NAT L INST. OF STAND & TECH R.I.C.

A 11 ID 4 D23254

NBS

PUBLICATIONS

NBSIR 79-1753

Radiation-Induced Acoustic

Cavitation; Threshold vs

Temperature for Some Liquids

M. Greenspan, C. E. Tschiegg

National Engineering Laboratory

National Bureau of Standards

Washington, DC 20234

May 1979

Final

Issued

I

j

Report to Department of the Navy

Office of Naval Research
f
1

2 D 1979

not c

NBSIR 79-1753

RADIATION-INDUCED ACOUSTIC

CAVITATION; THRESHOLD vs

TEMPERATURE FOR SOME LIQUIDS

M. Greenspan, C. E. Tschiegg

National Engineering Laboratory

National Bureau of Standards

Washington, D.C. 20234

May 1979

Final

Issued

Report to Department of the Navy

Office of Naval Research

Arlington, Virginia 22217

Government Order 808294

U.S. DEPARTMENT OF COMMERCE, Juanita M. Kreps, Secretary

Jordan J. Baruch, Assistant Secretary for Science and Technology

NATIONAL BUREAU OF STANDARDS. Ernest Ambler, Director

RADIATION-INDUCED ACOUSTIC CAVITATION;

THRESHOLD VS TEMPERATURE FOR SOME LIQUIDS

1

Martin Greenspan and Carl E. Tschiegg

National Engineering Laboratory

National Bureau of Standards

Washington, D. C. 20234

ABSTRACT

Neutron thresholds at various temperatures were measured for methanol,

ethanol, 1-propanol, 2-propanol, n-pentane, diethyl ether, fluorocarbon 113

and fluorocarbon 11, and fission thresholds were similarly measured for water,

1-propanol and 2-propanol. The work was done in 1969, but not reported then

because the project had not been completed owing to the pressure, of other

duties. However, there seems to be a revival of interest in this sort of

thing and we have been persuaded to work up and publish the data, such as it

is. So here goes.

Present address, 12 Granville Dr., Silver Spring, Maryland 20901
Contents

1. INTRODUCTION ................ ...... 1

2. THE "THRESHOLD OF CAVITATION" .......... ... 2

3. METHOD .... ......................... 2

4. RESULTS ................................. 5

4.1 Neutron thresholds ............. ...... 5

5. ACKNOWLEDGEMENT. ........ .............. 9

6. REFERENCES ... ........... ...... 11
RADIATION-INDUCED ACOUSTIC CAVITATION;

THRESHOLD VS TEMPERATURE FOR SOME LIQUIDS

1

Martin Greenspan and Carl E. Tschiegg

National Engineering Laboratory

National Bureau of Standards

Washington, D. C. 20234

1 . INTRODUCTION

In 1967 the present authors published a paper [1] in which it was

shown, among other things, that reproducible data on acoustic cavitation

could be got by the substitution of nuclei of cavitation produced by ionizing

radiation for those highly variable ones which occur naturally and often

adventitiously. A copy of this paper is bound with this report, for the

convenience of the reader.

In 1969 we undertook to measure the variation in "threshold" with

temperature in certain liquids. The program was interrupted under

circumstances beyond our control, but there seems now to be a demand for

whatever data we have, so we have worked it up for publication.

Numbers in square brackets refer to literature citations.
2. THE "THRESHOLD OF CAVITATION"

There is an important difference between the conceptual and an operational

meaning of the "threshold." We conceive of the threshold as a negative pressure

below which cavitation does not occur and above which it does. But in fact no

such pressure exists; what does exist in a way which is unambiguous for a given

piece of apparatus operated in a prescribed manner, is a relationship between

negative pressure and cavitation rate. See p. 308 of [1] for this where it is

also shown that the nature of this relationship is such that the operator can

determine a value of the negative pressure, which we will call the "threshold",

below which cavitations occur rarely and above which the rate is several per

minute. The procedure is of course subjective and the values obtained depend

also on the conditions of the experiment. Still it is easy to reproduce results

to + 1 dB and often to + 0.2 dB, and in the few cases for which results by others

are available, the agreement, although not what one might hope for, is yet not

too bad for this kind of work.

3 . METHOD

The test liquid was filtered and degassed as described on pp. 30A and 305 of

[1] and vibrated in a test cell which was either a cylinder having integral drive

as shown in Fig. 1 of [1] or a conical flask as shown in Fig. 3 of [1],

9

The cell was enclosed in a pressure vessel and thresholds were determined by

the "overpressure" method described in p. 304 of [1]. The pressure vessel was

housed in an environmental test chamber provided with a refrigeration unit,

2
electric heaters and a thermostat, and also a port through which an a-neutron

source could be introduced.

A calibrated thermistor cemented to the cell, together with an automatic

digital ohmmeter, permitted remote readout of the temperature.

The overpressure and the voltage on the transducer were also read remotely

and operation was by remote control so far as practicable. The test chamber and

neutron source were in a room shielded with concrete blocks and parafin; the

operating personnel, together with their instruments and controls, were in

another room across the hall. All applicable safety standards were met.

All of the work reported here was done with a 10-curie (160 g Pu) Pu-Be

source having a total output of 1.47 x 10 ^ n/s. In the case of the

neutron- induced thresholds given in Tables 2 to 9 and Figs. 2 to 9 the source

irradiated the test liquid directly. In the case of the fission thresholds given

in Tables 10 to 12 and Figs. 10 to 12 a salt containing a fissionable material

(together with the water of crystallization) had been dissolved in the test

liquid, which was therefore no longer pure. The salts used were natural uranyl

nitrate, UO (NO ) *6H 0 and thorium nitrate, Th(N0 ) *4H 0; both thermal and fast

2 3 2 2 3 4 2 fission occur in the former, and fast fission only in the latter. A large number

of neutrons was available, so that spontaneous fission and that induced by cosmic

neutrons had a negligible effect. These matters are discussed on p. 311 of [1],

3
It is perhaps worthwhile to recapitulate the overpressure method, described

also on p. 304 of [1]. Suppose that under some specified condition a cavitation

occurs at some negative pressure T (threshold, a positive number); then if p is

s the static pressure (i.e. the overpressure) and p

is the amplitude of the

cl acoustic pressure

T = p

- p (1) a s

The output of the cell is some voltage, V, supposed proportional to p so that

Eq. (1) is

V = (p + T)/m,

s

or

p = mV - T. (2)

*s

Thus if p be plotted against V a straight line results of which the

s

p -intercept, with the sign reversed, is the threshold, T. The method fails if T

depends on p as discussed in [1]. In practice, T is gotten from a least-squares

fit to Eq. (2). This is a matter of convenience only, and it is not claimed that

any statistical benefit results. In fact, V is treated as the independent

3

variable whereas actually p is. No significant error results because in every

s case the data fit a straight line very well, as shown by the small values of the

residual standard deviation of the fit given in Tables 2 to 12.

3 This error is a few tenths of one percent in a threshold which we report using

only two significant figures.

4
The overpressure method is of especial interest for at least two reasons.

First, the nature of the pressure field within the cell need not be known.

Second, it provides a method for the calibration of the small, rather insensitive

probes used in mapping ultrasonic fields, as explained on p. 304 of [1].

At the time [1] was written (1967) we thought the overpressure method to be

original. Later we found that it had been described in 1947 by Briggs, Johnson

and Mason [2], and we are happy to acknowledge their priority.

4 . RESULTS

4.1 Neutron thresholds

Table 1 lists the organic liquids tested, the range of temperatures over

which the tests were made, and some physical properties. These last are taken

from Schaffs' compilation [3] or, in the case of the fluorocarbons, from the CRC

handbook [4] and the values given do not pretend to any great accuracy. Table 1

also lists the number of the table and figure in which the results for each

liquid appear.

The raw data for a typical run are shown in Fig. 1 together with the

straight line, having the form of Eq. 2, fitted by least squares. The units for

pressure, namely psig, are used because the high-quality Bourdon- tube gage with

which the pressure was measured was so graduated. The points are fit very well

by a straight line (more on this later) and the hysteresis is seen to be small.

The use of the voltage V as the independent variable gives T = 71.17 psig whereas

5
the use of the overpressure p instead would have given T = 71.42 psig. The

s systematic errors greatly exceed this difference and we ignore it. The value

71.17 (psig) is divided by 14.50 (psi/10^Pa) to give 4.908 x 10~*Pa gage from

which is subtracted a standard atmosphere of 1.013 x lO^Pa to give 3.895 x lO^Pa

absolute which is rounded off to 3.9 and entered in Table 2 as the threshold for

methanol at 39.6° C.

The results are shown in Tables 2 to 9 and graphed in Figs. 2 to 9. The

residual standard deviation of the fit and the standard deviation of the

threshold are given not because they have any deep significance, but to show how

well the data are fitted by a straight line. In every case tabulated, the fit is

good enough to ensure that the threshold does not depend on the overpressure and

that hysteresis is negligible. Were it otherwise, as in some cases discussed by

Strasberg [5] (see also p. 304 of [1]) the overpressure method would fail.

We discuss briefly the results given in Tables 2-9 and on the corresponding

graphs. Figs. 2 to 9. In doing so we also compare the results with whatever

others are available, which are not many. In fact, we know of only the work of

Colin West [6] done at the AERE in Harwell in 1967. West used a crude "spinner"

or centrifuge and his results therefore apply at zero frequency. They are

denoted by circles on Figs. 2-9, and it will be seen that in most cases the

agreement is rather good, and in no case is it really bad. We can take this to

support two notions, (a) that the weak dependence (if any) of threshold on

frequency which we found to hold from 20 to 60 kHz or so extends down to

zero frequency, and (b) that the onset of cavitation with increasing acoustic

pressure amplitude is of such a nature that two independent realizations of
"threshold", both arbitrary and both subjective, may yet yield results not much

more discrepant than the systematic errors of either. With this pious hope in

mind we proceed to look at our tables and graphs one at a time although two

things need to be noted only once. First, the threshold for the most part

decreases as the temperature increases. Second, the curves, which are expected

to be smooth, are in fact jagged. We think this jaggedness is a measure of the

inability of the operator to repeat his settings.

Table 2 and Fig. 2. Methanol. We have two sets of data taken a week apart.

The (generalized) lunch-hour effect is seen to be not too bad if the two

low-temperature points of Jan. 6 are considered somewhat wild. West’s [6]

higher- temperature point is in good agreement with, and his lower- temperature

4

point about 13% below, ours.

Table 3 and Fig. 3. Ethanol. Here we have two modes, one at 46-48 kHz and

one at 27-28 kHz. About the same results are obtained at both frequencies. One

point appears to be wild, but an examination of the raw data gives no reason to

reject it. West’s [6] single point agrees very well.

Table 4 and Fig. 4. 1-propanol. There is nothing to remark here except that

the curve is very steep. Thresholds for temperatures below 50° c| were outside

the range of the apparatus. West [6] did not work with this liquid.

On the basis of gage pressure, which is what is measured, rather than absolute

pressure as shown on the graphs.

7
Table 5 and Fig. 5. 2-propanol. Here again we see that measurements taken

on different days more or less hang together. West's [6] point is about 16%

below ours.

Table 6 and Fig. 6. Diethyl ether. West's [6] point agrees very well with

ours

Table 7 and Fig. 7. n-Pentane. There is nothing special here.

Table 8 and Fig. 8. Fluorocarbon 11. West's [6] points agree pretty well

with ours, although his point at 21.1® C. is perhaps wild. The negative

threshold at 50.5° C. means that cavitation occurs although the liquid is in

compression. The normal boiling point is 23.7° C., but the liquid state is

maintained by a minimum overpressure of 2.1 x 10 Pa as indicated in Table 8.

Table 9 and Fig. 9. Fluorocarbon 113. We see that the 7 points obtained

before, and the 6 after repair of the cell as described in footnote (h) are not

unduly discrepant. West’s three points agree well with ours. As in fluorocarbon

11 (see Table 8 and Fig. 8) there is one negative threshold.

It is seen that in all cases the threshold decreases as the temperature

increases. Unfortunately those properties of these liquids with which the

threshold would be expected to be correlated, either positively or negatively,

vary monotonically with temperature. Therefore we cannot expect to get a toehold

on a theory from just a cursory glance at the curves."*

~*I have calculated roughly that the maximum linear energy deposit to be expected

in each of the liquids is about the same, so that this factor is of use only in

absolute calculations.

8
We tried also to measure some thresholds on clean water, using the steel

cell shown in Fig. 2 of [1], As pointed out on p. 304 of [1] the neutron

thresholds of water are high, and since our maximum overpressure was only about

0.8 MPa (say 8 bar) the measurements were confined to the higher temperatures,

and even there the accuracy was low. About all we can say is that the thresholds

are in the neighborhood of 40 or 50 bar at 66° C. , 20 or 30 bar at 74-78° C., and

perhaps 30 or so bar at 87° C. This type of temperature variation suggests a

correlation with compressibility, but the evidence is weak.

4.2 Fission thresholds.

These results, which are given in Tables 10, 11 and 12 and in the

corresponding figures, are only qualitative because the liquids are not pure and

we do not know the various physical properties of the solutions (although they

could be measured) . The thresholds of the two propanols are low and the errors

correspondingly high so that little can be said about them.

The fission thresholds of water are in the same range as the neutron

thresholds of some of the organics, so it was easy to get a considerable amount

of data, as shown in Table 10 and Fig. 10. Again we notice a tendency for the

curve to flatten out at the higher temperatures, suggesting a possible partial

correlation with the compressibility.

5 . ACKNOWLEDGEMENT

This work was sponsored by the Office of Naval Research to whose other

virtues we now add that of patience. We appreciate the ready cooperation of the

9
then Health Physics Section under the direction of Dr. A. Schwebel which labored

diligently to ensure that the work was carried out with the least possible hazard

to our neighbors and ourselves

10
6 . REFERENCES

[1] M. Greenspan and C. E. Tsehiegg. J. Research NBS 71C 299-312, (1967).

[2] H. P. Briggs, J. B. Johnson and W. P. Mason, J. Acoust. Soc. Am. 19_, 664-677

(1947).

[3] Landolt-Bomstein, New Series, Group II, Vol. 5, Molecular Acoustics by W.

Schaffs. Springer, New York, 1967.

[4] Handbook of Chemistry and Physics, The Chemical Rubber Co., Cleveland, 1970

or later.

[5] M. Strasberg. J. Acoust. Soc, Am. 31 , 163-176, (1959).

[6] C. West. Private communication dated December 29, 1967.

11
Table 1. Some Properties of the Liquids

Liquid B.P.

a Temp

Range b

P _ 9P°

3T

d

c

3 c

e 9T

Table

6 Fig

°C. °C. kg/m^ kg/m^ °C. m/

s

m/s °C No.

Methanol, CH.O

4

64.7 -20 to 50 792 0.9^° 1120 3.2 6

5°

2

Ethanol, C H 0

Z o 78.4 20 to 90 790 • 87

20

1159 3 ' 16

20

3

1-Propanol, CgHgO 97.8 50 to 83 804 o

o

CO

CM

00 CNJ 1222 3- 4

2-Propanol, CgHgO 82.5 24 to 82 786 (f) 1170 5

Diethyl ether, C^H^O 34.6 -50 to 34 714 1 13

30

I.-LOq 1006 6

n-Pentane C^H.^ 36.1 - 5 to 34 626 (f) 1030 5.0

30

-50

7

fluorocarbon 11,

CClgF 23.8 -50 to 50 1467 (f) (f) (f) 8

fluorocarbon 113,

C

2 C13F3 47.6 -28 to 59 1565 (f) (f) (f) 9

(a) Normal boiling point.

(b) Density at 20 °C. (25 °C. for the fluorocarbons).

(c) Temperature coefficient of the density averaged over the indicated temperature

range.

(d) Speed of sound at 20 °C.

(e) Temperature coefficient of the speed of sound averaged over the indicated temperature

range.

(f) Not readily available.

Figure 1. Plot of the raw data for methanol at 39.6 °C. , together with the straight

line fitted by least squares.

+ overpressure increasing

O overpressure decreasing

12
OVERPRESSURE

VOLTRGE , V

13
Table 2. Neutron thresholds, Pu-Be source

Material - Methanol, CH.O.

4

Threshold

Date Temp

Frequency

No . of

data

a Range^ R.S.D.

C

(absolute)

Value s7b.

e Additional

Notes

1969 °C. kHz 10

5

Pa 10

5

Pa 10

5

Pa % f

1/13 -19.7 32.7 19 0-6.1 0.13 8.0 2.8 g

1/13 -10.0 31.4 19 0-6.1 .12 7.6 2.7 g

1/6 0.4 30.6 19 0-6.1 .15 7.5 2.6 g

1/13 .6 30.6 19 0-6.1 .11 6.9 2.6 g

1/6 11.3 29.7 20 0-6.1 .15 5.6 2.6 g

1/6 22.3 29.1 19 0-6.1 .13 5.2 2.5 g

1/6 30.6 28.4 19 0-6.1 .19 4.7 4.9 g

1/6 39.6 27.7 19 0-6.1 .10 3.9 2.8 g

1/6 49.7 26.8 19 0-6.1 .07 3.3 2.4 g>h

(a) About half the data were

descending

taken with the overpressure ascending and half with it

.‘Vi r

(b) Range of overpressure taking zero as atmospheric pressure

(c) Residual standard deviation of the fit of the data to Eq. (2).

(d) From the least-squares fit of the data to Eq. (2).

(e) Standard deviation of the threshold, obtained from the fit, expressed in percent.

(f) The unit of pressure commonly used in cavitation work is the bar or the atmosphere,

taken as practically interchangeable. 1 bar = 0.987 atm = 10 5 Pa.

(g) In lead zirconate-titanate cylinder, 10.2 cm 0. D. by 15.2 cm long with 0.08 mmthick brass windows. (3, 0, 1) - mode. See Fig. 1 of [1].

(h) The cavitation cell did not operate properly at higher temperatures.

14
THRESHOLD,

MPa

FIGURE 2, Neutron thresholds of methanol as a function of temperature. The values

are from table 2.

* Measurements made Jan. 6, 1969

+ Measurements made Jan. 13, 1969

0 From West [6]

15
Table 3. Neutron thresholds, Pu-Be source

Material - Ethanol, C_H,0.

I 6

Date Temp. Frequency

No. of

3

data Range*

3 R.S.D.C

Threshold

(absolute)

Valued S.D.

Additional

e Notes

1969 °Cr kHz 10

5 Pa 10

5Pa 10

5 Pa % f

5/16 19.6 46.0 10 0-5.5 0.08 5.9 2.6 g

5/16 23.2 45.7 10 0-5.5 .09 7.1 2.7 g

5/16 29.3 45.0 8 0-4.1 .11 5.9 4.9 g > h

5/16 38 44.4 10 0-5.5 .04 5.1 1.3 g

5/13 38.2 28.2 10 0-2.8 .05 4.5 3.0 g>h,i

5/13 46 27.8 14 0-4.1 .05 3.7 2.0 g>i

5/16 48 46.0 10 0-5.5 .19 4.2 6.9 g

5/13 53 27.3 14 0-4.1 .04 4.1 1.4 g>i

5/16 64 48.0 10 0-5.5 .04 3.1 1.8 g

5/13 65 26.8 10 0-2.8 .06 2.3 4.1 g,h, i

5/13 75 27.7 12 0. 7-4.1 .05 2.4 3.1 g>i

5/20 82 47.7 8 1.4-5.

.04 1.9 2.6 g

5/13 89 26.8 12 1.4-4.

.11 1.8 8.4 g > i

(a) to (f) See footnotes to Table 2.

(g) In 500 ml

cm high.

conical flask

See Fig. 3 of

driven by

[1].

lead zirconate-titanate cylinder, 3.8 cm D. by

(h) Cell not stable at higher overpressures.

(i) For these the mode was different

,

and the frequency lower, than for the others

16
THRESHOLD,

MPa

00

<5?

® L 1 ! l i U

-50 -25 0 25 50 75

TEMPERATURE, deg C

FIGURE 3. Neutron thresholds of ethanol as a function of temperature,

are from table 3.

* High-frequency mode

+ Low-frequency mode

0 From West [6]

100

The values

17
Table 4. Neutron thresholds, Pu-Be source

Material - 1-propanol, C_H 0.

3 o

Threshold

Date Temp

Frequency

No. of

3

data Range^ R.S.D.

C

(absol

ValueCi ute)

e S.D.

Additional

Notes

1969 °C. kHz 10

5 Pa 105

Pa 10

5 Pa % f

7/14 50.6 45.3 10 0-5.5 0.14 9.9 4.1 g

7/14 54.0 51.1 10 0-5.5 .18 6.8 5.8 g

7/14 59.2 50.9 10 0-5.5 .15 6.7 4.9 g

7/14 61.2 50.5 10 0-5.5 .17 6.5 5.6 g

7/14 73.2 45.3 10 0-5.5 .09 3.8 3.4 g

7/14 82.5 50.9 8 0-4.1 .06 2.5 3.5 g>h

(a) to (f) See footnotes to Table 2.

(g) , (h) See footnotes to Table 3.

18
THRESHOLD.

MPa

TEMPERATURE, deg C

FIGURE 4. Neutron thresholds of 1-propanol as a function of temperature. The

values are from table 4.

19
Table 5. Neutron thresholds, Pu-Be

Material - 2-propanol, C^H

source

8°*

Date Temp. Frequency

No. of

a data Range^ R.S.D.

C

Threshold

(absolute)

Valued S.D.

e Additional

Notes

1969 °C. kHz 10

5Pa 105 Pa 105

Pa % f

7/9 23.9 45.4 10 0-5.5 0.08 8.9 2.3 g

7/9 49.6 45.7 10 0-5.5 .15 6.7 4.6 g

7/9 59.6 50.9 10 0-5.5 .18 5.3 6.0 g

7/9 69.6 49.9 10 0-5.5 .06 4.3 2.0 g

7/10 71.8 51.6 10 0-5.5 .56 3.9 7.9 g

7/10 82.0 50.3 8 1.4-5.

.06 3.5 3.6 g

(a) to (f) See footnotes to Table 2.

(g) See footnote to Table 3.

20
THRESHOLD

,

TEMPERATURE , deg C

FIGURE 5. Neutron thresholds of 2—propanol as a function of temperature. The

values are from table 5.

* Measurements made July 9, 1969

+ Measurements made July 10, 1969

0 From West [6]

21
Table 6. Neutron thresholds, Pu-Be source

Material - Diethyl ether, C.HL^O

4 10

Date TempFrequency

No. of

a data b

Range R.S.D?

Threshold

(absolute)

Value dS.D.

6

Addit ional

Notes

1969 °C. kHz 10

5

Pa 10

5

Pa 10

5

Pa % f

5/5 -50 26.5 12 0-3.4 0.17 5.7 7.5 g> h

5/5 -39 26.2 16 0-4.8 .10 4.5 3.6 g

5/1 -19.6 26.4 14 0-4.1 .09 4.2 3.4 g>h

5/1 1.8 27.9 14 0-4.1 .04 3.0 2.1 g

5/1 11.0 27.4 12 0-3.4 .06 2.4 3.2 g

5/1 21.0 26.8 10 0-2.8 .06 2.0 4.5 g

5/1 27.7 26.5 10 0-2.8 .03 1.1 2.0 g .

5/1 34.0 26.4 8 0.7-2.

.02 0.9 2.6

g

(a) to (f) See footnotes to Table 2.

(g) In

by

500 ml

7.6 cm conical flaskhigh. See Fig

driven by

. 3 of [1]

lead zirconate-titanate cylind er, 5.1 cm D.

(h) Cell not stable at higher overpressures.

22
THRESHOLD,

MPa

00

% <s?

CD

<S>

dr

% <S?

OJ

* Q

<S

<» G>

t

OJ

•*T.

I TEMPERATURE , deg C

FIGURE 6. Neutron thresholds of diethyl ether. The values are from table 6.

0 From West [6]

23
Table 7. Neutron thresholds, Pu-Be source

Material - n-Pentane,

Threshold

Date Temp. Frequency

No. of

a data Range

R.S.D?

(absolute)

Value4 sTd

6

Additional

Notes

1969 °C. kHz 10

5 Pa 105

Pa 10

5 Pa % f

4/7 -4.8 28.7 12 0-3.4 0.20 3.1 10.0 g > h

4/7 9.6 27.5 14 0-4.1 .07 2.7 3.1 g

4/7 20.2 26.8 12 0-3.4 .06 1.4 3.6 g

4/7 26.7 26.6 12 0-3.4 .02 1.9 0.8 g>h

4/7 34.2 26.4 8 0.7-2.

.02 0.6 3.1 g> h

(a) to (f) See footnotes to Table 2.

(g) , (h) See footnotes to Table 6.

24
THRESHOLD,

MPa

00

©

CO

<3

d-

*

<5?

CU

« ©

©«• ©

i

OJ

•50 -25 0 25 50 75

TEMPERRTURE, deg C

100

FIGURE 7. Neutron thresholds of n-pentane. The values are from table 7.

25
Table 8. Neutron thresholds, Pu-Be source

Material - Fluorocarbon 11, C Cl^F.

Threshold

cl No of , (absolute) Additional

Date Temp. Frequency data Range R. S.D.

C Value S.D.C

Notes

1969 °C. kHz 10

5 Pa 10

5 Pa 10

5

Pa % f

7/2 -50 35.4 8 0-4.1 0.14 5.8 6.1 g,h

6/24 -31 38.3 10 0-5.5 .07 4.6 2.3 g

6/24 -10.9 36.5 10 0-5.5 .11 3.6 4.1 g

6/24 3.8 35.0 10 0-5.5 .04 3.0 1.5 g

6/24 18.6 33.7 10 0-5.5 .09 2.5 4.0 g

6/24 32.1 25.0 10 0.7-3.

.04 1.4 3.8 g

6/24 41.5 24.1 10 1. 4-4.1 .02 0.4 3.4 g

6/24 50.5 23.3 10 2. 1-4.

.04 -.9 7.9 g j i

(a) to (f) See footnotes to Table 2.

(g) In 125 ml conical flask driven by lead zirconate-titanate cylinder, 1.5 cm D.

by 2.5 cm high. See Fig. 3 of [1],

(h) Cell not stable at higher overpressures.

(i) Cell not stable at lower overpressures.

26
CO

o“

FIGURE 8. Neutron thresholds of flurocarbon 11. The values are from table 8.

0 From West [6]

27
Table 9. Neutron thresholds, Pu-Be source

Material - Fluorocarbon 113, C^Cl^F^.

Threshold

Date Temp

Frequency

No of

3

data Range R.S.D.

C (absg

Value

lute)

S.D . 6

Additional

Notes

1969 °C. kHz 10

5 Pa 10

5 Pa 105 Pa % f

4/15 -27.8 27.5 17 0-5.5 0.12 4.9 3.7 g

4/17 -22.9 24.2 19 0-6.2 .21 4.9 5.2 g

4/15 -13.5 25.4 17 0-5.5 .13 3.9 4.0 g

4/15 - 9.1 26.3 15 0-4.8 .13 3.1 4.8 g

4/15 0.13 26.0 17 0-5.5 .09 3.2 2.8 g

4/15 9.3 25.4 15 0-4.8 .09 3.3 3.1 g

4/15 18.2 25.9 11 0-3.4 .06 2.2 3.5 g

4/17 24.3 24.3 13 0-4.1 .09 2.4 4.0 g>h

4/17 32.4 26.5 11 0-3.4 .06 1.9 3.4 g

4/17 36.1 28.8 11 0-3.4 .05 1.5 3.1 g

4/17 39.0 25.4 11 0. 7-4.1 .04 1.1 3.3 g

4/17 48 24.5 9 0.7-3.

.03 0.8 2.9 g

4/23 59 24.7 11 2. 1-5.

.06 -.3 .15 g

(a) to (f) See footnotes to Table 2.

(g) See footnote to Table 7.

(h) Sample changed and joint between flask and driver reglued.

28
THRESHOLD,

MPa

FIGURE 9. Neutron thresholds of fluorocarbon 113. The values are from table 9.

* Measurements made before apparatus was damaged + Measurements made after repairs (see footnote (h) of table 9).

0 From West [ 6]

.

29
Table 10. Fission thresholds, dissolved natural UO^CNO^^ exposed to

Pu-Be neutron source. Material - Water, HO, plus dissolved

natural UO^CNO^)^.

Threshold

No. of (absolute) Additional

Date Temp

Frequency data Range R.S.D.

C Value 0* S.D.

6

Notes

1969 °C. kHz 10

5 Pa 10

5

Pa 10

5 Pa % f

6/9 7.0 46.9 10 0-5.5 0.11 8.2 3.2 g>h

6/9 12.3 47.3 8 0-4.1 .08 7.6 3.4 g,h

6/9 16.0 47.5 10 0-5.5 .07 7.1 2.3 g>h

6/9 20.9 47.7 10 0-5.5 .16 6.4 5.2 g > h

6/9 23.3 47.9 10 0-5.5 .09 6.2 3.3 g>h

6/16 25.7 47.5 10 0-5.5 .14 5.8 4.5 g) j

6/9 36.0 48.4 10 0-5.5 .10 5.3 3.4 g>h

6/16 40.

47.9 10 0-5.5 .08 4.0 3.6 g. i »

j

6/10 47.2 48.8 10 0-5.5 .03 3.9 1.2 g, h

6/12 49.

48.9 10 0-5.5 .10 3.3 3.8 g , h , j

6/16 53.0 48.1 10 0-5.5 .13 3.3 6.1 g > i j j

6/12 62.5 49.1 10 0-5.5 .00 2.9 0.0 g>h, j

6/16 73.5 48.3 10 0-2.8 .09 2.4 5.9 g»i»j

6/12 79.5 49.2 10 0-2.8 .09 2.5 5.6 g>h, j

6/16 84.5 48.3 10 0-2.8 .13 2.2 8.7 g> j

6/12 89.8 49.1 12 0-3.4 .09 2.4 4.9 g>h, j

6/16 93.8 48.2 10 0-2.8 .03 2.2 2.6 g»i > j

6/12 102 49.0 10 0. 7-3.4 .03 1.7 2.4 g>h, j

(a) to (f) See footnotes to Table 2.

(g) See footnote to Table 8.

(h) 0.25 molar

(i) 1.8 molar

(j) These runs were made after the cell had been repaired and the transducer replaced.

30
<s

«

C\1

«

I -50

-J L— _i I I 1. . _ -25 0 25 50 75 100

TEMPERRTURE, deg C

FIGURE 10. Fission thresholds of water solution of natural uranyl nitrate,

values are from table 10.

* 0.25 molar solution

+ 1.8 molar solution

The

31
Table 11. Fission thresholds, dissolved natural UO^CNO^) exposed to

Pu-Be neutron source. Material - 1-propanol, C^HgO, plus

dissolved natural UC^CNOg^, plus some H^O.

Date TempFrequency

No. of

3

data Range^ R.S.D.

C

Threshold

(absolute)

Valued S.D.

6

Additional

Notes

1969 °C. kHz 10

5 Pa 105

Pa 10

5 Pa % f

8/15 -2.3 43.5 10 0-2.8 0.04 0.8 3.4 g> h

8/5 11.4 48.0 10 0-2.8 .08 1.2 5.9 g>i

8/5 11.6 45.0 10 0-2.8 .04 1.0 3.0 g »

8/15 16.7 42.6 10 0-2.8 .02 0.7 1.9 g>h

8/8 20.4 42.3 10 0-2.8 .03 1.1 2.1 g> i

8/15 23.8 44.4 10 0-2.8 .01 0.8 1.0 g j h

8/5 24.3 42.1 10 0-2.8 .03 1.0 2.6 g > i

8/5 31.7 46.3 10 0-2.8 .06 1.3 4.2 g» 1

8/5 39.6 49.9 10 0-2.8 .05 0.7 4.4 g,i

8/5 50.0 48.9 10 0-2.8 .03 0.5 2.8 g>i

8/8 60.0 44.3 10 0-2.8 .03 0.1 3.3 g > i

(a) to (f) See footnotes to Table 2.

(g) See footnote to Table 3.

(h) 0.2 molar.

(i) 0.4 molar.

32
THRESHOLD,

MPa

FIGURE 11. Fission thresholds of 1-propanol with dissolved natural uranyl nitrate.

The values are from table 11.

* 0.2 molar solution

+ 0.4 molar solution

33
Table 12. Fission thresholds, dissolved Th(NO^)^ or natural UO^NO,^

exposed to Pu-Be neutron source. Material - 2 propanol,

C H 0, plus dissolved Th(N0 o ). or natural U0o (N0 o )_, plus

J o n j h L 5 2.

Threshold

No. of (absolute) Additional

Date Temp

.

Frequency data Range R. S . D

.

Value S.D. Notes

1969 °C. kHz 10

5 Pa 10

5 Pa 10

5 Pa % f

8/26 4.7 46.5 10 0-2.8 0.08 1.0 6 .

6

g>h

9/2 14.6 28.9 6 0-1.4 .01 0.7 1.8 g > i> j

8/26 17.0 29.0 8 0-2.1 .02 0.7 2.6 g>h,j

8/26 23.3 45.6 10 0-2.8 .04 0.5 3.8 g > h

9/2 <r • CM 45.4 10 0-2.8 .05 0.8 4.7 g> i

8/26 34.1 45.0 10 0-2.8 .07 0.7 6.5 g,h

9/2 40.0 44.2 10 0-2.8 .02 0.2 2.0 g> i

8/26 43.3 44.1 10 0-2.8 .05 0.4 4.8 g»h

9/2 55.0 45.5 10 0-2.8 .02 0.3 2.2 ,g»i

8/26 57.3 45.5 10 0-2.8 .04 0.2 4.7 g>h

(a) to (f) See footnotes to Table 2.

(g) See footnote to Table 3.

(h) 0.4M U0

2 (N0

3

) 2

.

(i) 0.4M Th(N0 o )

.

3 4

( j ) Lower- frequency more than the other runs. Cell unstable at higher overpressures.

34
FIGURE 12 i Fission thresholds of 2-propanol with dissolved thorium nitrate or natural uranyl nitrate. The values are from table 12.

* 0.4 molar 002 ^0^)2

+ 0.4 molar Th(NO^)^

35
JOURNAL OF RESEARCH of the National Bureau of Standards — C. Engineering and Instrumentation

Vol. 71 C, No. 4, October—December 1967 Radiation-Induced Acoustic Cavitation;

Apparatus and Some Results*

Martin Greenspan and Carl E. Tschiegg

National Bureau of Standards, Institute for Basic Standards, Washington, D.C. 20234

(August 22, 1967)

Equipment and techniques for acoustic cavitation work are described. The test liquid and its container form part of a self-sustaining programmable oscillator. Emphasis is laid on the treatment

of the liquid necessary to yield reproducible results after artificial nucleation, especially by neutrons,

a-recoils, and fission. With neutrons, for instance, the cavitation rate rises rapidly with acoustic (negative) pressure, and at fixed pressure is proportional to neutron flux. The cavitation events are random, and no appreciable induction or decay times are observed. Each cavitation arises from the action of a single neutron (or a-recoil, or fission). The cavitation “threshold” (roughly negative pressure below which cavitation is rare) is highly variable from liquid to liquid. Thresholds at about room temperature for liquids irradiated with 10 MeV neutrons ranged from 1 to 2 bars for n-pentane, ether, and

freon 113 to over 50 bars for water.

Key Words: Acoustic cavitation, alpha-particle-induced cavitation, cavitation, cavitation nucleus,

cavitation threshold, fission-induced cavitation, neutron-induced cavitation, radiation- induced cavitation, threshold.

1. Introduction

Our interest in cavitation research was aroused

partly by the work of Lieberman [1959] but mostly

by that of Sette and Wanderlingh [1962]. Also we felt that it would be desirable to develop techniques ca- pable of yielding results more reproducible than those

in the literature. Of course most investigators were

aware that the day-to-day variability of their results reflected that of the population of nuclei in the liquid

under test;' indeed a cavitation experiment may be

designed so that the results are best interpreted as a determination of the distribution of nuclei, a point

emphasized by Messino, et al. [1963, 1967]. Still, we

felt that some improvements in both apparatus and

technique would be of value, and in this paper we

describe what we have done so far and give some

sample results which, although as yet uncoordinated

by theory, illustrate how data of potential importance

can be collected by relatively straightforward means. We revert to the work of Lieberman [1959]. He was

able to induce cavitation in acetone and pentane 2 by

neutron bombardment. The results, although very

interesting and so far as they go in substantial agree- ment with those of the present work, were hardly

surprising in view of what was then known about

bubble chambers. The situation is different in the case of Sette and his co-workers [Sette and Wanderlingh, 1962; Messino, et al., 1963] and later, of Finch

[1964 1 as well. Their results imply the existence, in water, of neutron-generated cavitation nuclei which

have a long half-life, sometimes an hour or more.

*Work supported in part by the U.S. Office of Naval Research.

1 The disparity of results of various investigators reflects, in addition, the differences in experimental techniques and conditions, and in definitions of “threshold.”

J Probably n-pentane.

The apparatus here described is suitable for de- termination of the following:

(1) Cavitation “thresholds” according to various

arbitrary definitions.

(2) Cavitation-event rate as a function of pres- sure above threshold.

(3) Effect of static pressure.

(4) Influence of various nuclei, natural or artificial. The natural nuclei can be filtered out and

replaced by others. Among these we emphasize

those which are radiation-induced; by neutrons,

by disintegration of dissolved a-emitters, and by

fission, both induced and spontaneous. In the case

of neutrons, the prevailing view [Lieberman, 1959]

is that the nucleation is connected with the deposition, in the liquid, of the kinetic energy acquired

by an atomic nucleus of one of the heavier elements

in the liquid as a result of an elastic collision with

a neutron. In the case of a- disintegration, the heavy

recoil nucleus (a negative ion rather than a positive

ion as in the previous case), is responsible, according to Riepe and Hahn [1961], who have examined

this process in a bubble chamber.

So far our apparatus is not well adapted to studies

of the effect of frequency.

For an overall view of acoustic cavitation the reader

is referred to Flynn [1964] whose article contains 152

references.

2. Apparatus, Major

Other things being equal, cavitation occurs in that region of the liquid where the (negative) pressure

is greatest; therefore it is necessary that the pres- sure at the walls of the container be substantially

299
less than that in the “test” region, else cavitation and

will occur preferentially on the walls (or on the trans- ducer, if it be immersed), and the results will not then represent properties of the liquid alone.3 In the case of traveling waves, they may be focused.

Sette and Wanderlingh [1962] used reflectors. The

radiation from the concave side of a transducer

which is the segment of a sphere is focused at the

center; this arrangement was used by Willard [1953],

and on a massive scale, by Sirotyuk [1962].

Standing-wave systems for the most part exploit

the radial modes of a liquid-filled spherical flask, an arrangement devised by Leonard [1946] for another

purpose and first adapted to cavitation work by Galloway [1954]. In such resonant systems the power

requirement is just that needed to supply the losses;

this advantage over traveling-wave systems is es- pecially important where high sound pressures are required.

In our own work we use resonant systems, either

cylinders or conical flasks.

2.1. Cylinders

The modes of vibration of a cylinder of fluid are well

understood; here we give a brief treatment just to

fix ideas. Modes that have an azimuthal dependence

give zero pressure on the axis and maximum pressure on the walls; these are undesirable for our purpose

and we consider radially symmetric modes only. The

velocity potential, ignoring losses and with the time

dependence exp ( ioit ) suppressed, is

<f) = Jo(krr)[A cos kzz + B sin kzz ], (1) with

k

2 = ojI

c

2 = k2 -\- kz \ (2)

the angular frequencies, at, are thus known in terms

of the radial wave numbers, kr , and the axial wave

numbers, kz , and the plane-wave speed of sound, c, in the liquid. The ratio B/A depends on the impedance

at the flat ends of the cylinder. Our practice is to use

a thin sheet for the ends to make the impedance nearly

zero; then with the origin at one end, and because the

pressure is proportional to <j>, A = 0 and kz = mrlL,

L being the length of the cylinder and n an integer.

Equations (1) and (2) reduce to

<f> = BJ0 (krr) sin (mrz/L) , (3)

and

k

2 = <o2lc2 = k$ + n

2

TT

2IL2

. (4) The pressure, radial velocity, and axial velocity are given by

p = -iwp(f), (5)

t/, = = — BkJ i(krr) sin (nnz/L\ (6)

:| Also, tin* apparatus may be damaged.

uz = 'd<f>ldz= {BmrlL)Ju(kri') cos (iitt/L). (7)

respectively, with p the undisturbed density <>! 1 1 il- liquid.

At r=a, the inside radius of the cylinder, the

ratio p/ur must equal the radial driving-point impedance, Z(co), at the wall. 4 Then, with k,<i = x. we get from eq (5), (3), and (6)

iojpaJo{x)l{x)Ji(x) = Z(o>), <8)

and from eq (4)

(o»/c) 2 = (x/a) 2 + (mr/L) 2

. (9)

Equations (8) and (9) determine simultaneous values

of co and x, Z (co) being supposed known.5 A difficulty common to all resonator systems is that the container must be pierced and provided witli

filling tubes for introduction of the sample. These

upset the sound field and also introduce losses. The

above analysis shows that the tubes should be lo- cated either in the lateral walls near the ends or in the ends near the circumference. For at the positions

r—a, z — 0 or L, both the pressure, p, and the radial

velocity, ur , vanish [eq (5), (3), (6)j. As for the axial velocity, uz , the ratio of its value at these positions

to the maximum value is just 7o(x)[eq (7) | which is also the ratio of the pressure on the lateral wall to that on the axis for any z. To prevent cavitation from

occurring on the wall, Jo{x) must be small — just how

small depends on the smoothness of the wall. A

“good” mode from this point of view therefore implies

a relatively small disturbance at the filling tubes.

Such modes are best found by trial; calculations from

eq (8) and (9) are possible but tedious. In the case of a spherical resonator all positions ol the neck are equally bad. The experiences of Finch

[1964] illustrate the point. These considerations,

among others, impelled us to use cylinders instead

of spheres. We will point out other advantages, and

many disadvantages, as they come up. Just now we

remark only that good geometry is easier to come by

in a hollow cylinder than in a hollow sphere.

a. Integral Drive Cylinders of piezoelectric ceramic are manufactured to close tolerances in a variety of sizes. We

have used mostly 7.5 cm OD by 7.5 to 10 cm high and

expect to try larger ones. As shown in figure 1, the

cylinder serves as part of the container, as the driving

transducer, and as a pickup. It can be of lead-zirconalc

titanate or of barium titanate; in either case the material should be one especially formulated for low loss (internal heating) at high drive.

4 We here ignore the dependence of Z( to) on z. ’From these simple equations we have calculated the resonant frequencies of liquid

filled cylinders and gotten good agreement with experiment. The pressure distributions, measured with a small probe, agree with those calculated, sometimes within a few percent

300
(b)

Kk.URE 1. Self-driven cylinder, schematic cross section.

i, il anil III). Mti riialc Irrminatinns and pla< em<*nt of filling luhes. The electrode config- oration on ill) is the saint' as on (a).

I < eramic, either lead-zirconate titanale or barium titanate. 2 . Metal rin^s. stainless steel or brass.

.’>. Sheet material, stainless steel or glass.

I. < ementetl joints.

5. Killing tubes.

6. KleOrode. ground.

7. Electrode anti etmnectitm, input.

8. Klee trode anti connection, output.

already mentioned. The second has to do with the

roughness and friability of the inside walls. We would

prefer to operate at the “breathing” mode [(r. d, z) = (1, 0, 1)] because the cylinder walls are for this mode more nearly pressure-release than for any other. Also, a larger fraction of the liquid is contained in the

high-pressure region. However, unless the pressures

are low, the wall motion in the (1, 0, l)-mode is so large

that the inside electrode (and sometimes the inner

surface of the ceramic) disintegrates and contaminates

the liquid. The overall performance is better in the

(3, 0, l)-mode and higher pressures are obtained.

There is a tendency for cavitation to occur on rough

spots on the wall, and this limits the maximum useful

negative pressure obtainable to the range 20 to 30

bars, depending on the particular cylinder and the

particular liquid. Such pressures are more than adequate for many organic liquids exposed to fast neutrons.

b. External Drive “Clean” water exposed to fast neutrons cannot

he cavitated in the ceramic cylinders described above.

A special cylindrical vessel was fabricated from stain- less steel tubing. The schematic, figure 2, is mostly

self explanatory.

The cylinder is operated in the (3, 0, 1) — mode,

and the driver is adjusted to resonate at the same

frequency at the temperature of test (in this case about 42.9 kHz at about 30 °C) in order to minimize

the stress in the epoxy joint between the driver and

a small milled flat on the cylinder.

“The cylinder is then repoled.

The metal rings allow for filling holes and connections. The flat ends are either stainless steel, 12 to 75

/xm thick, or glass, 250 pan thick. The glass, which is cut from microscope cover-glass stock, is fragile and

difficult to handle, but it allows one to see what goes

on. Ihe thinner material provides a better pressure

release than the thicker, but it is more easily excited

(parametrically, we think) into radial flexural vibrations.

The joints shown in figure 1 are best cemented with

a silicone-rubber adhesive which cures at room temperature. Many organic liquids attack this rubber,

however; for these, some other adhesive, such as an

epoxy, may serve. We have found no universal adhesive

nor one which lasts indefinitely with any single liquid.

Manufacturers supply cylinders electroded on both

the inside and outside with a fired-on silver-glass

mixture. The outside electrode configuration shown

in figure 1 is produced by dividing the electrode as furnished and the inner ground electrode is connected

with the outer ground bands by a conducting paint. In some cases we have removed the inner electrode

and replaced and extended it over the edges with

fired-on gold or platinum. K Tliese cylinders have two main limitations. The

first, namely limited life of the adhesives, we have

FIGURE 2. Externally driven cylinder, schematic cross section.

1. Stainless steel cylinder, 8.9 cm O.D. by 10.2 cm high, wall 0.16 cm thick. Inner surfaces

polished.

2. Stainless steel sheet, 75 /xm thick.

3. Silicone-rubber adhesive joints.

4. Filling tubes.

5. Composite, prestressed driving transducer, 13 mm O.D. The center section is lead zirconate-titanate; the ends and prestressing screw are of brass.

6. Wire strain gage.

7. Epoxy joints.

275-286 0- 67—4 301
FIGURE 3. Cortical flask.

1. Krlenmeyer Hask, neck removed.

2. Solid jilass |>lu|£ with 2 holes.

.1. Killing luhes.

4. Ceramic transducer.

5. Kpoxy joint.

At some temperature which fluctuates from day to day but is always within the range 29-31 °C, the overall Q is a maximum at about 12 000. Negative pres- sures of 160 bars are sustained by the water for a minute or so at a time, and of 210 bars for a few sec- onds. The cavitations are presumed to be nucleated

by either residual motes or adventitious neutrons. The readout is from a wire strain gage noninductively

wound around the circumference of the cylinder near

midheight. It consists of three double turns of 75 /xmdiaineter Karma wire cemented into a double Vthread, 50 fim deep, cut into the cylinder.

This cylinder could be used with various liquids

and at various temperatures for work at low pres- sures; however, we have used it only for high pres- sures in water at one temperature. A change in temperature detunes the system and requires the trans- ducer to he retuned. So far we have not found it worthwhile to do this.

2.2. Conical Flasks

Cylindrical geometry allows calculation of the pres- sure field and experimental verification (see footnote 5); this was one motivation for our choice. Nevertheless, we have made considerable use of the arrangement

shown schematically in figure 3 for which these

Figure 4. Circuit for use ivith cavitation cell. Schematic block diagram. The cell is the frequency-determining element of an oscillator.

advantages are absent. The container is made by re- placing the neck of an ordinary Erlenmeyer flask (125, 250, 300, 500, or 1000 ml) with a massive glass

plug, typically about 25 mm OD by 25 mm long.

It was found empirically that each assembly has

several modes for each of which there is a pressure

maximum on axis and almost no motion in the plug.

The flask can therefore be held by the plug without

much loss of Q\ the Q may reach 10 000. The resonant frequencies and the Q's depend on the particular

flask, transducer, liquid, and on the temperature,

and cannot be predicted.

The advantages here are (a) that the vessel is of one-piece, all glass construction with no joints and

(b) that the assemblies are cheap once the glassblower has taught himself how to eliminate rough

spots on the inside. These advantages often outweigh

the rather haphazard nature of the entire scheme,

and we have collected a considerable amount of valuable data using it. The drive is the voltage on, and the readout the cur- rent into, the transducer. See section 2.3.

2.3. Electronics

In all of our setups the cavitation cell, together with

its associated reactive elements, such as transducers,

is the frequency determining element of a self-sustain- ing oscillator. The scheme is shown in figure 4. The

wave filter, a simple combination of L,C-elemenls,

is adjusted so that its pass band is roughly centered on the frequency of interest. For some setting of the phase shifter the system will oscillate at the desired

frequency if the loop gain is large enough. Small

changes in the resonance frequency of the cavitation

cell, caused by temperature drifts, etc., are thus

automatically tracked.

The amplitude of oscillation is adjusted to any de- sired value by variation of the supply voltage to a transistor stage (“level set” in fig. 4). The level can be set manually or programed in any desired way.

302
— j CAVITATION CELL} °UTPUT

| VOLTAGE AMPLIFIER |—

[voltmeter

1 POWER AMPLIFIER] 1 RC OSCILLATOR |-- 3TMCH

tlGUHE 5. Circuit Jor use with cavitation cell.

Variant featuring easy portability.

For instance, the pressure in the cell can be caused

to increase linearly with time by application of a linear

voltage ramp to the “level set.” The “cavitation detector” rectifies and differentiates the amplified output of the cell. A cavitation event drops the Q of the system and therefore also the output amplitude; the resulting pulse can be made

to trip a relay and interrupt the supply to the “level

set,” stopping the oscillation. The cavitation detector

has adjustable sensitivity and can be made to trigger on mild events or on catastrophic events only. It can

also be disabled. The rectified signal is amplified and

applied to a small loudspeaker so that the cavitation events can be “heard.”

After the relay has been tripped it can be reset

after any desired elapsed time which exceeds the

minimum delay set by the Q of the system. Delays of

50 sec or less are obtained from the sweep voltage

available from the oscilloscope; longer delays are provided by a clock motor-switch arrangement.

The arrangement shown in figure 5 is not so versatile as the first, but is very simple and therefore well

adapted to portable equipment. The amplified output

synchronizes a Wien-bridge type oscillator. The oscillator functions as amplifier, filter, phase-shifter,

and amplitude control (level set). The main disadvantage is that each time the amplitude is changed the

frequency dial must be changed to restore the proper

phase shift, for at a given setting of the frequency

dial, the phase shift between the synchronizing and

output voltages depends on the amplitude of the

former [Owen, 1967J. A limiter at the synchronizing

jack would perhaps improve the performance.

In all of the above, the term “cell output” refers

to an electrical signal proportional to the maximum

sound pressure in the liquid. In figure 1, the output

is the voltage on the receiving bands (8). In figure 2,

it is the voltage across the strain gage (6) which has

a resistance of 510 ohms, carries a bias of about 14 mA,

and is coupled to an amplifier through a 1 to 14 step-up

transformer. The signal-to-noise ratio is poor so that

filtering is necessary. In this case the amplifier is stagger-tuned; the 3-dB bandwidth is about 2 kHz.

For the case of figure 3, the input voltage is applied

to the electrodes of the transducer; the output is the

current into the transducer. As shown in figure 6,

the current is sensed with a “clip-on probe,” a common

accessory for an oscilloscope. The probe measures

the algebraic sum of the current to the transducer

OUTPUT

Figure 6. Output system for conical flask.

('.an also be used with the cylindrical cells of figures 1 and 2. Especially convenient for remote operation. The capacitance of (3) is made equal to that of the leads plus that of the transducer; the probe then responds to the motional current only.

and that to the capacitor (3) with its leads reversed.

The capacitance of the auxiliary capacitor is made

equal to the sum of the “free” electrostatic capaci- tance of the transducer and the capacitance of the

leads; only the motional part of the current is measured. This arrangement makes it possible to have the

cell a hundred meters or more from the rest of the

equipment with only a single coaxial cable connection,

provided that the power amplifier is capable of deliver- ing the necessary in-quadrature current. Where a radiation hazard exists, this is a valuable feature.

2.4. Calibration

a. Probes A principal object of a typical experiment is the

determination of the maximum negative pressure in the liquid at the onset of cavitation. Those who work

with spherical flasks usually make use of a probe

microphone (probe). The active element is in most

cases a small ceramic tube or disk; it is mounted on

the end of a metal tube of diameter 1.5 to 3 mm which

protrudes through the neck of the flask so that the

active element is in a subsidiary pressure maximum.

The designs are numerous; for a complete description of an especially clever one, see Barger [1%4|.

We have built many such probes, a few novel but none remarkable. In our work we find it essential not to have the probe in the liquid during test. In- stead, the output of the cylinder is compared with

the reading of a calibrated probe which passes through

a small hole in the flat top of the cylinder during a separate run during which the sound pressures are

not so great as to produce cavitation on the probe.

Such a comparison has to be made for each liquid

at each frequency and at each temperature. The pro- cedure is tedious and in any case cannot be used in conical flasks. Also tedious is the calibration of the

probe itself. For instance Barger [1964] employed

a free-field reciprocity method, in water. We shall describe a novel method later on in this section.

303
b. Overpressure

We describe a method of calibrating a cell, that is, of relating the sound pressure in the liquid to the

reading of the output device, which is obvious but

subject to some limitations. Suppose that under some

specified condition a cavitation occurs at some negative pressure, T (threshold, a positive number); then

if p„ is the static, and p„ the amplitude of the acoustic,

pressure,

T=p,., — p*. (10)

The output is some voltage V, supposed proportional

to p„, so that eq (10) is V=(p*+T)lm , (11)

in which pa — mV. Two measurements of V for two

values of ps determine T and m. The method fails if T depends on p„. For instance, if the cavitation nucleus

is a gas or vapor bubble, somehow stabilized at (say)

atmospheric pressure against dissolution or condensation, respectively, then an increase in the static pres- sure ps will shrink the bubble and the liquid will be

“strengthened,” i.e., T will change with ps so that eq (10) is no longer linear. This phenomenon has been

discussed by Strasberg [1959J.

On the other hand, we find that if the cavitation is induced by neutron bombardment or a-disintegration,

then the threshold, T, is independent of the static pressure ps. The cell is enclosed in a pressure vessel

and the output, V, at threshold is determined for various values of />*. A plot of V as ordinate versus px as abscissa yields a straight line, of which the ps

- intercept, with reversed sign, is the threshold, T. There

is no measureable hysteresis. In practice, T is calculated from the data by least squares. The vessel is pressurized with nitrogen and the value of ps read on

a high-quality bourdon-tube gage. A piston arrangement (actually a hypodermic syringe) transmits the

pressure to the liquid, as will be described later. A major advantage of this “over-pressure” method

is that the nature of the pressure field in the cell does

not need to be known.

c. Calibration of Probes As a byproduct, the overpressure method provides a simple way of calibrating the small, rather insensitive

probes already discussed.

Some threshold, T, which as always has an arbitrary

definition, but which must be reproducible, is measured by the overpressure method in a cylindrical cell such as shown in figure 1. The maximum acoustic

pressure amplitude (at the center of the cell) is now

known in terms of the output voltage. A probe inserted

through a small hole in the top is then easily cali- brated against the output voltage; the result applies

at the frequency of test only. Other frequencies may

be gotten by changes of mode and/or liquid. For probes

which are sensitive on the flat end only, the response

may be extended over any frequency range by means

of an electrostatic actuator."

3. Apparatus, Auxiliary

3.1. Cleanup of Liquid

The exact nature of the natural nuclei in liquids

is unknown and almost certainly variable from sample

to sample and from time to time. Presumably they

are either bubbles (gas or vapor) somehow stabi- lized upon motes or motes which are poorly wetted:

in any case those larger than a specified size can be

removed by filtration. Membrane filters of large area, with uniform pores and relatively large flow rates are long since a common article of commerce.

General purpose types have a pore size as small as

0.01 pm. These are attacked by some organic liquids:

for many of these, other types having a pore size as small as 0.2 pm are available.

The degree of cleanup required depends on the nature of the case. For instance, suppose one wishes

to measure some cavitation threshold, Tt , under ir- radiation by neutrons from a particular source. Then it is necessary, in order to get reproducible

results, to remove from the liquid all nuclei upon

which cavitation can occur at stresses less than

about 2

'7V Because the rate of flow of a liquid through

a filter is smaller the smaller the pore size, a cleanup more drastic than necessary is undesirable.

In these respects, so far at least as T\ is concerned,

the most refractory liquid, among those we have so

far tried, is water. If all motes retained by a filter of

pore size 0.2 pm are removed, water will sustain

negative pressures in excess of 200 bar for a short

time, and of 100 bar almost indefinitely, so that conditions are satisfactory for the determination of

a value of 7j near 50 bar. However, it does not suffice merely to pour distilled water through a filter into the test container, for the latter contains dirty air; even if it is first evacuated, the water will become

contaminated by material on the walls. Rather it is necessary to make use of a scheme equivalent to that shown in figure 7. After the assembly shown is filled, the valves (2) may be set to form a closed sys- tem so that the water can be continuously circulated

by a bellows or diaphragm pump. Alternatively,

if a still is available which can produce water as

fast as it flows through the filter, the pump can be

dispensed with and the valves (2) set to admit and

discard the water continuously. The cleanup time is greatly shortened by acoustic agitation of the cell during the procedure and by the addition of detergent

to the inflowing water during the early stages. The

progress of the cleanup can be observed through

a dark-field microscope focused on the effluent

in a piece of precision-bore rectangular glass tubing.

7 The electrostatic actuator of Baliantine [19321 is described by Beranek |1‘H9|. p. 173. In our case it is not feasible to U9e it as an absolute device.

304
Fl<;URE 7. Cleanup system , schematic.

Some of the components are used only in special cases.

1 .2 = valves.

optically finished on the outside. The microscope

arrangement is rather crude, but it works well so long as the effluent is still rather dirty; however the

field of view is so small that after a few minutes of

operation the waiting time for passage of a mote be- comes long enough to fatigue the observer and render

his perception unreliable. Its main virtue is that

it makes it possible to determine whether or not the

shock wave caused by the collapse of a cavitation

bubble has dislodged additional motes from the

wall. In the case of water in a stainless steel cell, such dislodgment happens almost invariably, so that meaningful observations can be taken only at long

intervals, say 5 to 15 min.

A much less stringent procedure is required for organic liquids, at least the dozen or so we have so

far used. Two possible reasons come to mind; first, the thresholds, 7i, are lower than for water and sec- ond, the motes are either better wetted by, or more

soluble in the organics. Whatever the reasons, it turns

out that Tx is, in all cases so far, easily measured after only 10 or so minutes of circulation in an apparatus

like that in figure 7. (The microscope is omitted.) Valves

(1) are then closed and the connecting tubes detached

so that the cell and relief element can be removed for use. The relief element, which is a hypodermic sy- ringe, maintains the ambient pressure, or the over- pressure, on the contents. For some liquids pouring or pumping through a

filter into the flask, previously cleaned and rinsed

with the liquid, is sufficient. In others, even the filter- ing may be omitted, especially if the sample is from a

freshly opened bottle.

3.2. Gas Content of Liquid

Under some circumstances the cavitation threshold

is sensitive to the gas tension in the liquid. This ten- sion can be adjusted by allowing the liquid to come into

Figure 8. Apparatus for determination of oxygen, schematic.

1. Sensor, active tip in liquid.

2. Metering syringe, 5 cm3 Luerlok hypodermic.

3. Rack, hinged to plunger, engages pinion (not shown) on clock motor (not shown).

4. Sample or standard syringe, 10 cm' Luerlok hypodermic.

5. Stopcock, one-way, attached to syringe (4). 6. Stopcock, 3-way, attached to syringe (2). 7. Waste.

equilibrium with a gas at a partial pressure which is itself adjusted. For example, a liquid is easily satu rated by bubbling the gas through it at the particular

temperature and pressure for which saturation is desired. Also most of the dissolved gas can readily

be removed by pumping on the space above the liquid

in a closed container while stirring violently. A combination magnetic stirrer and hot plate is invaluable

for this purpose.

The gas tension may be measured by any of several

methods known to physical chemists. Strasberg [1959 J, and others since, made use of a Van Slyke blood-gas

apparatus, available from chemical supply houses. If the gas is air, which is usually the case,” one can use techniques peculiar to oxygen. We have found a polarographic technique based on the oxygen cathode to be very convenient. For a comprehensive review see Davies [1962J. We describe only the modifications

peculiar to our work.

In figure 8, (1) represents a sensor, about 1 mm in diameter, which is embedded in the wall of a tube

about 3 mm in diameter past which the test liquid flows. The sensor has a current output (a few microamperes)

which is proportional to the rate at which 02 is reduced

on an inert (gold, in our case) cathode separated from

the test liquid by a thin film of electrolyte and a teflon

H An exception is the study of sonoluminescence which is sensitive to the nature of the dissolved gas. 305
membrane. The 0_> reaches the cathode by diffusion

through the membrane so that the output current is proportional to the concentration of CV just outside it. The electrolysis depletes the liquid of 0>, so that the current output depends on the speed of flow in the

tube. The device shown in figure 8 standardizes the

flow rate and allows compensation for other variables

to be described. But first we note that the sensor, which is a modification of the “Clark cell” is easily

made. Ours is a modification of a commercial model.

The original Ag anode has been replaced by Ag—Ag20,

and instead of a KC1 gel we use, as electrolyte, 0.5A

KOH saturated with Ag2 0 and thickened with hydroxyethyl cellulose. This arrangement is more stable and

has a longer life than the original; it is based on the

work of Connelly and of Carrit and Kanwisher [see

Davies, 1962, p. 172j.

The metering syringe in figure 8 is driven by a clock

motor through a rack and pinion; the flow is 5 cm3/min

which amounts to about 2 cm/s past the sensor. Before making a measurement, a sample is withdrawn

from the apparatus into a 10-cm3 syringe provided

with a stopcock (5), taking the usual precautions to exclude air. At the same time a sample is withdrawn

into another, similar syringe from a bottle of the same

liquid in the oven and thus at the same temperature

as the test sample. This “standardizing” liquid is maintained saturated with air at the temperature of

the oven and the pressure of the atmosphere. In each

case the first withdrawal is discarded so that the

syringe is purged of air and residual liquid. The two

syringes, “standard” and “sample” with stopcocks

(5) closed are then allowed to come into temperature

equilibrium with the ambient at the location of the

apparatus in figure 8; the contents are then successively run through. The ratio of the “sample” reading

to the “standard” reading gives the oxygen tension

in percent relative to saturation at 1 atm total air pressure. Before taking a reading, the metering syringe

and associated tubing are purged with “test” or “standard” liquid by an obvious manipulation of the

stopcocks; the rack is hinged so that it can be lifted from the pinion to allow hand operation which facil- itates the process. The output current reaches a steady

value after about 1 cm3 of liquid has been expelled.

It will be seen that the scheme described eliminates

all of the important sources of error. These are (a) changes due to changes in flow rate past sensor,

(b) drifts due to aging of the cell, and (c) changes in sensitivity which arise from the high temperature

coefficients of diffusion in the liquid and in the Teflon.

3.3. Radiation Sources

As was mentioned in the introduction , cavitation has

been induced by neutron bombardment, by a-disintegration, and by fission.

a. Neutrons Most of the work so far done has been with (a, n) sources. In all cases the target atom has been Be1 ’;

the a emitters have been Ra [Sette and Wanderlingh.

1962], Po210 [Lieberman, 1959], Am2 ", and Pu239 [Hahn and Peacock, 1963]. The main disadvantage <>l a Ra source is its high y-ray background, about 6500

y’s/neutron. A Po source is small, but has a short

half-life (138 days). Of those sources we have had an

opportunity to use, the best from the standpoint ol size, half-life, and safety is Am-Be. The Pu-Be source

is about as good but larger; we now use Pu-Be because

of its lower price.

The characteristics of (a, n) sources are listed in NBS Handbook 72. The neutron energy spectra of such

sources are variable even among those nominally the

same, and they are known only approximately. Die

energy varies from zero to a maximum of 13.1. 10.9. 11.4, and 10.7 MeV for Ra, Po, Am. and Pu, respectively, and the average energy is about 4.5 MeV.

Most of our work has been done with a 10-curie

(16Qg Pu) Pu-Be source having a total output of 1.47 X 107 n/s. The data would be more easily interpreted if the more nearly monoergic neutrons produced by particle

accelerators were used. Finch [1964] worked with

14 MeV neutrons produced by the [T(d, a)/i] reaction.

We have made a few runs using this and also the

[D(d, n)He3

] reaction (2.5 MeV neutrons), but the

neutron fluxes were rather unsteady.

b. a-Disintegrafion

The short range of the heavy recoil nuclei from

disintegration of a dissolved a-emitter is a valuable- property; the cavitation data are more easily inter

preted. In order that the dissolved emitter not affect the

properties of the liquid too much, it should have a high activity, so that only traces are required. Po21 " perhaps represents a good compromise between high

activity and reasonable half-life; we have not yel tried

it for lack of facilities for safe handling. A possibledifficulty is that for some liquids too much of the Po

compound may be adsorbed on the walls of the container, leaving too little in the bulk of the liquid.

Ordinary thorium nitrate, Th(NO:jb • 4HjO is soluble in the lower alcohols and ethyl ether. We have- used concentrations of 1 to 10 g(Th) per liter in methyl,

ethyl and isopropyl alcohol with good results. I ranyl

nitrate UCMNOah • 6H2O, is also soluble in these

liquids. Although about three times as active as tho- rium, uranium is not as well suited to this work because

of the high spontaneous fission rate 9 of F

2 lh

.

It should be remembered that laboratory reagent

grades of thorium and uranium salts are contaminated with daughter products, many <>f which are- a-emitters.

c. Fission Cavitation occurs at relatively low stresses on

fission events in liquids. Any salt of the- fissionable

material, soluble in the liquid, may be- used. Slow, fast,

and spontaneous fission have been observed.

“About 25 n/g hr. For Th232, <0.15 n/g hr.

306
d. Natural Background

Cosmic-ray neutrons are a potential source of

cavitation nuclei and should be reckoned with under some circumstances. Watt [1967] has reviewed some

of the literature; as an average he takes the total Hux density to be 65 n/cnr/hr at sea level in the middle

latitudes. Of the total, most have low energies and

only 7 percent (4.5 n/cm 2 /hr, are above 10 MeV. Recent

measurements by Tajima, et al. [1967|, indicate a much lower flux density, at least in the range 2-10

MeV, and an altitude dependence like exp (— 0.0063 x )

x being the atmospheric depth in g/cm2

. In total flux density, the cosmic-neutron background

is equivalent to the neutron source in our laboratory

(1.47 X 107 n/s into 47t) at a distance exceeding 80

meters, and the former has a smaller fraction of neutrons at the higher energies.

4. Some Results

4.1. General

To fix ideas, we consider water at atmospheric pressure. The frequency of the sound pressure is in the

range 25-50 kHz and as a threshold we take the negative pressure at which the average waiting time for cavitation is (say) 30 sec. The threshold in ordinary tap

water or in distilled water, both of which contain numerous motes, varies markedly with the amount

of dissolved air, being higher the less air; furthermore

the threshold is variable from sample to sample and

from time to time in the same sample. Values range

from 1 bar or less at saturation (with air) to perhaps

10 bars at 10 to 30 percent saturation. Barger [1964J

studied these effects for a wide range of many of the

variables and Messino et al. [1967], added to the

water both wettable and unwettable motes; their results well illustrate the possibilities.

We have found the situation to be different, however,

if the water is cleaned up taking the precautions

described in section 3.1. In this case the threshold

rises as more of the motes are removed, no matter

what the air content, so long as it is below saturation

[Greenspan and Tschiegg, 1966a, bj. It seems that no

important purpose is served by protracted cleanup;

the threshold continues to rise unless (presumably)

the experiment is terminated by an adventitious

neutron. Table 1 summarizes a few results from the literature. The three sets are not strictly comparable although

Finch duplicated Galloway’s apparatus so far as possible. Note the marked effect of the amount of dis- solved air. Our measurements were taken at 43 kHz. At 46

kHz, Barger [1964] reports thresholds ranging from 1.2 bar at 760 torr partial pressure of air to 12.1 bar at 10 torr. These contrast with our thresholds of about

160 bar (several minute basis) or 210 bar (several

second basis) independent of air content from 120-

650 torr. Presumably the air content has less effect the cleaner the water.

Table 1 . Some cavitation thresholds in water

Galloway [1954] h,c Barger [1964] e

Threshold,1* bar

Partial pressure of dissolved air, torr.

0.2 4 100 250 700

200 d 110 8

8

3

3

1.1.70 Finch [1964] 9 ± 3

'

a Sound pressure amplitudes; static pressure 1 bar. The three threshold definitions are roughly equivalent. Frequency ~ 26 kHz.

h Interpolated from a curve.

c Spread about ± 12 percent.

d According to a private communication, Galloway to Finch

[1964] high value gotten sporadically. More often 15 to 20 bars.

e Spread not given.

f Another mode of operation gave 50 to 80 bars.

4.2. Neutron-Induced Cavitation

This effect was first found in acetone and in pen- tane by Lieberman [1959]. We have observed it since in water, isopropanol, and freon 1 13 (f d.lCf .GIT ) [Greenspan and Tschiegg, 1966aJ, in ethanol [Greenspan and Tschiegg, 1966b] and later in another dozen

or so organic liquids.

Two results stand out. First, the air content of the

liquid affects the threshold little if at all. Lieberman

also found this. Second, there is no appreciable induction or decay time for the effect. West and Howlett

[1967] have since investigated this point in detail;

in the liquid they used, tetrachloroethylene, the life- time of a bubble is about 2/xs. These results were

obtained in an elegant experiment using a pulsed

neutron source. We have already alluded to the results of Finch [1964] and of Sette’s group, which contrast markedly with, e.g., ours. They find a cumulative

effect; many minutes or even an hour of exposure to neutrons are required to “weaken” the liquid (water

in both cases) and the “strength’ returns at a similar

interval after exposure is terminated. Sette and his co-workers [Bertolotti et al. 1965, p. 1 09 1 feel that long lifetimes are characteristic of gassy (i.e., sat- urated with air at the static pressure) water; however

Finch’s water, which showed the effect, was only

0.5 percent saturated, and our water does not show

the effect even if gassy. Perhaps dirt is more important

than gas.

a. Statistics The question which obtrudes itself most forcefully

is whether or not the cavitations are single-particle

events, that is, whether each cavitation is traceable

to a single neutron or whether each is due to the

cooperative effect of two or more neutrons. In the

former case the cavitation rate would (a) follow a

307
Poisson distribution, and (b) satisfy the inverse-square

law for various distances of the neutron source from

the cavitation cell. Lieberman’s [1959] results in pentane were “rea- sonably close to a Poisson distribution.” We have

investigated this point in detail; the test liquid was

isopropanol (table 2). Two independent runs were made using the (3, 0, l)-mode of a lead zirconate

titanate cylinder of the type shown in figure 1(a). The temperature in each case was about 31 °C and

the frequency about 40 kHz. An Am-Be source radiat- ing 1.6 X 107 n/s into 4rr was used. For the first run, the interval distribution was analyzed, and for the

second, the events per unit time.

Run 1: With the source about 1 meter from the cell the apparatus was run at constant negative pressure

until 245 cavitation events had occurred; the times were automatically recorded on a strip chart. On

account of the dead time (1.31 s) 24 short intervals were missed. The total of 268 intervals were arranged

in 8 groups and analyzed as shown in table 2 using

the x

2 test [Evans, 1955, ch. 27|. No statistically significant departure from an exponential distribution

of interval lengths was observed and hence we may

regard the cavitation events as occurring individually

and collectively at random.

Table 2. Test of randomness ( interval distribution), in isopropanol

Class i. v *• X() Xe

c IV)

mm mm

1 0 i 57 57.6 .006 2 1 2 53 45.3 1.309

3 2 4 59 63.2 0.279 4 4 6 35 39.0 .410 5 6 8 27 24.1 .349 6 8 10 17 14.8 .327

7 10 13 9 12.3 .885 8 13 24 11 11.4 .014 2 208 267.7 3.579

X

2 = 3.58 F = 6 P = 0.73

H Time measured by length / on chart.

*’ Observed number of intervals of length / such that 6 =£ /< /2 .

' Expected number of intervals from x,. = 268 [exp (—0.242 Zi) — exp (—0.242 Is)]: 0.242 = mean number of events/mm.

Run 2: With the source at about 0.6 meter from the

cell, the negative pressure was adjusted so that about

14 events occurred per minute (gross). Events were

counted during 23 6-min runs. After adjustment for dead time (1.44 s/event) the counts were subjected

to x

2 analysis. The results were

X- = 24.6

F — 22

P= 0.30.

The average count rate was 21.5/min with a standard deviation from residuals of 6.1/min and an expected

standard deviation of (21.5) l/2 = 4.6/min. The conclusion is the same as for run 1. The inverse-square test is more difficult to do,

especially in a small room, because of the reflection

of neutrons from the sides and the furniture. Using

the same equipment and conditions as before, some

tests were made on isopropanol and more on Ireon 113 [Greenspan and Tschiegg, 1966a], We indicate

the results for the freon 113. At a fixed negative pres- sure 3 runs were made at each of the distances 0.91.

1.09, 1.28, 1.52, 1.83, and 2.11 meter. The products,

counts/unit time by square of distance, were averaged

for the 18 runs and used to calculate the expected

count for each run. The x

2 test gave R = 0.\ti. I he

experiment was repeated at a pressure amplitude 2 dB

higher with the result P= 0.22. It thus appears that the cavitation rate at fixed pressure is proportional

to neutfon flux. West and Howlett [1967] have per- formed a similar experiment on tetrachloroethylene

using a Po-Be source. They feel the inverse-square

law to have been verified within the experimental

error.

b. Threshold As a preliminary to the definition of a neutron thres- hold we consider how the cavitation rate varies with

the negative pressure, — p. Lieberman [1959 1 intro- duced the concept of “effective sensitive volume,”

Ve ; his argument may be paraphrased as follows. In the hypothetical case of a liquid populated by identical

nuclei, upon each of which cavitation occurs whenever it is in a region in which the negative pressure, — p, exceeds a fixed value T, called the threshold, the

“sensitive volume,” Vs , is that volume in which,

everywhere, —p>T. During each period of the pres- sure oscillation, there is a “sensitive time,” tx , during

which — p>T; this time varies with position in Fx . being greater the greater the pressure amplitude and

zero at the boundary of Vs. Then he defined

FP = f -dVs (12)

(t is the period), to which the cavitation rate might

be expected to be proportional under the assumed

conditions. Lieberman calculated, by numerical in- tegration, Ve as a function of — p/T for the case of a spherical resonator (sound pressure amplitude varies

like sin kr/kr). 10 His curve, which we have extended downward, is shown in figure 9. Shown also are our results" in freon 113 for the conditions given in table 3. It is seen

that the cavitation rate increases more rapidly with

negative pressure than does the effective volume.

From a similar experimental result Lieberman was

able to draw various conclusions about the action of

10 Koujih calculations show that the shape of the curve is nearly the same lot other pres sure distributions. "The results of Lieberman 1 1959]. in pentane, are qualitatively the same; those ol West

and Howlett |1%7|. in tetnuhloroethylene, very different. 308
CD

<r<

a> >

- p, dB re T

Figure 9. Cavitation rate versus negative pressure for freon 113; neutron irradiated.

See table 3 for conditions. Lieberman’s effective sensitive volume is shown in arbitrary

units.

neutrons in nucleating cavitation. These matters are beyond the scope of this paper; we only remark that we have made some rough measurements using nearly

monoergic neutrons which support Lieberman’s ideas. Part of the freon 113 data in figure 9 is shown again

in figure 10 together with data on methanol, isopropanol, and ether. The ordinates have been normalized

as shown in table 3, which also gives the test conditions. Although the actual cavitation rate spans the

range 0.37 per min (in freon 113) to 680 per min (in methanol), the points fall reasonably well on a universal curve although systematic differences from liquid to liquid are unmistakable (compare isopropanol with

ether). The result is consistent with the following:

(1) the cavitations are “single-particle” events;

(2) the range for — p/r, about 6 dB, is too small to show differences between the neutron spectra

of Am-Be and Pu-Be at their upper ends;

(3) over the same range, geometrical effects ( Ve ) as between cylinders and cones are not large.

Table 3. Test conditions for figures 9 and 10

Liquid Freon

113 Methyl

alcohol Isopropyl

alcohol Ethyl

ether

Source Am-Be Pu Be Pu Be Am-Be

n/ sec into 4xr 1.6 x 107 1.5 x 107 1.5 X 107 1.6 x 107 Distance, cm 91 (“) 91 25

( ell C) n < b

> n

Temperature, °C 31.5 25.6 31.5 28.5 Frequency, kHz 34.7 37.4 39.5 44.8 Normalization for figure 10 d 0.07 10 0.37 0.47

Source adjacent to cell.

11 Ceramic cylinder in (3, 0, 1) mode, see figure 1. 75 cm OD by 100 cm high.

' Conical flask, mode unknown, see figure 3. 125 ml.

*' Cavitations/min corresponding to the ordinate “1.”

Q

UJM

-I<

<£O

z

-p, dB re T

FIGURE 10. Cavitation rate versus negative pressure for four liquids; neutron irradiated.

See table 3 for conditions. The ordinate “1” corresponds to 0.07/min for freon 113 (A),

to 10/min for methyl alcohol (•), to 0.37/min for isopropyl alcohol (O), and to 0.47/min for diethyl ether (X).

As can be seen from figures 9 and 10, if a neutron source be placed adjacent to the cell, the operator can find a value of the electrical readout below which

cavitations occur rarely and above which they occur

at a rate of several per minute. The procedure is subjective and the reading obtained depends some- what on the neutron output of the source and on the

effective sensitive volume in the liquid, but nevertheless it can in most cases be reproduced to within ± 1 dB at worst and often to within ±0.2 dB. Such readings

are arbitrarily taken to correspond to thresholds,

and from a series of them taken at various over- pressures, a “neutron threshold” corresponding to the particular source is gotten as described in section 2.4b. The main advantage of the procedure is its speed and ease. It is desirable that our thresholds

be comparable to those obtained by others. Unfortunately very few thresholds for (a, rt) sources have

been measured. For n-pentane, Lieberman [1959]

got 2.1 bars in the room temperature region; we got

about 1.3. For acetone his values average to 5.5; ours is 4.8. We have a private communication from

C. West [Harwell] giving 6.5 ±1.2 bar in tetrachloro- ethylene, not far from our 7.8. These are all we can

find, and although the agreement seems marginal,

those familiar with cavitation data may find it rather

good. Both authors cited worked at about 20 kHz,

and our results are for 28 and 35 kHz in rc-pentane,

for 40 kHz in acetone, and for 49 kHz in CwCI). We

have made this comparison because there is some

evidence that the neutron threshold depends little on frequency in the range 20—60 kHz, at least; nevertheless this point requires investigation.

309
Tablk 4. Some neutron thresholds , Pu-Be source

Liquid Normal

boiling point Temp.

Fre- quency

Threshold

(absolute) Notes

°c °c kHz Bur

Pari 1

Methanol. (!ll|() 64.7 27 39 5.0 (a) Methanol CH,0 27 52 5.1 (b) Klliannl. C.ILO 78.4 28 42 6.7 la)

J -Propanol, ( ,lGO 97.8 27 56 14.4 (b)

I -Butanol, CiHinO 117.5 26 41 15.0 (c)

2-Propanol. C-,HxO 82.5 29 40 8.6 (a, d)

Pari 2

n-Pentane, 36.1 24.5 28 1.5 (e) 26 5 35 1.0 (c) n-Hexane. ( M 68.7 26.5 41 2.4 (el n-Mexane, C«Hm 26.9 35 2.5 (e)

Pari 3

Diethylelher. GjHioO 34.6 24.8 55 1.9 (b) Diethylether. C4 HmO 27.4 54 1.4 (b)

Freon 1 13. G->CI;jF;< 47.6 0 39 3.8 (e) 26 35 1.8 (e) 28 35 2.0 (e) 29 35 i .6 29 45 1.8 (0

Freon 11, C( l.iF 23.7 26.5 44 1.7 (g) Freon 1 1 , < T3 ,F 27.0 45 1.9 (g)

Part 4

Ktliyl bromide, C .H-,Br 38.4 30 47 3.1 (c) 31 36 3.1

Carbon tetrachloride. CCb 76.7 29 50 4.9 (g) Trichloroethylene, CZ H( .I , 86.7 30 48 4.5 (g) Tetrachloroethylene, CaCI 4 120.8 27 49 7.5 (b)

Part 5

Methylene chloride, CHjCL 39.5 26.3 35 3.0 (c) 27.2 43 5.1 (c) 27.4 29 3.3 Methylene chloride, CH2CI2 28.7 53 4.5 (c)

•' In Ba TiOi cylinder, 7.5 cm D by 7.5 cm high, (3, 0, l)-mode. Sec figure 1(a). 'MOO ml conical flask, mode unknown. See figure 3.

' 125 ml conical flask, mode unknown. See figure 3.

'* 2-propanol is out of place, but is shown for companion.

*' In lead zirconate-titanate cylinder, 7.5 cm OD by 7.5 cm high, (3, 0, l)-mode. See figure Kb).

' As (e). but mode unknown. “250 ml conical flask, mode unknown. See figure 3.

Some neutron thresholds obtained by the method

described are given in table 4. These are intended to be illustrative only, but some possible trends emerge.

1. There is some evidence for frequency independence (part 1, methanol; part 2, freon 113; part 4,

ethyl bromide).

2. In a homologous series, the neutron threshold in- creases as the series is ascended. Part 1 lists 4 nor- mal alcohols and part 2, two normal alkanes.

3. In general the threshold decreases as the temperature increases. The dependence is stronger for temperatures closer to the normal boiling point.

See parts 2 and 3. To interpret the results for freon 113

(part 3) this way we have to suppose that these thresholds are subject to an error of at least 0.2 bar.

4. One gets the impression that, other things being

equal, low boiling liquids have a lower threshold than

high. However, freon 11 and freon 113 contain the same elements, and have approximately the same

TABLE 5. Neutron threshold versus neutron enerji\ T = 29 °C. F = 44-52 kHz.

Neutron Threshold, bar

MeV Freon 113 Methanol Ethanol

2.5 [ D(d, n)He:t ] 4.4 10.4 13.4 Pu-Be (10.4?) 1.8 5.0 6.7 14 [T(d, a)n] 0.7 2.4 4.0

density, thermal expansion coefficient, surface tension, specific heat, and latent heat (per mole): 1 - yet

they have about the same threshold at (say) 27 °C

although the vapor pressure of freon 11 at this temperature is almost twice that of freon 113.

5. Note how the effects of atomic composition can

be separated from those of gross physical properties. Examples are the isomers 1-propanol and 2- propanol in part 1, and the pair 1-butanol in part 1 and diethyl ether in part 2, both of which are CjHioO.

6. Part 5 is included to show a liquid, methylene

chloride, in which the neutron thresholds as measured

vary irregularly with frequency even though the

original data look good. We suspect that the sensitive

volumes were so small in relation to the available

neutron flux, and varied so much from frequency to frequency, that the measured “thresholds” are not comparable. The neutron thresholds as defined would

be much more determinate if the source were either

larger, more nearly monoergic, or both.

Some miscellaneous results are given in part 4.

c. Threshold Versus Neutron Energy

We have made some preliminary measurements of

threshold as a function of neutron energy. In table 5, it is tentatively presumed that what are being seen in the

Pu-Be source are the neutrons of maximum energy.

The 2.5 MeV neutrons are from the D — D, and the

14 MeV, from the D — T, reactions. 1 * The results are probably only rough because the neutron generator was operated near its minimum output where the (lux

is both unknown and irregular. The implications of

these results with respect to a principle for neutron

spectrometry is obvious.

4.3. Alpha-Recoil Induced Cavitation

An a-emitter dissolved in a liquid provides cavitation nuclei in any concentration desired [Greenspan

and Tschiegg, 1966 a, b]. As Riepe and Hahn |]%1|

who worked with a-emitters in a bubble chamber have

pointed out, the heavy recoil nucleus, although it

12 The properties listed are those which are considered significant in various theories. The viscosity has been omitted, but this is larger for freon 113 than for freon II, which would be expected to further increase the threshold for 113 compared to that for 1 1. ,n We are indebted to Frank Sentfle and his co-workers of the U.S. Geological Survey

for making available and operating the neutron generator.

310
carried only about 2 percent of the total energy, is the

responsible agent, because of its very small range rela- tive to that of the a-particle. Indeed the range is in most cases so small that all of the energy is deposited

in the immediate neighborhood of the impending cavitation, so that if all disintegrations were of the same

energy all cavitation nuclei would correspond to the same threshold. In this case the function, cavitation

rate versus negative pressure, would be expected to be

nearly the same as Lieberman’s effective sensitive

volume function already discussed and shown in figure 9. We have made measurements on methanol and on

diethyl ether; the a-emitter was ordinary reagentgrade thorium nitrate at a concentration of 3 g/1, which corresponds to about 300 disintegrations per

minute (dpm) for the parent and each daughter in equilibrium with it. The age of the salt is unknown,

but rough ar-range measurements in air show that a considerable amount of the last a-emitter in the chain

(ThC') is present. The ThC' has the highest a-disintegration energy, 8.95 MeV, in the chain, and if in equilibrium would yield 200 a s/min on account of

branching in the decay of its parent, ThC, which would

0 12 3 4 5 6 7

(/)

>-

CC<

CC

CD

CC<

<D >

-p, dB re T

MOI RE 11 . Cavitation rate versus negative pressure for methanol and ethyl ether; a — disintegrations.

im lliaiml al >(< °C. in 125 ml conical (task (see fifi. 3)./= 37 kHz.

0 ethyl ether al 28 °C, in similar cell, (see fig. 3) /= 45 kHz.

1 he -iilitl line is I ieberman s effective sensitive volume curve.

I lie dashed lines show it shifted ±0.2 dB.

provide about 100 a’s/min of energy 6.05 MeV. Five

other a-emitters are also present; their a energies

range from 4.00 to 6.77 MeV.

The results are shown in figure 11 superimposed on Lieberman’s Ve curve in such a way as to give the

best fit by eye. The dashed curves are drawn to show the errors in the cavitation rates produced by a ±0.2 dB drift in the apparatus. The methanol results show good agreement as would be expected if only

the ThC' disintegrations were effective and the

ether results indicate that the lower-energy disinte- grations come into play as the negative pressure

increases. It is hardly likely that one situation prevails

for methanol and the other for ether, so the results must be considered as preliminary to further work

with single-isotope solutes. The “a-thresholds” were

11.0 bars for methanol and 4.0 bars for ether.

4.4. Fission

Messino, et al. [1963], reported that the cavitation

threshold of water was lowered from 1.6 to 0.55 bar

by the addition of 5 percent uranyl nitrate, and as- cribed the result to fission of the U2:ir> fraction (0.7%)

by cosmic neutrons thermalized by the water. In spite of the low cosmic-neutron flux the hypothesis is consistent with the authors’ view that the cavitation

nuclei have a long lifetime, although it is not clear

that the authors gave due consideration to the competing sources of spontaneous fission in U

23K and of

the laboratory neutron source (see section 3.3). We have observed fast fission in solutions of thorium

nitrate in isopropanol and in methanol, at thresholds

not very well defined, but about 10 dB below the

neutron threshold. The spontaneous fission rate of

Th232 is about 0.15/g hr and that from cosmic neutrons < 0.003/g hr [Segre. 1952J. A solution of natural uranyl nitrate in clean water

exposed to neutrons from our Pu-Be source cavitates

at negative pressures in the range 10 to 20 bars. The events appear to be as abrupt as those induced

by neutrons or a-recoils and cavitation ceases immediately as the source is encased. No such effect is observed at much higher stresses if other heavy

metal salts are substituted, and without doubt both

thermal and fast fission are observed in the natural

uranium, for which the fission cross sections are about 4 and 0.5 barns, respectively.

Uranium in methanol exhibits some peculiar fea- tures. Many of the events leave large bubbles which

are trapped in the pressure nodes, and which persist

until the sound field is removed, even though the liquid

has been first degassed. It is difficult to say anything

about the effect of cosmic neutrons on the fission,

because we can remove our encased source (23 cm

of paraffin) only to about 40 meters from the cell. At

this distance the output of the shielded source is still comparable to the cosmic flux. Only a few fissions per

hour are observed.
5. Remarks 6. References

We have described several types of apparatus and

procedures for their use which allow the acoustic

cavitation properties of liquids to be determined

with much greater reproducibility than hitherto

attained. They are susceptible to further improvement, so that eventually it should be possible to make measurements as precise as the statistical nature of cavitation properties, and the imperfect

characterization of the test liquids, permit.

Contaminants can be removed, with some ease or with considerable difficulty, depending on the nature

of the liquid, so that over a range of (negative) pres- sure levels cavitations occur only when nucleated by

certain ionizing radiations. The cavitations are always

single-particle events, at least under the conditions of our experiments. The results presented are mostly for

illustration; more systematic investigations, which we

hope refinements in the apparatus will make possible,

will yield a body of empirical data which can be

expected to support some existing theories of the

process and cast doubt upon others, and perhaps to point the way to their modification. Presumably the

theories of ultrasonic cavitation, of the bubble chamber, and of the static strength of liquids, are inter- related, and some features of these processes are doubtless shared by hydraulic cavitation as well. Ionizing particles provide reproducible nuclei for studies of ultrasonic cavitation per se, but the possibility of using radiation-induced cavitation in nuclear

instrumentation has intrigued many, beginning with

Hughes [I960]. Hahn and Peacock [1963] proposed a neutron detector discussed at greater length by

Bertolotti, et al. [1965]; more definitive experiments were performed by West [1965]. Our work extends

these notions to a wide variety of liquids and opens

up the possible development of a neutron spectrometer.

Ballantine, S. (1932) J. Acoust. Soc. Am. 3, 319-360.

Barger, James E. (1964) Thresholds of Acoustic Cavitation. Technical Memorandum No. 57, Acoustics Research Laboratory. Harvard University, ONR Contract Nonr 1866(24). Beranek, Leo L. (1949) Acoustic Measurements (Wiley & Sons,

Inc., New York. N.Y.).

Bertolotti, M., Sette, D. and Wanderlingh F. (1965) N'ucl. Inst, and

Meth. 35, 109-112.

Davies, Philip W. (1962) Chapter 3 of Physical Techniques in Biological Research, Vol. IV, (Academic Press). Evans, R. D. (1955) The Atomic Nucleus (McGraw-Hill Book Co.. New York. N.Y.). Finch, R. D. (1964) J. Acoust. Soc. Am. 36, 2287-2292.

Flynn, H. G. (1964) Chapter 9 of Physical Acoustics, Vol. I, Part B. W. P. Mason, Ed. (Academic Press, New York). Galloway, W. J. (1954) J. Acoust. Soc. Am. 26, 849-857. Greenspan, Martin and Tschiegg, Carl E. (1966a) J. Acoust. Soc. Am. 39, 1236 (abstr). Greenspan, Martin and Tschiegg, Carl E. (1966b) J. Acoust. Soc. Am. 40, 1239 (abstr). Hahn, B. and Peacock, R. N. (1963) Nuclear Inst, and Methods 20,

133-134. Lieberman, D. (1959) Phys. Fluids 2 , 466-468 (additional details in his thesis “Radiation-Induced Cavitation”, Tech. Report No. XII, Project NR 014-302 of U.S. Office of Naval Research. I niv. of

Calif., Los Angeles).

Leonard, R. W. (1946) J. Acoust. Soc. Am. 18, 252. Messino, C. D., Sette, D. and Wanderlingh, I'. (1963) J. Acoust.

Soc. Am. 35. 1575-1583. Messino, C. D., Sette, D. and Wanderlingh, F. (1967) J. Acoust.

Soc. Am. 41, 573-583. Owen, R. E. (1967) General Radio Experimenter 41, No. 2, 3-11. Riepe, G. and Hahn, B. (1961) Helv. Phys. Acta. 34, 865-892.

Segre, E. (1952) Phys. Rev. 86, 21. Sette, D. and Wanderlingh, F. (1962) Phys. Rev. 125, 409-417.

Sirotyuk, M. G. (1962) Soviet Phys-Acoust. 8, 165-169.

Strasberg, M. (1959) J. Acoust. Soc. Am. 31, 163-176. Tajima, Eizo; Adachi, Minoru; Doke, Tadayoshi; Kubota, Shinzou; and Tsukuda, Masahiro (1967) J. Phys. Soc. Japan, 22, 355-360. Watt, D. E. (1967) Health Physics 13, 501-507. West, C. (1965) Nucl. Inst, and Meth. 33, 361-362. West, C. and Howlett, R. (1967) Some Experiments on Ultrasonic Cavitation Using a Pulsed Neutron Source. U K Atomic Energy

Authority Research Group Memo AERE-M1880.

Willard, G. W. (1953) J. Acoust. Soc. Am. 25, 669-686. Paper 71C4-261)

312
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U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION OR REPORT NO.

NBSIR 79-1753

2. Gov’t

V-

5. Reciprent’s Accession No.

4. TITLE AND SUBTITLE

RADIATION- INDUCED ACOUSTIC CAVITATION; THRESHOLD VS

TEMPERATURE FOR SOME LIQUIDS

5. Publication Date May 10, 1979

antzation Code

. v 7. AUTHOR(S)

Martin Greenspan and C. E. Tschiegg

8. Performing Organ. Report No.

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, DC 20234

11. Contract/Grant No. 808294

12. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (S treet, City, stete, ZIP)

Department of the Navy

Office of Naval Research

Arlington, VA 22217

13. Type of Report & Period Covered NBSIR - Final Report

3/30/78-3/30/79

1 15. SUPPLEMENTARY NOTES

| | Document describes a computer program; SF-185, FIPS Software Summary, is attached.

16. ABSTRACT (A 200-word or leas factual summary of moat significant information. If document includes a significant bibliography or

literature survey, mention it here.)

Neutron thresholds at various temperatures were measured for methanol, ethanol,

1-propanol, 2-propanol, n-pentane, diethyl ether, fluorocarbon 113 and fluorocarbon 11

and fission thresholds were similarly measured for water, 1-propanol and 2-propanol.

The work was done in 1969, but not reported then because the project had not been

completed owing to the pressure of other duties. However, there seems to be a revival of interest in this sort of thing and we have been persuaded to work up and

publish the data, such as it is. So here goes.

17, KEY WORDS (six to twelve entries; alphabetical order; capitalize only the first letter of the first key word unless a proper name;

separated by semicolons)

Acoustic cavitation; cavitation; cavitation threshold vs temperature; radiationinduced cavitation; temperature dependence of cavitation threshold; threshold

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