Type: Semester project
There is preliminary experimental evidence that the rain-fed thin-film flow around a vertical cylindrical rod, capped by a hemispherical dome (fig. 1), breaks axisymmetry and exhibits a fingering-like instability.
The thickness of a rain-fed film coating a sphere is uniform, as is the constant-flow-rate film around an infinite vertical cylinder; however, these two thicknesses are unequal. The matching region likely presents a capillary ridge [1], which is known to usually be linearly unstable [2].
Firstly, the stationary, axisymmetric base flow will be computed, either by using the Comsol Multiphysics Moving Mesh solver, or by employing matched asymptotics techniques (depending on the student’s interests). Secondly, a linear instability analysis will be performed, resulting in a prediction for the most unstable number of fingers.
References:
[1] QIN, J., Y.-T. XIA, & P. GAO (2021), “Axisymmetric evolution of gravity-driven thin films on a small sphere,” J. Fluid Mech. 907.
[2] KATAOKA, D. E. & S. M. TROIAN (1997), “A theoretical study of instabilities at the advancing front of thermally driven coating films,” J. Colloid Interface Sci. 192.
Supervisors: Simeon Djambov & François Gallaire