Capacitance Probe - Measure bubbles in almost any liquid medium 

Capacitance probe works as the capacitance between two electrodes changes as the gas bubble passing throgh the probe. The capacitance change is proportional to the bubble penetration length and thus the bubble diameter and the signal duration can be used to measure the bubble speed.

The following figure shows a simplified version of the capacitance probe.

The bubble signal is a "dent" in the capacitance probe signal output. The depth of the "dent" is proportional to the penetration length (chording length) of the probe. It can be used to calculate the bubble size. The time duration of the bubble signal, on the other hand, is inversely proportional to the bubble's rising speed and therefore can be used to compute its value.

Following is a typical bubble signal obtained by the capacitance probe. A microphone signal (red) is also plotted to show the bubble's release.

Signal Processing and Data Analysis for the New Capacitance Probe

The bubble signal depth and the signal duration time need to be extracted before the bubble size and bubble speed can be calculated. This task is carried out by a signal processing program. The results from this program include the spectrum of the bubble's chording length and the spectrum of the bubble's signal duration time. The "chording length" is the vertical length that the probe actually measured out of a bubble. As shown in the following graph, it can range from 0 to the maximum vertical bubble dimension and its spectrum is complicated by the bubble's non-uniform distribution. The theoretical chording length distribution of a uniformly distributed ellipsoid shapped bubble is a "ramp" function.

Because the chording length spectrum has a natural spread, getting the real bubble size distribution out of it is a complicated process. It involves probe calibration, single size bubble study and spectrum de-convolution. The final result, however, is fair good. The following graph shows the chording length spectrum generated by bubbles with a single size. After de-convolution, this single bubble size is clearly identified and the fit between the theoretical spectrum and the measured spectrum is very good.