DEVELOPMENTS IN MICRO-BUBBLE MEASUREMENT TECHNIQUES FOR CAVITATION AND PIV EXPERIMENTS

Abstract

Several benchmark tests have been carried out to compare the bubble size distributions, generated by electrolysis and microfluidics and measured by phase Doppler anemometry, shadowgraphy and interferometric techniques. The differences in the mean diameter range from 50% in a less controlled environment to 15% in a highly controlled environment. Mainly due to optical access, a defocussing technique such as IPI or ILIT appears as the most practicable technique for an experimental use in cavitation tunnel (like GTH at DGA TH) or a towing tank (like the DWB at MARIN). Its development still requires a reliable concentration measurement. First, the cross-sectional area of the laser beam was measured using bubbles with a very narrow size distribution, which has proven to be difficult and time-consuming. Second, efforts were done to produce a stable cloud of water droplets in a sealed vessel filled with oil. However, the dispersed droplets dissolved almost completely within 1.5 hours. Third, a semi-empirical model was developed of the measurement volume using the specified diameter of the laser beam and the measured bubble intensity data originating from defocus technique. The results were mostly good but an unexpected dependency on the exposure time was observed. Fourth, a bubble cloud was generated by electrolysis and a reference technique based on defocused shadowgraphy was applied. Simultaneous concentration measurements with the reference and defocus technique still need to be carried out.

Full text

DEVELOPMENTS IN MICRO-BUBBLE MEASUREMENT TECHNIQUES FOR
CAVITATION AND PIV EXPERIMENTS
Miloš Birvalski, MARIN, The Netherlands
Romuald Boucheron, DGA Techniques Hydrodynamiques, France
Martijn van Rijsbergen, MARIN, The Netherlands
Didier Frechou, DGA Techniques Hydrodynamiques, France
Several benchmark tests have been carried out to compare the bubble size distributions, generated by
electrolysis and microfluidics and measured by phase Doppler anemometry, shadowgraphy and
interferometric techniques. The differences in the mean diameter range from 50% in a less controlled
environment to 15% in a highly controlled environment. Mainly due to optical access, a defocussing
technique such as IPI or ILIT appears as the most practicable technique for an experimental use in
cavitation tunnel (like GTH at DGA TH) or a towing tank (like the DWB at MARIN). Its development
still requires a reliable concentration measurement. First, the cross-sectional area of the laser beam was
measured using bubbles with a very narrow size distribution, which has proven to be difficult and time-
consuming. Second, efforts were done to produce a stable cloud of water droplets in a sealed vessel filled
with oil. However, the dispersed droplets dissolved almost completely within 1.5 hours. Third, a semi-
empirical model was developed of the measurement volume using the specified diameter of the laser
beam and the measured bubble intensity data originating from defocus technique. The results were
mostly good but an unexpected dependency on the exposure time was observed. Fourth, a bubble cloud
was generated by electrolysis and a reference technique based on defocused shadowgraphy was applied.
Simultaneous concentration measurements with the reference and defocus technique still need to be
carried out.
1 Introduction
Micro-bubbles are naturally present in most cavitation tunnels. Their size vs. concentration spectrum is
mostly influenced by changing the dissolved gas content and the ambient pressure. Some tunnels have a
more sophisticated control system which injects nuclei upstream of the test section and resorbs them
downstream of the test section. For several decades, the essential role of nuclei in cavitation inception is
acknowledged in maritime research. However, the relation between measured spectra (size and
concentration) and observed cavitation characteristics is not yet understood. This is clearly illustrated by
the several orders of magnitude difference in measured nuclei concentrations in the same cavitation
tunnel and between tunnels in the report of the ITTC specialist committee on water quality and cavitation
[1]. More specifically, Heinke et al. [2] have observed a strong increase of the cavitation occurrence on
a 5-bladed propeller (from 2 to 4 blades with fully developed sheet cavitation) with an increase of the
oxygen content from 60 to 77% in the HYKAT but the measured nuclei concentration showed only a
negligible increase from 0.42 to 0.45 cm-3. The following challenges still remain:
1. To obtain an accurate measurement of the spectra of both gas and solid nuclei. The available
measurement techniques give large differences in concentration in the same cavitation facility. Some
techniques can measure only gas nuclei and others both gas and solid nuclei.
2. To measure the nuclei content in the flow upstream of the cavitating object (non-intrusive, in-situ).
3. To investigate systematically the sensitivity of cavitation and cavitation-induced noise to several
aspects of the nuclei content such as phase (gas or solid), size and concentration.

For PIV measurements, the water is normally seeded with particles near the density of water. In some
cavitation tunnels, the use of such small particles would give mechanical problems in seals, but PIV
measurements would still be desirable. Therefore, the use of micro-bubbles as tracers is thought to be the
solution. These micro-bubbles need to be small enough to follow the flow and large enough to reflect the
light. Reliable in-situ measurements of micro-bubble (nuclei) size vs. concentration spectra are needed
to better understand cavitation inception mechanisms and to verify bubble injection systems for PIV
measurements. This paper reviews the state-of-art on nuclei measurement systems, discusses the current
activities in the Community of Practice on Nuclei within the Hydro Testing Forum and gives a future
perspective on the application of nuclei measurements.
2 Size distribution
2.1 Brief technique description
Many techniques are available to size microbubbles. The most used are shadowgraphy, Phase Doppler
Anemometry and defocused techniques. The principle of these 3 techniques are briefly described in this
section. It has to be noticed that microbubbles could also be measured by holography [3], a Centerbody
Susceptibility Meter [4, 5] and for larger bubbles by fibre-optic probes. Due to practical access and non-
intrusive issues, only optical techniques are useful in maritime testing environments.
Shadowgraphy is a relatively simple technique consisting of back illuminating an environment. A camera
captures the image allowing sizing any object in the field of view. This technique needs an in-situ
calibration and is sensitive to out-of-plane object for non-perfect in-line set up. Image processing is also
challenging for very small bubbles.
Phase Doppler Anemometry (PDA) is based on phase differences of the light scattered by a particle. The
classical set up is depicted by Figure 1.
Figure 1. Left: Principle of PDA. The phase difference is measured by two photomultipliers at an angle
in a given plane [6]. Right: Scattered light pattern generated by an air bubble in water for
perpendicular/parallel polarized light (from DANTEC).
Two photomultipliers record light scattered by a particle. Phase differences are observed between the
two signals and can be linked to the diameter of the particle if the optical indices of the media are known
(in our application air and water, as shown by Figure 1, right). Only some discrete scattering angles are
available, mainly due to light intensity.

The defocus technique (designated in this paper as Interferometric Particle Imaging, IPI or
Interferometric Laser Imaging Technique, ILIT) is an imaging technique for sizing spherical bubbles.
This technique uses a laser beam (or a laser sheet) which is illuminating a bubble observed by a defocused
optical system as presented by Figure 2a.
Figure 2. Left: principle of IPI technique, adapted from [5]. Centre: illustration of Lorentz-Mie
scattered light of a 80µm air bubble in pure water exhibiting the oscillating behaviour against
scattering angle. Right: Example of an image of a bubble exhibiting the vertical fringes.
For microbubbles with diameters larger than the wavelength of the laser (typically hundreds of
nanometres), the scattered light can be described by the Lorenz-Mie theory [7–9]. An example of the
pattern generated by a 532 nm laser scattered by a 80 µm air bubble in water is presented in Figure 2b.
The technique is based on measuring the oscillating behaviour of light intensity against scattering angle.
The calibration factor used in this technique depends only on the effective collecting angle of the optical
system and the scattering angle [6]. The coefficient linking the fringe spacing and the diameter Kw
depends on the mean scattering angle and wavelength of the light, as depicted by Figure 3.
Figure 3. Calibration factor Kw for IPI technique for red/green/blue laser (660/514.5/488 nm
respectively) against mean scattering angle. This figure is based on results published in [5].
2.2 First benchmark tests
As a first step in the collaboration, a series of benchmark tests have been carried out in a small water
tank to measure bubble size distribution with various techniques, compare the results and investigate the

causes of the differences. A small water tank was designed with 4 optical quality windows to allow for
simultaneous measurements with different techniques, see Figure 4. The water tank was filled with 20
litre demineralised water and 2 g/l NaCl as electrolyte. Microbubbles were generated by two platinum
wires with a thickness of 100 m. A power source at constant current mode enabled a stable bubble
production.
Figure 4. Left: design of water tank: 300 mm cube and 4 optical quality windows; Centre: insert with 2
platinum electrolysis wires; Right: bubble curtains rising from anode (left/back producing large
oxygen bubbles) and from cathode (right/front producing small hydrogen bubbles). Laser beams of
PDA are focussed at the oxygen bubble curtain.
MARIN hosted the benchmark tests and provided the water box with electrolysis set-up and nuclei
measurements were carried out by Rostock University, Dantec and Insean (CNR-INM). The original idea
was to measure simultaneously with several techniques. Due to practical reasons such as conflicts
between the required space for the different set-ups, the measurements were carried out sequentially. The
temperature of the water was not measured.
Figure 5 shows the measured bubble size distributions at the cathode and the anode wires. At the cathode
large differences were found between the measurement techniques. The PDA size distribution shows the
smallest bubbles with a mode diameter of 25 m. The IPI size distribution shows slightly larger bubbles,
but the shadowgraphy size distribution indicates much larger bubbles. A mode of 75 m can be seen, but
this value is most likely influenced by the clear cut-off: no bubbles smaller than 40 m were found due
to limitations in the resolution and the image processing algorithm. At the anode, the differences between
the measured distributions are smaller, the mode diameters range from 85 to 125 m; this is still a
difference of 50%. Again, the shadowgraphy technique 1 indicates the largest bubbles. Now the PDA
size distribution does not show the smallest bubbles, but IPI and shadowgraphy 2.
Various causes are thought to have contributed to the differences in the size distributions, such as
systematic errors in the calibrations, limitations in measuring range, measurement position relative to the
wires and reproducibility of the electrolysis bubble generation process. The latter may also have been
affected by deviations in water temperature.

Figure 5. Results of shadowgraphy, PDA and IPI techniques at a current of 33 mA. Left: hydrogen
bubbles; right: oxygen bubbles. All bubbles larger than 250

m are collected at the bin with 255

m
centre diameter.
2.3 Second benchmark tests
Tests have been performed at DGA with a microfluidic device generating monodisperse microbubble
train. The main objective of these tests was to understand the results spread observed in many
experiments and to understand (and therefore improve) the complete set-up of each technique. Figure 6
presents the set-up of the tests done with Phase Doppler Anemometry, shadowgraphy and the defocus
technique (labelled as ILIT in Figure 6).
Figure 6. Experimental set up for comparison of three techniques dedicated to bubble sizing. Left:
global view during PDA measurement. Centre: top view showing angles in set-ups. Right: typical
bubble train captured by shadowgraphy system. This figure is based on results published in [6].
The injector used in this experiment allows a quasi-stable working point after approximately 30’ running.
The large number of bubbles generated allows also a good estimate of statistics. In order to enhance the
measurement accuracy, all important parameters of each technique have been analysed. Particular efforts
on calibration and on image/signal processing for each technique have been made. The combination of
the three techniques on the same experimental apparatus is very challenging, especially if we want to
optimize each technique. The PDA technique is sensitive to the angle between laser and receivers, so the

available optical access limits the optimisation of the design. The ILIT (defocus) technique is also
sensitive to the angle between the laser and the camera and particular attention has to be paid to the angle
set up in order to calibrate the imaging system accurately [5, 6]. Figure 7 shows comparisons of the size
distributions and mean diameters measured with the various techniques.
Figure 7. Left: Comparison of the size spectra for the same working point of the micro-bubble injector
for the 3 techniques. Right: comparison of mean diameter measured by each technique for 5 different
working points. The semi-emperical model by YLEC (injector manufacturer) was fitted previously to
shadowgraphy data. This figure is based on results published in [6].
The left graph in Figure 7 shows the comparison of the microbubble size spectra for the same working
point of the microbubble injector. This comparison is not direct and easy because the volume/area of
each technique is different. The large number of bubbles detected by shadowgraphy allows to filter the
results spatially close to the measuring volume of the other techniques. The light-red spectrum was
measured by shadowgraphy close to the measurement volume of the PDA (represented in dark red). The
light-blue spectrum was measured by shadowgraphy close to the measurement volume of the ILIT
(represented in dark blue for the blue laser and in green for the green laser). Even though the analysed
number of bubbles are quite different which can cause some discrepancies in shape, the mean diameters
observed by the techniques are clearly different. Some of these differences could be explained by
parameters not taken into account (like the different incidence angles refracted by the glass windows). A
thorough analysis is done in [6] showing the order of magnitude of the main set up parameters of each
technique. Nevertheless, as can be observed in the right-hand graph in Figure 7, a dispersion of the mean
diameter of approximately 15% (around the average diameter of 100 µm) remains due to the different
techniques.
3 Concentration measurement
The crux of a nuclei concentration measurement is to determine the measurement volume that is used
together with the detected number of nuclei to arrive at the nuclei concentration (in e.g. cm-3). The
measurement volume in the IPI system applied in MARIN is cylindrical, since the laser is in the form of
a beam. The volume is calculated by multiplying the length of the beam visible in the FOV by the cross-
sectional area of the beam. The cross-sectional area, however, is dependent on the size of the bubble
crossing the beam; a larger bubble scatters more light and is therefore visible in a larger area than a
smaller bubble.

3.1 Laser beam cross-section
The first approach to arrive at the measurement volume was to measure the cross-section of the laser
beam directly [10]. This was done by submerging a microfluidic chip with an X-junction of 100 μm into
a water-filled vessel (Figure 8). A microfluidic pump provided flow of air and water at controlled rates.
The outlet of the chip was pointed upwards and it produced bubbles of several hundred micrometers in
diameter at several bubbles per second. The bubble train produced in this way was translated in the
direction of the IPI camera, which was perpendicular to the direction of the laser beam coming from the
side. IPI images of the bubbles were captured at a high speed as the bubbles were rising through the beam.
The chip was translated in steps of 50 μm across the beam (Figure 8c) and a series of images was recorded
at each position. The images were then processed using an in-house developed IPI processing script; the
results are shown in Figure 9.
Figure 8. Experimental setup used to determine the measurement volume in IPI: a) water-filled tank,
camera, laser and microfluidic chip, b) side-view of the microfluidic chip producing a bubble train that
is translated to intersect the laser beam, c) a scheme of the method to determine the measurement
volume by translating a bubble train across the laser beam, d) a raw IPI image of a bubble in the laser
beam. This figure is based on results published in [10].
Figure 9a shows the intensity of the IPI bubble images (an example is shown in Figure 8d) which were
recorded when three bubbles passed through the laser beam. The IPI processing algorithm detected the
bubbles at time instances marked with the red line. The distance travelled by the bubble was calculated
by multiplying the time it took the bubble to cross the laser beam with the rise velocity (measured using
a separate shadowgraphy system); this distance is shown as the vertical coordinate in Figure 9b. When
the bubble paths across the entire laser beam are joined together, they form an image of the detection
area in the cross-section of the beam for a particular bubble size. The area of this image (0.78 mm2) is
multiplied by the beam length (87.3 mm) to arrive at the size-dependent measurement volume (68.1 mm3
for a bubble diameter of 292 μm). This measurement needs to be repeated for a number of bubble sizes
in the expected diameter range (~20 – 400 μm) to obtain a full measurement volume vs. bubble size
curve.

Figure 9. Measured laser cross-section area resulting from the method applied in Figure 8: a) light
intensity of three bubbles crossing the laser beam at one position; the red part of the curve is showing
where the image processing algorithm has detected a passing bubble, b) light intensity in the entire
laser cross-section; the determined area is multiplied by the length of the laser beam in the FOV to
arrive at the measurement volume for a particular bubble size. This figure is based on results published
in [10].
The advantage of the present method is that it is direct, which means it is less prone to errors. However,
the difficulty of this method is that it relies on having a very stable bubble generation. In particular, the
bubble size should stay near constant during the measurement, which might last up to half an hour
depending on the number of steps in the cross-wise direction at which the images are recorded. If the
size of the bubbles changes during this time (e.g. if there is a slow drift), the measurement volume also
changes, and the measurement needs to be repeated. Achieving such a high stability of bubble production
is very difficult, even with microfluidic equipment. A good microfluidic system might have a difference
of 10% in the bubble sizes during the time needed to perform one measurement. This makes the
application of this method—with all the failed and repeated measurements that are needed—very time
consuming. Finally, the production of a wide range of bubble diameters with several microfluidic chips
to cover the range of diameters expected in the real flow is also a difficult and time-consuming task.
3.2 Cloud of water-in-oil droplets
The second approach was to generate a stable cloud of neutrally buoyant droplets using the microfluidic
system [11]. This means that neither the number nor the size of the droplets in the cloud should change
for at least an hour (i.e. until the IPI measurements were done). It was reasoned that by oil and water
having similar densities (when compared to air and water), the droplets should not be floating to the
surface or accumulating at the bottom, especially when some flow is created in the bulk of the liquid
using the magnetic stirrer. Also, the size of the droplets should remain the same, since the dissolvability
of water in oil is low. Although such a droplet cloud may not seem representative for a bubble cloud, it
has the potential of staying the same for a longer time than a bubble cloud. Furthermore, by choosing
water-in-oil droplets, the ratio of the refractive indices is smaller than 1, just as with air bubbles in water.

The idea was to exploit specifically the ability of the microfluidic system to produce droplets one by one.
If the microfluidic chip is observed using a high-speed camera fitted with a microscope lens, all the
produced droplets could be sized and counted. Effectively, this means that the droplet cloud that was
produced—despite not being of uniform size—is fully characterized and its particle size vs. concentration
distribution is easily calculated. The IPI system could be applied to the same cloud in order to obtain the
particle size vs. particle number curve. This curve could then be calibrated (converted) into the particle
size vs. concentration distribution by comparing it to the distribution measured by observing the
microfluidic chip. The experimental setup to generate the droplet cloud is shown in Figure 10a. The
microfluidic chip is discharging water-in-oil droplets into an oil-filled vessel.
Figure 10. Experimental setup used in measurements of the droplet cloud: a) the microfluidic device is
introducing water droplets in an oil-filled vessel; the vessel is closed and the humidity inside is
measured, b-d) images of a droplet cloud 1, 13 and 25 minutes after droplet production stopped; the
cloud is disappearing as the water is dissolving into the oil. e) the number of droplets during and after
droplet production with sunflower and silicone oil in saturated conditions. This figure is based on
results published in [11].
An initial test, performed without the lid on the vessel, showed that the droplet cloud disappeared in
20 – 30 minutes after the production of droplets stopped. It was thought that the water was absorbed in
the oil and then transported through the air-oil interface into the atmosphere. The lid was then installed
to obtain a hermetically sealed vessel. A humidity sensor was installed on the inside of vessel (Figure
10a) to measure the humidity of the air pocket above the oil. Assuming equilibrium conditions, the
relative humidity in the air is the same as in the oil.
A new set of measurements was performed at (nearly) 100% humidity, which was confirmed also by the
appearance of condensation on the inner wall of the vessel. In these conditions, the droplets were
discharged for 30 minutes after which the production was stopped; the liquid was continuously and the
camera recorded photographs at 5-minute intervals. The droplets were detected and counted in these
images and the results are presented in Figure 10e. In the period from t = -30 minutes to t = 0, the number
of droplets increased as the droplets were being added to the flow. At t = 0, the production stops and the
number of droplets immediately decreased; the number reduces to almost zero before 100 minutes have
e)

passed. This procedure was followed for two types of oil: sunflower oil (which can absorb ~0.1% v/v of
water) and silicone oil (which can only absorb ~0.005% v/v). In both cases, the volume of water added
by the droplets is sufficient to exceed the 100% humidity level in the oil, even in cases with humidity
levels 91 – 97%. Despite of this, the droplets were disappearing in all cases, likely because the water was
(still) being dissolved in the oil. No other mechanism that would influence the dispersion stability (e.g.
Ostwald ripening, droplet coalescence, aggregation, breakup or sedimentation) was observed.
3.3 Semi-empirical method
After the effort to produce a stable droplet cloud was shown to be unsuccessful, a simpler and more
practical approach of determining the nuclei concentration was adopted [12]. The method used the
diameter of the laser beam specified by the manufacturer (usually given as diameter at 1/e2 power) and
assumes the beam has a Gaussian profile. This information is used together with a parabola fitted to the
measured maximum nuclei image intensities originating from IPI images to calculate the measurement
volume for each nuclei size class. An example of the measured nuclei image intensities is shown in
Figure 11a; all the bubbles recorded during one run in MARIN’s depressurized wave basin using the IPI
system are sized and their intensity are shown on the vertical axis. The plot shows both bubbles that were
correctly sized and those that were incorrectly sized. The line separating the two regions is the parabola
placed at approximately the position representing the maximum intensities recorded for different bubble
sizes. From the same graph, the minimum intensities of the different bubble sizes could also be
determined (not shown, the value was ~10 counts). With these two curves, the assumption of the
Gaussian distribution of the laser light intensity and the diameter of the laser beam, the measurement
volume shown in Figure 11b was calculated. The volume is seen to increase until a diameter of 400 μm,
after which it remains constant. This is because—in this particular case—the camera sensor saturates at
4095 counts, which is the intensity of 400 μm bubbles. Larger bubbles than this can be measured, but the
shape of the measurement volume is not a full cylinder anymore; it is hollow, since the bubbles in the
core of the beam are oversaturated and cannot be sized.
Figure 11. Method to determine the measurement volume by using the measured data and laser
specifications: a) intensity of nuclei images measured in MARIN's depressurized wave basin; a
parabola represents the maximum intensity for various nuclei sizes, b) the measurment volume
determined theoretically using the specified laser diameter and the parabola fitted in a). This figure
was previously published in [12].

Besides this, the water velocity creates—together with a finite shutter time of the camera—a
measurement volume that is slightly extended in the sailing direction. The effect is quite small in this
case (‘V motion’ in Figure 11b).
The results of the above-described method are presented in Figure 12. A variation of the system
parameters (framerate, defocus level and exposure time) was performed. The framerate variation (Figure
12a) had no effect on the results; two flow conditions were measured (characterized by a certain
combination of basin pressure p, model velocity v and electrolysis current i) and the curves measured at
different framerates correspond well to each other. The same conclusion was drawn from the variation
of the defocus level (which is effectively the area of the individual nuclei images recorded by the camera).
Here, there are again two groups of cases, measured at the same nominal flow conditions, but on different
days. Apparently, the resulting nuclei distribution is different from one day to the next, but the effect of
the changing defocus level between the cases measured on the same day was shown not to influence the
results. The variation of exposure time, however, had a significant effect on the results, see Figure 12c.
These cases were measured on the same day and at the same flow conditions, so it was expected that all
the curves would correspond to each other. This was not the case and it appears that the change from one
curve to the other (with e.g. increasing exposure time) is not linear. An additional pair of measurements
was done at texp = 125 μs and texp = 250 μs and these corresponded to each other, like in Figure 12c. It
appears, therefore, that the behaviour presented in Figure 12c is not incidental, but repeatable.
Although this theoretical method is simple and works when changing the system parameters such as
framerate and defocus level, the fact that it does not perform as well when changing the exposure time
means that it can only be used for further measurements after it has been validated (and possibly
calibrated) in the laboratory. Comparing the results of the current method to either a known flow or to a
reference concentration measurement technique would make it possible to identify and correct an error
causing the behaviour seen in Figure 12c.
Figure 12. Results from nuclei measurements in MARIN’s depressurized wave basin. Three system
parameters were varied: a) framerate, b) defocus level, c) exposure time. This figure was previously
published in [12].
3.4 Bubble cloud
The most recent activity at MARIN has been directed towards generating a representative flow of bubbles
(of the correct size distribution) and measuring this flow using both the current IPI technique and a

reference technique based on defocused shadowgraphy. In this way, the current IPI technique can be
corrected, after which it can again be applied in a model basin or at full scale.
The first step in performing combined measurements in laboratory conditions using IPI and the defocus
technique is making a suitable flow. The current approach is to use electrolysis in a small water-filled
vessel and pass the current through graphite electrodes submerged in the water. A combination of
graphite electrodes with a solution of Na2SO4 in water as the electrolyte resulted in a steady stream of
bubbles with the correct size distribution (approx. 10-300 μm) and no visible by-products after several
hours of operation. In order to spread the bubbles more evenly throughout the volume, a stirring rod
powered by a magnetic stirrer is used. Due to buoyancy, the bubbles in the flow tend to rise towards the
surface, but due to the strong bulk flow their lifetime in the bubble cloud is substantial. After a short
initial period, the flow reaches steady-state conditions with a bubble cloud well-distributed throughout
the bulk of the liquid. Further testing and characterisation of the flow will follow, but the first result with
the current setup are promising.
The next step is to develop a reference technique which can determine the bubble size distribution in the
vessel. It was decided to apply the defocused shadowgraphy technique (see e.g. [13] and references
therein) which works by observing the particles using a microscope under backlighting. The particles are
sized directly and their position in the depth direction (perpendicular to the FOV) is determined from the
level of blurring of particle edges. The blurriness (quantified by calculating the image gradient) increases
with increasing distance between the particle and the front focal plane of the lens. By knowing the depth
position (Z) along with the two positions in the image (X and Y), the full 3D position of the particles is
determined; at the same time, this determines the measurement volume of the shadowgraphy system.
Figure 13a shows the experimental setup that was used in the current research. It consists of a water-
filled vessel, into which a glass plate is submerged; the plate is held in place by a traversing system which
can move it in the depth (Z) direction. Plastic (PMMA) particles of ~100 μm diameter are fixed to the
front side of the glass plate using transparent tape. An LED panel was placed at the back and provided
illumination to the camera positioned at the front. The image is formed using a long-range microscope.
Figure 13. Experimental setup used for defocused shadowgraphy (a) and images (raw and gradient) of
a solid particle as it is translated through the front focal plane (b).
A series of raw images recorded with this system and their gradient is shown in Figure 13b. The glass
plate is translated through the front focal plane for several millimetres in steps of 100 – 250 μm. When
it is at -1.5 mm from the focal plane, the particle is blurry, with a minimum gradient level. The image is

then becoming less blurry as the particle is approaching the focus and attains maximum sharpness
(maximum gradient level) at the focal plane. The reverse occurs as the glass plate is translated further,
towards the +1.5 mm position.
The value of the maximum gradient of images such as shown in Figure 13b is plotted as a function of the
depth position in Figure 14. The plots present four cases in which either the aperture opening or the
exposure time was varied. This was done to verify that changing these parameters does not influence the
size of the detected particles (these results are not presented). Besides this, the measurements show how
the defocus technique can be used for concentration measurements. Namely, all the curves have a
maximum and are relatively symmetrical around the zero position. From these curves, a threshold level
can be determined and applied to the gradient images in order to select only the particles (or bubbles)
which are inside the rectangular volume whose depth is shown on the abscissa. The optimal threshold
level is at the position where the curves have an inflection point. Here, the gradient of the curves (not of
the images) is maximum, which means that deviations or errors in calculating the image gradient produce
the smallest error in the measurement volume. In Figure 14a, the optimal image gradient is at the distance
~1.25 mm and ~0.5 mm from the focal plane for the 20% and the 45% aperture opening case, respectively.
In Figure 14b, the optimal gradient level is at ~0.5 mm for both cases. It is important to notice that it is
possible to change the position of the optimum gradient level—and thereby the measurement volume—
by changing the aperture opening. In some cases, it might be necessary to do this. For example, in a flow
with a very high bubble concentration, the measurement volume can be reduced in order to reduce the
likelihood of overlapping bubble images and thereby causing detection errors.
Figure 14. Results from the defocused shadowgraphy study: a) variation in the maximum image
gradient at different aperture openings, b) variation in maximum gradient at different exposure times.
It was checked that the aperture opening level and the exposure time do not influence the size of the
detected particles (not shown). The images shown in Figure 13 correspond to the case with texp=250 μs
(b).
4 Discussion
It has been hypothesized that the inhibition of cavitation inception—regularly found in several
facilities—is caused by an inadequate size range and/or concentration of free-stream nuclei. Lagrangian

tracking computations do indicate that the size range of free-stream nuclei—that can induce sheet
cavitation inception on a propeller blade—decreases with decreasing propeller diameter, but still a
diameter range between 10 and 400 µm remains [14]. In cavitation tunnels, the bubble concentration in
this diameter range varies between 0.1 and 10 per cm3, but in some tunnels concentrations of 100 to 600
per cm3 have been measured [2, 5, 15]. Without a specific control system to regulate the bubble spectrum
(size and concentration) in a tunnel, it varies with the dissolved gas content, the pressure in the test section
and the running time. Geometrical scaling of the typical full-scale bubble concentrations (1 to 3 per cm3
[15]) would lead on model scale to such high concentrations that the cavitating object would not be
visible. For example, Heinke et al. [2] show that in a K15A tunnel at a high dissolved gas content, “the
cavitation at the top of the blade almost cannot be observed due to the large amount of big bubbles”. At
this condition, which is not considered as normal, nuclei concentrations between 20 and 80 per cm3 were
measured. Furthermore, Aumelas et al. [16] show that for a diameter range between 30 and 50 m, a
concentration of ~100 per cm3 is already difficult to see through and a concentration of ~1000 per cm3 is
almost fully white due to the lighting. This, together with the example from [2] as mentioned in the
introduction, shows that reliable nuclei concentration measurements are required to enable a better
understanding of the cavitation inception process.
Nuclei concentrations above 50 per cm3 are typically measured with PDA, because defocus techniques
such as IPI suffer from overlapping bubble images. Remarkably large concentrations measured with IPI
in the order of 300 – 600 per cm3 are reported in [17], without explaining how their method was able to
measure such high concentrations. Furthermore, their cavitation observations do not indicate any
visibility problems. A cylindrical lens as applied by Maeda et al. [18] might enable the measurement of
such high concentrations.
Micro-bubbles as tracers for PIV measurements need to be small enough to follow the flow. Aumelas et
al. [16] evaluated the relaxation time for a 50 m bubble and concluded that this size is suitable as tracers
for PIV. However, a local pressure gradient can a large effect on tracers with a large difference in density
relative to the liquid in which it is suspended. Liu & Brennen [19] indicated that the induced velocity
normal to the trajectory of a bubble is proportional to the pressure gradient and the radius of the bubble
squared. So the larger the bubble, the stronger its response to a pressure gradient, due to gravity, a
stagnation point or minimum pressure on a foil [14]. Next to the search for an optimum bubble size, there
is also the challenge to generate an homogeneous seeded flow with ideally a monodisperse nuclei
spectrum in the desired plane/volume of measurement. Furthermore, the concentration should be very
high for PIV and moderately high for PTV applications.
In summary, not only a global description of the nuclei content in model-scale is required, but also the
detailed configuration of the technique and the global set-up of the whole campaign is required. Moreover,
a nuclei measurement should be done as close to the cavitation inception location as possible, for which
optical techniques are well-suited, due to their non-intrusive features.
5 Concluding remarks
The present paper summarizes the results obtained so far by the Community of Practice on Nuclei within
the Hydro-Testing Forum. Several experiments with different microbubble generation systems have been
carried out to test and enhance the accuracy of optical measurement techniques. Among the three

techniques chosen, the defocus imaging technique (IPI or ILIT) appears as the most practical. In a highly
controlled environment, the deviation in mean diameter between the techniques is approximately 15%.
Concentration measurements with IPI are available, but their values still need to be verified in well-
controlled conditions using a reliable reference technique, such as defocussed shadowgraphy.
Although the absolute accuracy of nuclei measurement results still leaves room for improvement, the
obtained trends can be used to support cavitation tests and PIV tests with micro-bubbles as seeding.
Further understanding of the physical processes can be expected after further optimization of the nuclei
measurement techniques.
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