Bubble-Based Chemical Sensing
An elegant liquid analysis technique combines passive acoustic listening and active ultrasonic Doppler observation to ascertain the physical properties of even opaque liquids.
Naveen Neil Sinha
An acoustic technique has been devised that is capable of characterizing and identifying different liquids by monitoring all stages of an air bubble’s evolution, from formation and growth at a nozzle to rise toward terminal velocity. This novel approach could lead to simple, automated sensors for characterizing liquids in applications such as process and quality control in the chemical, medical, and food processing industries.
Background on the Research
There are three stages to a gas bubble’s evolution:
Previous measurement techniques including high-speed photography, laser Doppler anemometry, and passive acoustic measurements have focused on only one of these stages.
Several equations have been previously developed to explain bubble behavior. For example, the Minnaert equation (Equation 1) describes the bubble resonance frequency. The frequency, f0, of the oscillation is described by:
Other equations describe the bubble’s terminal velocity after detachment from the nozzle and the shape oscillation frequency [1,2]. In the Doppler measurement, the speed, V, of the bubble is related to the speed of sound, the source frequency, and the received frequency:
These equations can be solved in Mathematica , in terms of measurable parameters such as the resonance frequency, terminal velocity, and shape oscillation frequency. Using these equations, and the measurements obtained from this technique, it is possible to determine the density and surface tension of the liquid as well as the size of the bubble.
A small aquarium pump forced air through the needle, forming a series of evenly spaced, millimeter-sized air bubbles. A hollow cylindrical piezoelectric transducer was located around the needle, and a dual-element Doppler probe was placed several centimeters above the tip of the needle. The piezoelectric transducer converted the sound waves produced by the resonating bubble into an electrical signal that was amplified 1000 ×. All measurements were made with the water at room temperature (~20°C).
To monitor the speed of the bubble as a function of time, a simple frequency-mixing system was constructed (see Figure 2).
This system mixes the output of the Doppler probe receiver (which detects the sound reflected from the bubble) with the ouýput of the function generator to form the sum and difference frequencies. By putting the signal through a low-pass filter, only the difference or Doppler frequency is obtained. The Doppler frequency is related to the speed of the bubble. The speed of the bubble vs. time can be obtained by monitoring how that frequency changes over time.
The Discovery Phase
By looking at specific portions of the graph in Figure 3, different stages in the evolution of the bubble can be observed.
At t1 there is an initial slight spike in the resonance signal when the bubble first forms at the tip of the underwater nozzle, probably caused by a meniscus forming at the syringe tip. The bubble grows while it is attached to the nozzle from time t1 to t2, and this can be seen in the Doppler data as a very low frequency signal.
The growth process begins with the bubble rapidly expanding upwards and then growing horizontally, which appears as a decrease in velocity in the Doppler signal soon after t1. When the bubble detaches and resonates, the event can be detected in the bubble resonance data.
After t2, the bubble accelerates to its terminal velocity, and oscillations in its speed are produced. These shape oscillations are due to changes in the bubble’s shape as it transitions from a sphere to an ellipse. This phenomenon has been studied previously using high-speed photography, but the optical procedure is complicated. The Doppler-based approach, combined with the Origin software, is simpler and, moreover, not limited to clear liquids.
The Crucial Link
The STFT provided a visual image of the Doppler frequency over time. With these curves it is possible to “see” the entire evolution of the bubble; without the plots, neither bubble growth nor shape oscillations would have been detected. The STFT of the Doppler data was also used to determine the bubble terminal velocity.
Observations in Various Liquids
The effect a surfactant (dishwashing liquid in a concentration of 1:100 mL H2O) had on the rising bubbles was compared to their behavior in plain water (see Figure 5).
The resonance peak increased in frequency by 1 kHz and became more damped. The increase in resonance peak frequency is due to the decreased size of the bubbles; because of the lower surface tension, they detached from the nozzle sooner and were smaller in the soap solution than in plain water. In addition, the terminal velocity decreased by almost half; the bubbling rate increased by more than a factor of two; the shape oscillations became too small to be observed; and other characteristics of the rise changed significantly. All of these observations were most likely due to the presence of surfactant molecules at the air-liquid interface.
Solutions of isopropyl alcohol and water in various concentrations were used to study the effect of organic chemical contaminants on the bubbles. As shown in Figure 6A , the alcohol clearly shifted the resonance peak to a higher frequency and increased the damping. In addition, the terminal velocity was significantly reduced; the bubbling rate increased; and the shape oscillation frequency increased (see Figure 6B).
The period of bubble growth was also shorter, showing that the bubbles detached from the nozzle sooner. The effects were similar to those of the surfactant, since both the alcohol and the soap lowered the water surface tension.
When a suspension of turmeric powder was added to pure water (1 g/L, see Figure 7A), the particles had little effect on the resonance of the bubble. The most likely explanation is that the preceding bubbles removed particles from the area in front of the syringe needle. The rise of the bubble changed significantly, however, as particles collected on the bubble surface (see Figure 7B).
Instead of a gradual acceleration, the bubbles in the contaminated water quickly reached their terminal velocity. Furthermore, the shape oscillations disappeared completely. These changes occurred because the suspended particles stuck to the air-water interface of the bubble, creating a rigid surface.
Figure 8 gives a summary comparison of the measurements of the bubble behavior in the various liquids vs. the theoretical predictions.
These experimental results agree well with the theoretical predictions. The four liquids could easily be diff6rentiated by comparing the four measured parameters.
By rearranging the equations describing bubble behavior, the physical properties of the liquid can be solved in terms of the observable quantities. The result is three equations relating the liquid physical properties to the measured parameters:
These equations show the way liquid properties can be determined from multiple measurement parameters made with the combined resonance-Doppler technique. This is demonstrated for the case of water and a water-isopropanol mixture (see Figure 9).
The experimentally determined values agree well with the literature values, typically within 5%. It is worth pointing out that the equation for terminal velocity applies only for relatively high Reynolds numbers (450<Re<1900), so this process does not yield realistic values for the other liquids tested in this study. A more general-purpose terminal velocity equation may allow extraction of physical parameters for a wide range of liquids. By using smaller bubbles (Re<1), which obey Stokes’s law, it should be possible to determine viscosity as well. The bubble resonance damping may also provide a qualitative measure of the viscosity.
The original version of this article appeared in Philosophical Magazine, Vol. 83, No. 24, August 21, 2003, pp. 2815–2827.
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Naveen Neil Sinha was in his junior year at Los Alamos High School, Los Alamos, NM, when he carried out the research described here. He won one of the top three prizes (Intel Foundation Young Scientist Award) at Intel’s 2002 International Science and Engineering Fair, and has applied for a patent based on this research. He is now a first-year student at Stanford University, and can be reached at firstname.lastname@example.org.