Squeeze flow of a Bingham-type fluid with elastic core

•We investigate the squeeze flow of a yield-stress fluid.•We consider axisymmetric geometry.•We treat the unyield part as a linear elastic solid.•We study zero order approximation.•We perform numerical simulations.

The squeeze flow of a Bingham-type material between finite circular disks is considered. The material is modelled assuming that the unyielded region behaves like a linear elastic core. A lubrication approximation is considered. It is shown that no paradox can arise, such as that has been pointed out for many years by various authors when the unyielded region in the fluid is supposed to be perfectly rigid. The unyielded region is shown to be always detached from the axis of symmetry. Some numerical simulations are worked out for different squeezing rates.