Fall 2016
Seminars are held on Mondays from 2:30 - 3:30PM in Cullimore Hall, Room 611, unless noted otherwise. For questions about the seminar schedule, please contact David Shirokoff.
Date: September 12, 2016
Speaker: William Batson
NJIT,
Title: "Oscillatory Excitations in Interfacial Fluid Dynamics"
Abstract:
The unifying theme of this talk, which is divided into two parts, is dynamical motion of fluid interfaces driven by an oscillatory excitation.
The first part will focus on Faraday waves—those which appear as standing waves at liquid interfaces once vibrations of sufficient amplitude are imposed to the holding container. Fundamentally the phenomenon is an example of parametric resonance, and the Mathieu equation offers the simplest relation between the observed wavelength and the imposed vibrational frequency. Typically these waves have been investigated for wavelengths that are much smaller than the lateral container dimensions, which promotes the generation of spatially extended patterns. This work instead considers large wavelengths that are associated with low excitation frequencies, and, as a result, wavelength selection is discretized and the observed pattern depends significantly on the lateral container geometry. The main results that will be presented pertain to experiments that have been conducted using an immiscible liquid system contained within a cylindrical cell. Topics of discussion include comparison of the experimental instability threshold with the linear theory for viscous fluids, sources non-ideality, nonlinear features, and two-frequency excitation.
The second part will focus on a thermocapillary film flow driven by an oscillatory gas temperature. Specifically, fluids that exhibit a well-defined minimum surface tension with respect to temperature are considered. Invoking the long-wave approximation, a nonlinear PDE describing the spatiotemporal evolution of the film thickness is derived. As a result of the nonlinear surface tension, the oscillatory excitation contributes a time-averaged driving force for instability that is absent for typical fluids whose surface tension decreases linearly with temperature. The nonlinear dynamics associated with the evolution equation are investigated numerically on spatially periodic domains, and ‘steady’ wave flows that are periodic in time are found for excitation frequencies set approximately equal to the magnitude of the linear growth rate. The physics of the saturating mechanism, the roles of the thermal boundary conditions and the excitation frequency, bifurcation, and dynamics on ‘large’ periodic domains will be presented. Furthermore, the dimensional values of model parameters for real fluids and the validity of the model assumptions will be discussed.