Mean flow produced by small-amplitude vibrations of a liquid bridge with its free surface covered with an insoluble surfactant

Abstract

As is well known, confined fluid systems subject to forced vibrations produce mean flows, called in this context streaming flows. These mean flows promote an overall mass transport in the fluid that has consequences in the transport of passive scalars and surfactants, when these are present in a fluid interface. Such transport causes surfactant concentration inhomogeneities that are to be counterbalanced by Marangoni elasticity. Therefore, the interaction of streaming flows and Marangoni convection is expected to produce new flow structures that are different from those resulting when only one of these effects is present. The present paper focuses on this interaction using the liquid bridge geometry as a paradigmatic system for the analysis. Such analysis is based on an appropriate post-processing of the results obtained via direct numerical simulation of the system for moderately small viscosity, a condition consistent with typical experiments of vibrated millimetric liquid bridges. It is seen that the flow patterns show a nonmonotone behavior as the Marangoni number is increased. In addition, the strength of the mean flow at the free surface exhibits two well-defined regimes as the forcing amplitude increases. These regimes show fairly universal power-law behaviors.

Streaming controlled by meniscus shape

“…where β ≈ 2 for both symmetric and antisymmetric cases. This indicates that the secondary circulation is caused by the quadratic nonlinearity of the velocity field, which is consistent with the direct numerical simulations of Carrión et al (2017). Note that the flow velocity near the boundary is not resolvable by PIV, so the integration in (2.1) excludes the region within 0.034 cm of the lateral boundaries.…”