Characterization

(1) Constant flow bubble cases

Photo for constant flow bubbles    The signal for constant flow bubbles in time and frequency domains The total energy vs flow rate (nitrogen)  The total energy vs jet velocity (nitrogen)The total energy vs flow rate (methane)The total energy vs jet velocity (methane)

(a) Total energy vs flow rate, (b) total energy vs jet velocity, (c) total energy vs flowrate²/diameter³, and (d) total energy vs jet velocity× bubble generation rate×time for both nitrogen and methane.

(2) A few bubble cases

  Photo for a few bubbles    The signal for a few bubbles in time and frequency domains

The histograms of resonant frequency for different  needle diameters and flow rates (nitrogen)

The histograms of resonant frequency for different  needle diameters and flow rates (methane)

(a) The resonant frequency vs the diameter of the needles, where µL/min in the legend denotes the flow rate and the solid line is the regression line, and (b) The resonant frequency vs 1/R₀, where R₀ is the effective radius of a spherical bubble.

(3) Bubble size distributions

(a) Sound frequency spectrum for several pressure for nitrogen gas with the needle number being G14. (b) Frequency spectrum under pressure of 10 psi with the peak frequencies and corresponding bubble distribution marked. Inset: corresponding photo with some referenced bubble size marked.

Bubble number percentage histogram for Nitrogen gas with all needles and flowrates.

Bubble number percentage histogram for methane gas with all needles and flowrates.