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

Area of Science:

• Fluid Dynamics
• Materials Science

Background:

• Post-impact oscillations of liquid drops on solid substrates are complex phenomena.
• Traditional methods for analyzing droplet dynamics can be labor-intensive.

Purpose of the Study:

• To investigate the application of Proper Orthogonal Decomposition (POD) for analyzing liquid metal drop oscillations.
• To determine the free oscillation frequencies of sessile liquid metal drops.

Main Methods:

• Liquid metal drops were impacted on wettable solid substrates.
• High-speed imaging (1000 images/s) captured post-impact oscillations.
• Proper Orthogonal Decomposition (POD) was applied to image data to extract oscillation frequencies.

Main Results:

• POD successfully identified vertical and horizontal vibration frequencies of the drop center of mass.
• The first POD mode correlated with vertical displacement frequency.
• Subsequent POD modes captured horizontal displacement frequencies.

Conclusions:

• POD is a viable and standardized method for determining the free oscillation frequencies of liquid metal drops.
• This technique can be applied to other vibrating sessile drops for routine measurements, particularly in sensor applications.