October 2003
Table of Contents

Bubble-Based Chemical Sensing
for the Process Industries

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


Testing the quality and consistency of liquids used in the process industries poses challenges that are currently being addressed by many universities and other research institutions. This article presents a novel technique that takes advantage of the complex behavior of air bubbles as a way to analyze a liquid. The behavior of bubbles in liquids has traditionally been studied using techniques such as high-speed photography and laser Doppler anemometry that can analyze only a single aspect of a bubble’s behavior, and furthermore are limited to transparent liquids. There is a need for a new, simple approach that overcomes the present limitations and lends itself to automated analysis.

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
The first phase of the research focused on observing the bubble’s behavior—its resonance frequency, terminal velocity, shape oscillation frequency, and rise path. The next step evaluated the ways these parameters were affected by the properties of the liquid. The work ultimately led to the idea of using the bubble as a liquid characterization sensor.

There are three stages to a gas bubble’s evolution:

  1. Formation and growth at the tip of a submerged nozzle
  2. Detachment and resonance
  3. Rise to terminal velocity

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:

equation (1)


R0   =   bubble radius
  =   ratio of specific heat at constant pressure to constant volume
p0   =   hydrostatic pressure of surrounding liquid
  =   liquid density

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:

equation (2)


c   =   speed of sound in liquid of interest
fr   =   received frequency
fs   =   source frequency

These equations can be solved in Mathematica [3], 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.

Test Setup
As shown in Figure 1, the experimental setup consisted of a metal syringe needle positioned vertically at the bottom of a liquid-filled tube.

Figure 1. The test setup was designed to produce bubbles in water and analyze their behavior in response to the presence of additives. The Doppler-based technique could be used for water-quality monitoring and for QC in the process industries. Figures reprinted by permission of Philosophical Magazine and Taylor & Francis Ltd.

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).

Figure 2. To monitor bubble speed as a function of time, the output of the Doppler probe receiver was mixed with that of the function generator to form the sum and difference frequencies.

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
The measurements were made with a digital storage oscilloscope and then imported into a desktop computer for graphing and data analysis by Origin scientific graphing and analysis software [4]. One of Origin’s built-in analysis tools was used to perform the Fourier transform to determine the resonance frequency. Since Origin is fully programmable, a custom Origin C program was created using the software’s built-in Numerical Algorithms Group function set to compute the short-time Fourier transform (STFT) of the Doppler instrument data. Origin was also used to plot the data on the speed of the bubble over time.

By looking at specific portions of the graph in Figure 3, different stages in the evolution of the bubble can be observed.

Figure 3. Data on complete bubble evolution, from formation, to detachment from the needle tip, to rise toward terminal velocity, are collected with a digital storage oscilloscope and imported into a desktop computer for graphing and analysis. The original resonance signal is plotted in (A), and the short-time Fourier transform of the Doppler data in (B).

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
Fast Fourier transforms were used to find the resonance frequencies of the bubbles, from which their size could be determined. To analyze the data from the Doppler probe, the custom-made STFT routine divided the signal into short segments and then took the Fourier transform of each (see Figure 4).

Figure 4. A comparison of the original time-amplitude plot (A) and short-time Fourier transform (STFT) contour plot (B) reveals how joint-time frequency analysis can be applied to actual bubble data.

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
Bubble behavior was studied in various liquids including water and water with dishwashing soap, with isopropyl alcohol, and with suspended particles of turmeric. In each instance, there were very observable differences in the patterns.

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).

Figure 5. When a surfactant (dishwashing liquid) is added to the water, the bubbles become smaller and their resonance frequency increases markedly (A). A short-time Fourier transform of the Doppler data reveals that the bubbling rate increases, terminal velocity decreases, and shape oscillations disappear (B).

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).

Figure 6. The addition of isopropyl alcohol reduces the size of the bubbles and increases their resonance frequency, as shown by a Fourier transform of the resonance signal (A). A short-time Fourier transform (B) shows that bubbling rate increases, terminal velocity decreases, and the shape oscillation frequency increases.

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).

Figure 7. With turmeric added to the water, a Fourier transform shows the bubble resonance signal unaffected by the suspended particles (A). A short-time Fourier transform of the Doppler data (B) indicates a reduced terminal velocity and a disappearance of the shape oscillations. (Note that the time scale is expanded from previous plots.)

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.

Figure 8
Comparison of Measurements in Four Liquids
Freq. (Hz)
Bubbling Rate
Water (Exp.)
(Theor. Pred.)
1.44 ±0.05
86.7 ±5.5
0.311 ±0.009
Alcohol (Exp.)
(Theor. Pred.)
1.05 ±0.02
100 ±9.5
0.192 ±0.008
Soap (Exp.) 1.12 ±0.09 none 0.190 ±0.006 ~6
Turmeric (Exp.) 1.42 ±0.07 none 0.248 ±0.051 ~2

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:

equation (3)

equation (4)

equation (5)


  =   liquid surface tension
fo   =   bubble resonance frequency
fn   =   shape oscilation frquency
VT   =   terminal velocity
k   =   1.8 for monocomponent liquids and 1.0–1.4 for mixtures

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).

Figure 9
Liquid Property Determination
Liquid Observable
Calculated Value Literature Value
(c = 1.8)
fn = 86.7 Hz = 0.988 ±0.039 g/cm3 = 1.000 g/cm3
f0 = 2273 Hz R0 = 1.465 ±0.038 mm N/A
U0 = 0.311 m/s = 77.0 ±1.5 mN/m = 72.9 mN/m
Isopropyl alcohol/
(c = 1.0)
fn = 100.3 Hz = 0.931 ±0.13 g/cm3 = 0.940 g/cm3
f0 = 3249 Hz R0 = 0.963 ±0.08 mm N/A
U0 = 0.192 m/s = 36.0 ±0.955 mN/m = 27.38 mN/m

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.

A technique has been demonstrated that can monitor all stages of an air bubble’s evolution. Easy visualization of differences of bubble behavior in liquids is possible with advanced software and a standard desktop computer. This technique should work for any liquid through which sound can travel, including denser liquids. In contrast to the requirements of high-speed photography, the liquid need not be transparent. The technique therefore has several potential industrial applications. It could be adapted for water-quality monitoring and for process and quality control in various industries such as chemical, medical, and food processing.

The original version of this article appeared in Philosophical Magazine, Vol. 83, No. 24, August 21, 2003, pp. 2815–2827.

1. Leighton, T.G., The Acoustic Bubble, Academic Press, London, 1994.

2. Fan, L-S., and K. Tsuchiya, Bubble Wake Dynamics in Liquids and Liquid-Solid Suspensions, Butterworth-Heinemann, Boston, 1990, pp. 36–43.

3. Mathematica: A popular symbolic mathematics application for scientific research and engineering analysis and modeling.

4. OriginLab Corp.: Versatile scientific graphing and analysis software designed for the industrial and academic sectors.

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 naveen.sinha@stanford.edu.

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