A rich spectrum of interfacial dynamic with and without  contact-line resistance have been studied. Drops are found to pinch off from a rivulet on the underside of an inclined plane when two conditions are met: a jetting mechanism when drop front steepens beyond a critical value and a pinching mechanism when the transverse curvature exceeds another.
 

Falloff by the jet mechanism at high flow rates.A steepened hump is observed behind the jet.

Fall off by the pinch-off mechanism.The last hump is barely supercritical while the first two are barely subcritical.The subcritical drops traverse the entire plane without falling off.Different drops are on different sides of criticality because, at this critical condition, a fallen drop can reduce the local flow rate to subcritical values.

 Both conditions are determined analytically by matched asymptotycs and correlated to experimental data. Rivulet formation from a straight contact line driven by gravity can occur, when the film behind the contact line cannot sustain a nose coonfiguration across the entire front as the film thins.
 

A typical set of fall-off data for the glycerin-water solution with error bars attached. The solid lines correspond to our theoretical  predictions.The the limiting pinching asymptote is also shown

The liquid rolls in a nose front and suffers less resistance than the sliding motion in a wedge front  - the alternative front configuration specified by gravity and capillary forces. As a result, only parts of the front continue to roll and form rivulets. The position and speed at the point of rivulet formation are determined by matched asymptotics.
 

Fingering of Castor oil on dry (a) and prewetted (b, c) plane. On a dry plane, fingering behavior of highly-wetting Castor oil is qualitatively similar to that of glycerine.The solid line is thepredicted onset position from our theory. (b)With thick prewettingfilm, there is no fingering. (c) For thinner film, the saw-toothpatterns, qualitatively similar to that of complete wetting fluids,are evident.

(a) Normalised position plots for the straight front before fingering and a finger and a minimum after fingering for (+) the Castor oil and (o) glycerine data. (b) Normalised plots of the front and finger position as functions of time for 5 glycerine runs.

Representative publications: 

[77], [79], [105], [112], [114], [115], [118], [119], [121]