The Rayleigh problem for a yield stress fluid with spurt

We consider a generalized Newtonian fluid which exhibits a yield stress and spurt when the yield stress is reached. The constitutive behavior above the yield stress is assumed linear. We solve the associated Rayleigh problem. The solution is not self-similar and exhibits a propagating front separating yielded and unyielded regions. The behavior near t=0 is crucial for starting the numerical simulation. We find that the position of the front behaves like −tlnt.