponent 1 n 3/2. We also consider extrusion between parallel plates, in which the shear-thinning fluid displaces the inviscid fluid and fills the cell completely up to a grounding line, beyond which it separates from the boundaries to extend freely. In this case, we find similarity solutions for values of the power-law exponent n 1.