Bubble-Based Resonance-Doppler Sensor for Liquid Characterization

Transcription

1 Bubble-Based Resonance-Doppler Sensor for Liquid Characterization Naveen N. Sinha Los Alamos High School Los Alamos, New Mexico (55) Abstract I have developed a novel acoustic technique that can monitor all stages of an air bubble s evolution, from its formation and growth at a nozzle, through its detachment and resonance, to its rise towards terminal velocity, in order to derive multiple physical properties of the surrounding liquid. Other methods, such as high-speed photography and laser Doppler anemometry can study only one aspect of the bubble evolution. This technique, on the other hand, uses passive acoustic listening combined with active ultrasonic Doppler observation to study all aspects of the evolution. The setup consists of a metal syringe needle positioned vertically at the bottom of a water-filled tube. A small aquarium pump forces air through the needle, forming a series of evenly spaced, mm-sized air bubbles. A hollow cylindrical transducer is located around the needle and a dualelement transducer is positioned several centimeters above the tip of the needle. To continuously monitor the motion of the bubbles, I constructed a frequency-mixing-based Doppler system and used the Short-Time Fourier Transform technique. The cylindrical transducer detects the resonance of the bubble following its detachment. The Doppler setup detects both the growth and rise of the bubble, including shape oscillations and the terminal velocity. All steps in the evolution of the bubble are affected by the presence of contaminants (surfactants, suspended particles, and alcohol). Each measurement agrees well with theory. This technique has a real potential for use as a novel liquid characterization sensor in many industrial applications (e.g., chemical, environmental, food and medical).

2 Table of Contents INTRODUCTION... 1 METHODS... 3 RESULTS... 5 CONCLUSIONS... 9 REFERENCES... 1 Introduction The behavior of gas bubbles in liquids has been studied in the past several decades with a variety of techniques, including high-speed photography, laser Doppler anemometry, and passive acoustic measurements (Leighton, 1994). All of these methods focus on only a single aspect of the bubble evolution, such as only the formation, the detachment, or the rise through a liquid. My goal is to develop a general technique that can monitor all these aspects with a single system. This technique consists of two main components: (1) passive listening of the bubble with a hollow cylindrical transducer to study bubble resonance, and (2) an active Doppler (Time- Frequency) method to study all the other aspects, such as bubble growth, rise path, terminal velocity, and shape oscillations. There are three stages to a gas bubble s evolution: (1) formation and growth at the tip of an underwater nozzle, (2) detachment and resonance, and (3) rise to terminal velocity. First, the bubble grows to a finite size at the nozzle opening, determined by the radius of the nozzle opening and the properties of the surrounding liquid (Longuet-Higgins et al., 1991). As the bubble pinches off and detaches from the nozzle, it resonates (breathing-mode) at a natural frequency determined primarily by its radius and the liquid density. The frequency f of this oscillation was first calculated by Minnaert (Leighton, 1994): 1 3κ p f =, 2π R ρ (1) where R is the bubble radius, κ is the ratio of specific heat at constant pressure to constant volume, p is the hydrostatic pressure of surrounding liquid, and ρ is the liquid density. After the 1

3 bubble detaches, it accelerates to its terminal velocity U, which depends on the buoyant and drag forces on the bubble (Bozzano and Dente, 21): U 8 3 gr 2 =, (2) C D where g is the acceleration due to gravity and C D is the drag coefficient. The drag coefficient depends on physical properties of the liquid and bubble size. The presence of contaminants (e.g., surfactants, suspended particles) has a major effect on the rise of the bubble by immobilizing the air-liquid interface. Also as the bubble rise, it undergoes shape oscillations (dimarco et al., 21). The frequency of these oscillations (Leighton, 1994) is given by: 2 σ ω n ( n 1)( n + 1)( n + 2) ρ R = (3) where ω n is the angular frequency of oscillations, n is the mode number, and σ is the surface 3 tension. The rise of the bubble can be studied by observing the Doppler frequency shift of sound reflected from the bubble. Two shifts in frequency occur: (1) as the moving bubble intercepts sound waves from the transmitter, and (2) as the bubble reflects the incident sound waves, which are detected by the receiver. The speed, U, of the bubble is related to the speed of sound, the source frequency, and the received frequency (Andrews, 2) as: ( f r f s ) U = c (4) ( f + f ) r s where c is the liquid sound speed, f r is the received frequency, and f s is the source frequency. The objective of my research is to observe the entire evolution of an air bubble in liquid, from its formation and growth at a nozzle, through its detachment and resonance, to its rise towards terminal velocity, with a single acoustic setup to determine multiple physical properties of the surrounding liquid. It should be possible to derive multiple physical characteristics (density, surface tension, viscosity, presence of contaminants) of a liquid by studying the evolution of a rising bubble with a combined Resonance Doppler technique that has never been used before. 2

4 Methods To produce the bubbles, an aquarium pump (Penn-Plax Silent-Air X2) forced air through a metal syringe needle, connected by a thin plastic tube. The flow rate was adjustable both by a valve and by changing the voltage applied to the air pump with a Variac (variable voltage regulator). The syringe needle passed through the bottom of a plastic tube (12-cm long, 4.8-cm inner diameter, 1.8-mm thick), which was sealed with a silicone sheet. The tube was filled to 6 cm above the syringe needle with water. All measurements were made with the water temperature at 19 C. Doppler probe Doppler system x1 Bubble Plastic tube Syringe needle Water Cylindrical transducer DSO 21 To computer Valve To air pump Figure 1: Resonance-Doppler setup A hollow cylindrical piezoelectric transducer (2.55-cm long, 2.3-cm inner diameter, 1.2-mm thick, Valpey-Fisher, MA), placed around the tip of the syringe, converted the sound waves produced by the resonating bubble into an electric signal. This signal was amplified 1 times by a differential input amplifier (Allison Tech. Corp. model DFA 5). To monitor the speed of the bubble as a function of time, I constructed a simple frequencymixing based Doppler system. This used a function generator (Telulex SG-1) to excite the 3

5 transmitter of a Doppler probe (dual-element, 9.4 MHz, 1-cm long, 9.5-mm diameter, Parks Medical Pencil Probe), normally placed 6 cm above the syringe tip. The receiver of the Doppler probe detected the sound reflected from the bubble. The amplified (54 db, Panametrics Ultrasonic Preamplifier, model #5662) and high-pass filtered output of the Doppler probe was mixed (Mini Circuits Mixer, model ZAD-8) with the input signal to produce the sum and difference frequencies. This signal was then low-pass filtered to obtain the Doppler difference frequency (Eq. 4). The Doppler setup is shown schematically below: Doppler Electronics Function Local Generator Local oscillator oscillator T T Doppler probe R R 54 db To DSO High-pass filter F c = 5MHz Mixer Low-pass filter F c = 1kHz Figure 2: Schematic illustration of Doppler electronics setup. The output of both the cylindrical transducer and the Doppler system was sent to a 2-channel, digital storage oscilloscope (Link Instruments DSO-21, 1MHz max. sampling rate). The DSO digitized the data and transferred it through a parallel port to a computer for analysis. The two main analysis techniques that I used were Fast Fourier Transforms (FFT) and Joint Time- Frequency Analysis. The FFT was used to determine the frequency spectrum of the resonance of the bubble (see Fig. 3): Amplitude (V) Original Signal Time (sec.) Amplitude (V) Fourier Transform Frequency (Hz) Figure 3: Example of the Fourier Transform applied to a bubble resonance signal 4

6 In contrast, a Time-Frequency Analysis, performed using the Short-Time Fourier Transform technique (STFT), shows the frequency content of a signal as a function of time. The STFT works by dividing the signal into small segments and then performing an FFT on each segment of the data. I used the time-frequency analysis to study the dynamics of the bubble growth and rise. Results To study the formation of the bubbles, the Doppler probe was positioned 2.5 cm above the needle and Resonance-Doppler measurements were made (see Fig. 4). A t 1 there was a slight spike in the resonance (cylindrical transducer) signal probably due to a meniscus forming at the tip of the syringe (left). From t 1 to t 2 the bubble grew on the top of the syringe (low frequency Doppler signal). The growth process started with the bubble rapidly expanding upwards, and then growing horizontally, which showed a decrease in velocity in the Doppler signal soon after t 1. At t 2 the bubble detached and resonated. After t 2 the bubble accelerated to its terminal velocity while undergoing shape oscillations (oscillations in STFT signal, right). Amplitude (V) Transducer and Doppler t 1 Doppler Resonance t Amplitude (V) Velocity (m/s) Time-Frequency Plot t 1 Theoretical Terminal Velocity t 2 Amplitude Time (s) Time (s) Figure 4: Entire Bubble Evolution. Left Original resonance (from cylindrical transducer) and Doppler data. Right STFT of Doppler data. Next, I studied the effect that a surfactant (Shaklee Satin Sheen Dishwashing Liquid) had on the rising bubbles. The soap solution (1 ml in 1 ml water) had an enormous effect on the bubbles (see Fig. 5). The resonance peak increased in frequency and became more damped (left). The 5

7 increase in resonance peak frequency is due to the decreased size of the bubbles. The bubbles were smaller in the soap solution than in plain water since they detached sooner, because of the lower surface tension. In addition, the terminal velocity was almost half as high, the bubbling rate increased by over a factor of two, the shape oscillations disappeared, and other characteristics of the rise changed significantly (right). All of these observations were most likely due to the presence of surfactant molecules at the air-liquid interface. FFT Amplitude Bubble Resonance FFT Frequency (Hz) Pure Water 1 ml Soap Velocity (m/s) Velocity (m/s) Bubble #1 #2.2.1 Bubble #1 STFT of Doppler Time (sec.).5 #3 Bubble #2 1 ml soap added Time (sec.) #4 Plain Water #5 Figure 5: Effect of Surfactant. left Fourier Transform of bubble resonance signal. Right STFT of Doppler data. Solutions of isopropyl alcohol and water (76% water, 24% alcohol by volume) were used to study the effect of organic chemical contaminants on the bubbles. The alcohol clearly shifted the resonance peak to the higher frequency and increased the damping (left). In addition, the terminal velocity was significantly reduced, the bubbling rate increased, the shape oscillations became smaller, and a deceleration of the bubbles became visible (right). The period of bubble growth is also shorter, showing that the bubbles detached from the nozzle sooner. The effects were similar to those of the surfactant, likely since both the alcohol and the soap lower the water surface tension. 6

8 FFT Amplitude Bubble Resonance FFT 1% Water 34% Alcohol, 66% Water Frequency (Hz) Velocity (m/s) Velocity (m/s) STFT of Doppler Bubble Growth Theoretical Terminal Velocity Time (s) % water, 34% alcohol Theoretical Terminal Velocity Bubble Growth 1% Water Time (s) Figure 6: Effect of isopropyl alcohol. left Fourier Transform of bubble resonance signal. Right STFT of Doppler data The measurements below show the effect of suspended particles (turmeric) in water. I started with pure water, and then added 2 ml of a suspension of turmeric in water at the maximum concentration. The suspended particles had little effect on the resonance of the bubble (left), probably since preceding bubbles removed particles from the area in front of the syringe. However, the rise of the bubble changed significantly (right) as the particles collected on the bubble surface. Instead of a gradual acceleration, the bubbles in the contaminated water quickly reached their terminal velocity. Also, the shape oscillations completely disappeared. These changes occurred because the suspended particles stick to the air-water interface of the bubble, making it a rigid surface. Bubble Resonance FFT.5 STFT of Doppler FFT Amplitude Water With suspended particles Frequency (Hz) Velocity (m/s) Velocity (m/s) Time (s) No Shape Oscillations Plain Water Suspended Particles Time (s) Figure 7: Effect of suspended particles. Left Fourier Transform of bubble resonance signal. Right STFT of Doppler data. 7

9 The table below summarizes the experimental results of various aspects of bubbles and compares some of the results with theoretical predictions: Bubble Radius (mm) Shape oscillation Freq. (Hz) Terminal velocity (m/s) Bubbling rate (bub./s) Water (Exp.) ~ 2 (Theor. Pred.) Alcohol (Exp.) ~ 4 (Theor. Pred.) N/A Soap (Exp.) none.19.6 ~ 6 Turmeric (Exp.) none ~ 2 Bubble radius: Equation 1 was used to calculate the experimental bubble size. For the theoretical predictions I used the Longuet-Higgins (Longuet-Higgins et al., 1991) theory. The theory applies only to very low flow rates, which was not the case in the present experiment, leading to a discrepancy. The addition of either soap or alcohol lowered the bubble radius, most likely due to a decrease in the surface tension. Incomplete mixing of the solutions may have been a small source of error. Shape Oscillations: The frequency of the oscillations in the time-frequency plots was determined by averaging the period of four oscillations and taking the reciprocal. The theoretical frequencies (Eq. 3) were determined for a second-order (n=2, ellipsoidal) oscillation and agrees very well with experiment. Alcohol increased the frequency of the shape oscillations as expected (smaller bubble radius). Bubble Rise: The theory by Bozanno and Dente (Bozanno and Dente, 21) was used to determine the drag coefficient, which was then used in Eq. 2 to find terminal velocity. The theoretical value agreed well with the experimental value. The decrease in the terminal velocity of the isopropyl alcohol/water mixture is consistent with theory (smaller bubble radius). I used a linear extrapolation to determine the density and viscosity of the alcohol/water mixture, which 8

10 likely led to the greater discrepancy with the experimental value. The slight differences between trials could be due to changes in the path of the bubble. Physical Property Determination: Surface tension was determined from the bubble radius and shape oscillation measurements made with the Resonance-Doppler technique. The predicted values were.74 mn/m for water (actual =.73) and.41 mn/m for the alcohol/water mixture (actual =.37 1 ). This shows how Resonance-Doppler measurements can be used to determine physical properties of the liquid. Conclusions This study clearly demonstrates that it is indeed possible to monitor the entire evolution of a bubble using a novel, Resonance-Doppler technique. Moreover, it also shows that bubble evolution can provide information about the physical characteristics of the surrounding liquid. To the best of my knowledge, this is the first time that bubble growth, shape oscillations, and terminal velocity have been studied using an ultrasonic Doppler technique. All aspects of the bubble evolution are affected by the physical characteristics of the liquid (e.g., surface tension, viscosity, density, presence of contaminants), which may allow this technique to be used as a novel, multi-purpose, bubble-based liquid characterization sensor. I plan to study a greater range of liquids with this technique in order to better determine the relationships between properties of the liquid and bubble behavior. This could lead to simple, automated sensors for characterizing liquids. My ultimate objective is to develop a simple, noninvasive, bubble-based sensor for liquid characterization that can be used widely in many applications, such as in water quality monitoring, or in the chemical, medical, and food industries. 1 Based on water-ethanol mixture, the value for a water-isopropanol mixture may be slightly different 9

11 Acknowledgements I would like to thank Mr. Pat Turner of Interferometrics, Inc. for donating equipment necessary to produce the bubbles such as the various types of syringes, needles and valves, the silicone sheet, and plastic tubing. He also gave very helpful advice about controlling the bubble flow. Dr. Greg Kaduchak of LANL first showed me how to use the MATLAB programming language. Learning MATLAB helped me greatly in the analysis of the data. I would also like to thank my dad for his help in photographing the setup and proofreading the paper. References Andrews, DGH, An Experiment to demonstrate the principles and processes involved in medical Doppler ultrasound, Phys. Educ. 35(5) September (2) Bozzano, G. and M. Dente, "Shape and terminal velocity of single bubble motion: a novel approach," Computers & Chemical Engineering. 25 (21) Di Marco P., Grassi W., Memoli G., Experimental Study on Terminal Velocity of Nitrogen Bubbles in FC-72, Proc. Experimental Heat Transfer, Fluid Mechanics and Thermodynamics 21, ed. by G.P. Celata, P. Di Marco, A. Goulas and A. Mariani, Thessaloniki, GR, September 24-28, 21, ETS, Pisa, pp Leighton, T.G. The Acoustic Bubble. London: Academic Press, Longuet-Higgins, Michael S., Bryan R. Kerman, and Knud Lunde, "The release of air bubbles from an underwater nozzle," Journal of Fluid Mechanics. 23 (1991) p

12 Appendix MechanicalSetup Doppler probe (dual-element Transducer, 9.4 MHz) Hollow cylindrical piezoelectric Transducer (2.5 cm diameter, 2.5 cm length, 1.25 mm thick) Silicone sheet Needle (B-D 25G1 1 / 2,.33 mm diameter) To air pump (Penn-Plax Silent Air X2 Aquarium Pump) Flow-control valve Complete Resonance-Doppler Setup Tube with Doppler probe, transducer, needle Laptop computer Air pump Variac Digital Storage Oscilloscope Doppler instrument 11 Amplifier

13 Short-Time Fourier Transform (STFT) A Fourier Transform is an analysis technique to determine the amplitude, frequency, and phase of the sine waves needed to create any given time-series. An example of a Fourier Transform is shown below for a signal composed of four superimposed sine waves of different frequencies. This shows up as four peaks in the Fourier Transform: Original Signal Fourier Transform The Fourier Transform does not work for signals that have frequency components which change over time, since it treats the signal as if it extends infinitely in time. This problem is illustrated below: Original Signal Fourier Transform Both signals have the same frequencies present, so the Fourier Transforms are identical. However, the frequency components of the second signal change with time, which is not shown in the Fourier Transform. 12

14 STFT (cont d) In order to gain information about the times at which each frequency is present, a Short-Time Fourier Transform (STFT) can be used. This divides a signal into short segments, then takes the Fourier Transform of each segment. The separate Fourier Transforms can be displayed as a waterfall plot, as shown below: Original Signal Short-Time Fourier Transform I needed to determine how the Doppler signal changed as the bubble rose, so I used the STFT to visualize changes in the Doppler frequency over time. Although the STFT is used extensively in a variety of fields, to the best of my knowledge this approach has never before been used to study bubble rise using ultrasonic Doppler. 13