The hydrodynamics of the spreading of one liquid on the surface of another

The mechanisms involved in the spreading of one liquid on the surface of another are considered for the case of a positive spreading coefficient. Taking into account the effects of gravity, capillary pressure and the spreading coefficient, the general equations determining the spreading are derived. These are then solved for the situation where the spreading liquid is introduced onto the surface of a uniformly flowing substratum at a position upstream of a barrier on the substratum surface. In this manner a steady-state situation is achieved for which the variation of spreading-liquid thickness with position is obtained as a function of the deposited volume of spreading liquid and the velocity of the substratum.