Viscous-gravity spreading of time-varying liquid drop volumes on solid surfaces

Viscous-gravity spreading of liquid drops of time-dependent volume over a solid surface is considered. A self-similar solution for the drop configuration is obtained, in the case the liquid drop volume varies as a power-law function of time, along with the spreading laws in both cases of cylindrical and axisymmetric geometries. Results compare favorably with published experimental results and previous theoretical work. The limitations of the model are discussed, along with a comparison with viscous gravity spreading of oil on water. The validity of using approximate spreading laws is considered, and an approximate method is suggested to provide the dynamics of spreading in the general case where the drop volume does not necessarily vary as a power-law function of time.