The proper orthogonal decomposition: A powerful tool for studying drop oscillations

Abstract

Liquid metal drops are released onto different wettable solid substrates. Their post-impact oscillations are recorded at 1000 images/s as soon as the triple line is at rest. The proper orthogonal decomposition (POD) is used to get and identify the frequencies involved. The POD is a technique widely used in the fluid dynamics community to study turbulent flows, but it is not used to determine droplet-free oscillation frequencies. The vertical and horizontal vibration frequencies of the sessile drop center of mass are successfully extracted from the images by POD. The first POD mode captures the vertical displacement frequency, and the second or third POD mode captures the horizontal displacement frequency of the drop center of mass. The spatial structure of the modes is the characteristic of the vertical and horizontal movement. Therefore, the POD can be used instead of the interface displacement tracking to determine the free oscillation frequencies of liquid metal drops and, more generally, of any vibrating sessile drops. As it is a standardized method, it can be used with confidence for routine measurements, especially for sensors.