Group invariant solution for axisymmetric spreading of a thin fluid film with slip at the fluid-base interface

The axisymmetric spreading of a thin fluid film with slip at the horizontal base is investigated. A nonlinear diffusion equation is derived which relates the height of the free surface to the slip velocity. The equation possesses a Lie point symmetry provided the slip velocity satisfies a first-order quasi-linear partial differential equation. Group invariant solutions are derived with no singularities at the moving contact line. Vortices can exist close to the axis or at the base. The thin film spreads by slipping at the base or by a rolling motion in the vicinity of the moving contact line.