Spreading of a liquid drop over a plane rigid substrate due to   intermolecular forces
  Self-similar solutions of the equation that describes spreading of a liquid layer due to intermolecular forces are found. It is supposed that, when the thickness of the layer reaches some magnitude of the order of the molecular size, it turns into a monomolecular layer, which can be liquid or gaseous. To describe the spreading of a drop, the solutions of the equations that describe evolution of liquid or gaseous monomolecular layers are matched with the self-similar solutions with using relevant boundary conditions. 
A. N. Tyatyushkin