Stick-slip singularity

When the stress for the Newtonian flow is infinite at a singularity, the corresponding viscoelastic flow problem becomes singular. Let us consider first the stick-slip singularity. 

Let us notice Uq and ao (resp. U i and Oi) velocity and stress tensor at X=0 (resp. derivative according to X of velocity and stress tensor at X.=0 ). The velocity field Uo is the solution of an homogeneous Stokes problem with a "stick-slip singularity ( = jt) and a singular solution (Uo(r,8)= r IJo(e)) exists. As it is easily verified Ui is the solution of the following inhomogeneous Stokes problem ... 

Apelian, M. R., e. a. (1988). hnpad of the constitutive equation and singularity on the calculation of stick-slip flow The modified upper-convected maxwell model, /. Non-Newtonian Fluid Mech. 27 299-321. 

In general, the pinning effect and the corresponding stick-and-slip movement of the triple line can be attributed to singular lines on the surface where there is a rapid change in 0-a, such that 6-a decreases as x increases. 

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