The Kaye effect is a fascinating phenomenon of a leaping shampoo stream which was first described by Alan Kaye in 1963 as a property of non-Newtonian fluid. It manifest itself when a thin stream of non-Newtonian fluid is poured into a dish of fluid. As pouring proceeds, a small stream of liquid occasionally leaps upward from the heap. Shear-thinning viscosity is advanced as the critical ingredient to understand this effect. We consider a Carreau-Yasuda model and numerically identify the parameters eventually yielding to the Kaye effect. The numerical algorithm consists of a projection method coupled with a level-set formulation for the interface representation. In this talk, we focus on two aspects: (i) the numerical approximation of the capillarity force and (ii) the entropy residual technique used to stabilize the finite element approximation of the level-set evolution. This is based on a joint work with J.L. Guermond and S. Lee.