The study of the dynamics of capillary wetting has started in the 1920s with the studies of Lucas, Washburn, and Rideal. The LWR law states a square root dependency with time for the penetration distance. This property was shown to be valid for arbitrary, uniform cross section microchannels.
However, the dynamics of capillary wetting in non-uniform cross section channels is still a subject of investigation.
In this work an analytical model for piecewise varying cross section channels is developed. It is shown that the model compares favorably to experiments. Moreover the results are also in agreement with a former numerical approach.