Rivulet of a non-Newtonian fluid draining on an inclined superhydrophobic surface

A rivulet of a power-law-rheology fluid steadily draining from a point source on an inclined superhydrophobic plane is considered. An equation for the shape of the cross section of the rivulet has been derived in the thin layer approximation with the inhomogeneous slip boundary condition (slip coefficients are power functions of the spatial coordinates). Under the assumption that the rivulet is symmetric with respect to its middle plane, the conditions for the existence of a class of self-similar solutions of one ordinary differential equation of the second order have been determined. For some slip parameters of the superhydrophobic surface and some rheological indices of the draining fluid, analytical and numerical solutions from the found class have been constructed and the shape of the cross section of the rivulet and the geometry of the wetting spot have been analyzed.