The instantaneous slow flow of a visco-elastic fluid between two concentric spheres

Summary

A theoretical analysis is made of the flow of an incompressible viscoelastic fluid contained between two concentric spheres when the outer sphere is moved instantaneously in a given direction, whilst the inner sphere remains at rest. The solution is developed by successive approximations, the first corresponding to the instantaneous slow flow of a Newtonian viscous fluid. By allowing the radius of the outer sphere to approach infinity, the result obtained can be used to give an approximate solution to the equations of motion of a visco-elastic fluid flowing slowly past a fixed sphere.