The study deals with the fluid-structure-interaction problem of longitudinal annular flow about a rigid axisymmetric centre-body externally interfaced by an elastic shell. The gap between the centre-body and enclosing shell may be initially filled with a thin fluid layer or devoid of it. We employ elastic shell theory and the lubrication approximation to show that the problem is governed by a forced nonlinear diffusion equation in fluid pressure. The case of an advancing liquid front in an initially unpenetrated interface is a particular case in which the equation degenerates into the porous medium equation, which admits nonnegative weak solutions with compact support and finite speed of propagation. The study presents several solutions of the flow-field and solid-deformation for various time-varying inlet pressure and external forces. The presented interaction between viscosity and elasticity may be applied to fields such as soft-robotics and micro-swimmers.
