The Faraday instability in rectangular and annular geometries: comparison of experiments with theory
Abstract
Abstract
A longstanding question on the mechanically forced Faraday instability in rectangular geometries arises from a disparity
between theory and experiments (Craik and Armitage in Fluid Dyn Res 15:129–143, 1995). It can be stated as: do corners in
a rectangular geometry Faraday experiment cause the disparity between prediction and experiment? This study is an attempt
to settle this question by comparing the Faraday instability for two fluids in rectangular geometries where corners must be
present with equivalent annular geometries where such corners are necessarily absent. Non-idealities, i.e., damping, arising
from a slight meniscus wave motion and induced sidewall damping are observed for thin gaps, causing discrepancies between
the predicted instability thresholds and those determined experimentally. However, even for thin-gap geometries, experimental agreement between the tested rectangular geometry and its corresponding annular geometry remains excellent. This
suggests that corner effects on the system stability are negligible for rectangular geometries and thus any disparity between
theory and experiment is due principally to the damping caused by proximity of the lateral walls.