Prediction of two-dimensional dripping onset of a liquid film under an inclined plane

Instability and dripping of electrified liquid films flowing down inverted substrates

“…In borderline cases, it can take many wavelengths from the inlet for a drip to develop. Our simulations indicate that (non-transient) dripping takes place as an instability of individual solitary pulses, agreeing with the discussions in [39]. For the electrified problem the agreement is less striking, but the A/C threshold still remains a good order-ofmagnitude estimate for complete dripping suppression, something that cannot be obtained from a temporal stability analysis.…”

“…They attribute dripping to a secondary instability of travelling wave solutions. We note that, the dripping thresholds computed by Kofman et al [39] improve in their agreement with the A/C threshold predictions as the length of the periodic domain increases (in the region where the A/C curve in terms of thickness and inclination angle is monotonic). We emphasize that due to nonlinear effects, dripping and absolute instability should not align exactly, however a predictor for dripping phenomena based on linear theory is useful.…”

“…The authors reported a large discrepancy with the results of the inertialess Benney equation away from zero Reynolds numbers, and found a fluid-independent critical angle below which only convective instabilities exist for their models. Kofman et al [39] employed DNS for the 2D problem with spatially periodic boundary conditions, finding that the dripping onset did not coincide closely with the A/C transition curve obtained from the WIBL models in [38]. They attribute dripping to a secondary instability of travelling wave solutions.…”

“…Following [19,39], we investigate the relationship between absolute instability and dripping of hanging films, both with and without electric fields. The working fluid for the DNS is the same as used in experiments by Brun et al [19], and we took care to faithfully reproduce the experiments in silico, consequently investigating electric field effects through extensive computations that could be hard to sample experimentally.…”

“…The working fluid for the DNS is the same as used in experiments by Brun et al [19], and we took care to faithfully reproduce the experiments in silico, consequently investigating electric field effects through extensive computations that could be hard to sample experimentally. To this end, and in contrast to [39] where spatially periodic boundary conditions are used, we initialize with a flat interface and excite the most unstable waves with time-periodic forcing at the inflow (as used in [36] for the computation of solitary waves on overlying films). Hence, we both mimic experimental conditions and are able to produce solutions with a regular spacing of waves/drops.…”