Tiny bubbles bring about dramatic changes in physical phenomena

Most test systems measure something. In an unusual twist, the Acoustic Bubble Spectrometer® (ABS) developed by DYNAFLOW, INC. (Fulton, MD, http://www.dynaflow-inc.com/) under the direction of Dr. Georges L. Chahine focuses on measuring what's absent -- the percentage of a given volume of a liquid that doesn't consist of that liquid and instead is made up of air bubbles or gases that gather in various sizes and shapes. Further, PCI data-acq cards from United Electronic Industries (Watertown, MA, www.ueidaq.com) are helping researchers make large strides in their research by enabling them to refine their measurement strategies.

Figure 1. ABS setup. On the right you can see a plexiglass cell filled with water with a stream of bubbles in the center. Also visible are the two hydrophones (and on front, the PowerDAQ BNC Panel)

Not only does the ABS measure the total "void fraction" (fraction by volume of the gas phase in a fluid), this unusual instrument also measures the distribution of the sizes of the bubbles, and hence its designation as a spectrometer. This difficult-to-measure characteristic proves invaluable in a number of areas, an obvious one being oceanographics. The top tens of meters of the sea contain many bubbles that greatly affect acoustic properties by scattering signals and creating noise. Knowledge of bubble-size distribution is also important when modeling chemical or biological processes. For instance, the ABS has obvious uses in the development of processes that mix a gas in a liquid such as waste treatment and the design of aeration systems.

In another application area, the ABS, for which the initial efforts to develop the device were funded by Small Business Innovation Research (SBIR) awards from the National Science Foundation, proves invaluable in any engineered system that might experience cavitation. Cavitation is the formation of vaporous and gaseous filled bubbles or "cavities" in a liquid typically due to a sudden change in pressure as occurs, for example, along the flow path through a pump or over a propeller blade. It can have a dramatic effect on both the performance and integrity of such devices. In particular, cavitation significantly affects the performance and operation of propellers, hydrofoils and pumps. Not only can the collapse of the cavitation bubbles cause substantial physical damage, it creates considerable noise. Scientists have learned that the distribution of bubble nuclei (tiny bubbles) strongly influences the propensity for cavitation. This is particularly important if one wishes to experimentally scale a device subject to cavitation -- it's necessary to properly control and account for the underlying bubble nuclei distribution in the liquid.

Just look into a small pool of moving water and you can get an idea of how difficult it must be to measure not only the number of bubbles but also their distribution. "In the past, scientists tried to measure the distribution of bubbles visually or optically, but that process is quite painstaking and isn't optimum when you're dealing with a large setup or system," relates Dr. Ken Kalumuck, principal research scientist at DYNAFLOW. "Further, it becomes extremely difficult to distinguish small particulates from small bubbles." Because bubbles are much more sensitive to acoustic waves than particulates, the ABS can readily pick out small bubbles in a liquid containing particles.

Bubble resonance

To solve problems associated with traditional methods, the DYNAFLOW team developed the ABS, which works with a pair of hydrophones, one a transmitter and one a receiver. A researcher places these two transducers in the liquid, and the distance between them can vary from just a centimeter to a meter or more. The transmitter emits monochromatic sine waves in short bursts of a few cycles at a number of frequencies depending on the expected range of bubble sizes. An example test setup involves stepping through frequencies from 10 kHz to 300 kHz in selected increments.

Any bubbles in the liquid have an effect on the strength of the signal that reaches the receiver as well as the speed at which the signal travels between the emitter and the receiver. In particular, bubbles of a given size have a resonant frequency where effects are the strongest, but the bubbles affect signals of all frequencies. For each burst, the system measures changes in the speed of sound and the signal amplitude -- with more bubbles, the speed drops and also attenuates the signal's amplitude. The ABS software then compares the set of incoming signals at all frequencies to an influence matrix whose calculations are based on a model that indicates what a set of bubbles should do at specific frequencies. By making this comparison, the system can determine the distribution of bubble sizes with a high degree of accuracy.

The ABS system is built around a PC-based Windows platform. It employs a high-speed analog output card to generate the transmitted signal and then uses a 1.25 MS/s simultaneous-sampling card from UEI to measure both the transmitted and received signals. This high-speed operation is required because the signal bursts are so short. Further, because the system must determine any changes in the speed of sound, true simultaneous sampling is mandatory; pseudosimultaneous sampling even at high speeds proves inadequate for this application, especially when the distance between the two hydrophones can be as small as 1 cm or less.

The copyrighted ABS software then analyzes the results by solving two Fredholm integral equations of the first kind. These equations are ill-posed and are a challenge to solve, especially when the data contain noise. Nonetheless, DYNAFLOW was able to develop a novel algorithm that accurately solves these equations using a constrained optimization technique.