conversion of electromagnetic to acoustic energy by surface heating

13,10; 12.5 Received 17 June 1966

Conversion of Electromagnetic to Acoustic Energy by Surface Heating

LUKE S. GOURNAY

Field Research Laboratory, Mobil Oil Corporation, Dallas, Texas 75221

The stresses that evolve in a thermally shocked liquid were examined. The magnitude and time duration of stress transients generated by a Q-switched ruby laser were measured in the absence of a phase change and compared with results calculated from a simplified thermodynamic model. It is shown that the model agrees with experimental data over a wide range of incident electromagnetic intensity and for large varia- tions of liquid properties. Results are also presented to show the effect of liquid vaporization on the stress transients and the parameters associated with formation of a gas phase.

INTRODUCTION

N the process of absorption of electromagnetic radiation, a portion of the incident energy is con- verted to an elastic wave in the absorbing medium. •.•' The mechanical stress generated in this manner becomes significant in the limit of extreme thermal shock and can vastly exceed radiation pressure. It is the purpose of this paper to examine, with certain restrictions, this method of generation of elastic waves.

A one-dimensional mathematical model is developed that assumes uniform heating at and near the surface of an absorbing body. If the incident intensity is uniformly distributed, there results a temperature gradient normal to the surface that is characterized by physical properties of the medium and the input intensity. The thermal expansion that results produces a strain in the medium and a stress wave that propa- gates away from the heated region. The time history of this wave depends upon the temporal variation of input energy and the boundary conditions at the heated surface.

For energy inputs of nanosecond duration and media of low thermal conductivity, we assume an adiabatic process, a simple temperature-time relationship, and negligible heat loss due to thermal conductivity. Radia- tion damping is assumed to be negligible; i.e., most of the input energy degenerates to heat in the medium.

Experiments were performed using a Q-switched ruby laser as the energy source and various absorbing

x R. M. White, J. Appl. Phys. 34, 3559-3567 (1963). •' E. F. Carome, N. A. Clark, and C. E. Moeller, Appl. Phys.

Letters 4, 95-97 (1964).

1322 Volume 40 Number 6 1966

liquids as elastic media. Physical quantifies were varied in a series of experiments in order to test the validity and range of the assumed model of stress generation. These experiments are described and limitations of the model are discussed.

I. MATHEMATICAL MODELS

A. Equations of Motion

Assume that a uniform beam of electromagnetic radiation is directed at an absorbing body whose surface is in the plane X--0. Upon progressing through the medium, the radiation intensity is reduced by absorption and is given by

where I (X) is the intensity at distance X from surface, I0 is the intensity at the surface, and a is the absorption coefficient of medium. Absorption of energy is accompanied by a temperature rise and a strain in the medium of

•= Ou(x,t)/Ox=•O(x,t), (2)

where u is the X component of particle displacement, fi is the coefficient of linear thermal expansion, and O(x,t) is the temperature rise due to absorption. It is assumed, for the purposes of this model, that

and, therefore, Ou/Oy=Ou/Oz=O, (3)

•uu= •=0. (4)

The strain of Eq. 2 could have been produced under

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13:58:55

CONVERSION OF LIGHT TO ACOUSTIC ENERGY

isothermal conditions by a mechanical stress of

•r xx= -- BfiO, (s)

where B is the modulus of elasticity. For a medium that experiences both heating and stresses, Love a presents the stress-strain relation as

•rx•= Be•-- B•O, (6)

where we restrict ourselves to a situation of negligible lateral inertia and shear, e.g., liquids and thin rods of diameter less than elastic wavelength.

Letting p be the density of the medium, the equation of motion is

0% O• 0% O0 p = =B --Bfi--. (7)

Ot •' Ox Ox • Ox

Rearranging terms and letting

c= (8)

where C is the velocity of elastic-wave propagation, we have

0% 1 O•'u O0 =fi--. (9)

Ox •' C •' OF' Ox

Solutions to this nonhomogeneous wave equation are developed for two boundary conditions and the follow- ing temperature distribution.

B. Temperature Distribution

We examine the temperature rise for a source of constant input intensity with exponential absorption in the medium and short time duration. Consider

radiation of intensity I0 that is turned on at t=0 and off at t= T. By virtue of Eq. 1, we now have a heat source in the region X>0 whose heat-production rate is

A (x,t)= gloe -"x, (10)

where g is a constant of the medium. The heat flow is essentially one-dimensional as long as the penetration depth a -1 is much less than the diameter of the region receiving heat. For the case of heat flow only in the positive X direction, a solution for the temperature distribution is given by Carslaw and Jaeger 4 as

O(x,t)=2gIø(td)«i erfc ---e -"x Ka 2(td) ,

glo erfc[a (td) «_ (t••l •- e (ot2td--otX ) 2Kd' 2

1 n t- e (•2ta+"x) erfc (11) 2Ka • (td)• '

a A. E. H. Love, A Treatise on the Mathematical Theory of Elasticity (Cambridge University Press, Cambridge, England, 1927).

• H. S. Carslaw and J. C. Jaeger, Conduction of Heat in Solids (Oxford University Press, London, 1959), 2nd ed., Chap. 2.

where K is the thermal conductivity d is the thermal diffusivity, err is the error function, erfc= 1--err, and ierfc=(--1)l(1--erf). Ready 5 has examined Eq. 11 for nanosecond time intervals of heating in media of low thermal conductivity such as nonmetallic solids and liquids. For intense heating in the time range 10-50 nsec, Eq. 11 can be approximated by

O(x,t) =alote-•X/JpS, (12)

where J is the mechanical equivalent of heat and S is the specific heat of medium. This approximation implies that the input energy flux to the medium is much greater than that lost by thermal conduction and radiation. The input under consideration is that available from a Q-switched laser, e.g., 50-100 MW/cm •, but a consequent temperature rise of only tens of degrees.

An interesting feature of this type heating is the extremely large temperature gradient and rapid temperature rise. In water colored by a dye to give a= 10 •', one can expect gradients as high as 7.5X10 a deg/cm and temperature rates of change of 2.5X10 ø deg/sec at the surface during the laser pulse.

In nonmetallic media, the temperature decay for t> T is a slowly varying function of t and becomes significant only for t greater than milliseconds. Since the elastic transients under consideration propagate away from the heated region in a matter of micro- seconds, we assume that for t> T

O(x,t)=aIoTe-"X/JpS. (13)

For impulsive heating, therefore, we seek a solution to Eq. 9, using Eq. 12 and 13 as source functions.

C. Solution for Two Boundary Conditions

1. Constrained Surface

Through use of Eqs. 12 and 13, we have

0% 0% ! C•'Wte-"X' t< T, •=CLq - (14) Ot • Ox e t C•'WTe -"x, t> T,

for wave equations during and after the heating pulse and where

Let us consider first the initial conditions

Ou/Ot l Jr.o= u(X,o) = o (16)

and boundary conditions for a constrained surface

(17)

Taking the Laplace transform of Eqs. 14 with respect

6 j. F. Ready, J. Appl. Phys. 36, 462-468 (1965).

The Journal of the Acoustical Society of America 1323


13:58:55

L. $. GOURNAY

to t over the range of t from 0 to oo, we have

s•'œ[u (x,t) ]-- su (x,O)---- Ot x,0

0 • C2W (18)

Application of initial conditions reduces this to

02 C*W

s*œEu(x,t)]=c*•-•œEu(x,t)]+--•-El-e-'•e -"x. (19) A complementary solution is obtained by letting

W=0, (O*/Ox•)œe -- (s•/C•)œ•= 0 (20)

and

œc=A (s)e--(x/e)*nUB(s)e(X/C)*. (21)

Since u(x,t) and thus œ0 must remain finite as X --• oo, B (s) must be set to zero and therefore

œ0= A (s)e -(x/c)*. (22)

A particular integral is determined by substitution of

œ•,= He -"x (23)

in Eq. 19 to obtain

s2He-"X=C*o?He-"XnbW--(1--e-•)e-"x (24)

and

tI=C•'W(1-e-'•')/s2(s2-a•'C2). (25)

The complete solution for the transform is

.eEu(x,t)]= A (s)e +EC*W(1-e-'r)/s2(s*-a2c2)]e -"x. (26)

From the bo•dary conditions •at u(0,t) = 0 and hence •Eu(0,t)]=0, we evaluate the constant

A (s)= -EC•W(1-e-'r)/s•(s•-a•C•)] (27)

and can rewrite Eq. 26 as

s'(s'-a'C'). (28)

After expanding Eq. 28 into rational fractions, we take inverses and obtain particle displacement u(x,t) applicable to various time intervals. Substitution of Ou/Ox in Eq. 6 leads to an e•ression for stress in the medium as a function of time and distance from surface.

The equations for displacement and stress ar• T (t<X/C:

u(x,t) = (W/. •) { (e-"x/.C) (1 - cosh. Cr) sinhaCt + (e-"X/aC) coshaCt sinhaCT-- Te-"X}, (29)

a(x,t)= (Cglo/JS){e-"X(1--c *or) sinhaCt} ; (30)

x/c<t<x/c+T: u (x,t) = (W/.•) { (e-"x/.C) (• -- cosh.½r) sinhaCt

q- (e--"x/ac) coshaCt sinhaCT -- (1/aC) sinhaC (t--x/c)

-- re-"Xnbt--x/c}, (31)

cr (x,t) = (Cl•Io/JS) { e -"x (1 - e -"or) sinhaCt --coshaC(t-x/c)n u l} ; (32)

t>x/c+T: u (x,t) = (W/a 2) { (e-"X/aC) [ (1 -- coshaC T) sinhaCt

q- coshaCt sinhaCT_• q- (1/aC) EsinhaC (x/c-- t) q-sinhaC (t--x/c-- T) •

+TO-e-"x)}, (33)

a(x,t) = (Ct•Io/JS) { e -"x sinhaCt(1-e -"c•') -- (1 -- coshaCr)[coshaC (t--x/c) •

--sinhaC(t--x/c) sinhaCr}. (34)

In restricting ourselves to a one-dimensional heat problem, we required that the depth of heating be much smaller than the diameter of heated zone dh. A

consequence is that a-l•<dh and a plane wave is propagated away from the surface. We can thus examine Eqs. 29-34 in the limit of aX>>I by dropping those terms containing exp--[aXnuCt]. A reduced time

r=t--x/c (35)

is introduced to simplify the expressions, and we obtain

lima(x,t) = •X>>I

'[1-- e-"erie "c•, r< 0,

Ct•Io [2--e-"C•--e"C(•-z)], 0<r<T, (36) 2JS [e"Cr-1] e-"c•, r> T.

The maximum stress occurs at r= T/2 and its value

Ëmax = (Clglo/2JS)(1-e -"c•/2) (37)

approaches the limiting value of Cfitlo,/2JS for aCT/2>> 1.

• 0.4 --

I

•-• ct = 670 cm -I

a = 335 cr• I ß ..

_ . 0.1 0.2 ß r (MICROSEC)

F•o. 1. Computed stress in water as a function of reduced time, constrained surface. C = 1.5 X 10 5 cm/sec. T = 2 X 10 -• sec.



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CONVERSION OF I. IGHT TO ACOUSTIC ENERGY

Conversely, small values of aCT lead to

O'm•,x = (CfiIo/2JS) (aCT/2). (38)

Equation 36 was evaluated for various values of aCT and the results are plotted in Fig. 1.

2. Free Surface

The boundary condition at the surface is

•(o,t) = z3E Ou (O,t) / o• - z3•o (o,t) = o,

and, therefore,

Ou(O,t)

Ox I fialot/JpS, t < T, •=g0(0,t)= tgalor/JpS, t> r.

Noting that, if

œ•u (x,t) •lx=0 = fo u (x,t)e-"tdtl x=0, then

o fo © Ou(•,t) .e-*'atl Ox Ox

we can write

,oeEu(x,t)•l •=0= te-*'dt+ Te-8'dt Ox

W { 1--e -*v ot s 2

(39)

(40)

(4•)

(42)

(43)

We take the partial derivative of the right-hand side of Eq. 26, evaluate it at X=0, and equate the result to that of Eq. 43 to obtain an expression for A (s):

A (s)= --•CW(1--e-*V)/as(s2--a2C2)•. (44)

The complete transform is now

x/c.( t ( x/cn t- T:

filo { e -'•x u(x,t)=j--• ['sinhaCt--sinhaC(t-- T)• a--•

coshaC (t-- X/C) 1 ! -- Te -'•x-- t-• , aC aC,

C•Io v(x,t) = •{ [sinhaCt-- sinhaC (t-- T) •e -•x

JS

-- sinhaC ( t- X/C) }; t>x/c+T:

filo { e -•x u(x,t) = j-• ['sinhaCt--sinhaC(t-- T)• a---•- coshaC (t-- X/C)

_ ye-aX- aC

(48)

(49)

coshaC (t-- X/C-- T)

aC (50)

•(x,t) = (C•Io/'JS) { ['sinhaCt-- sinhaC (t-- T) ]e -"x

-- sinhaC (t-- X/C)q-sinhaC (t-- X/C- T) }. (51)

Again, if the observation of stress is made with aX>>I, we have, in terms of the reduced time r,

r<0,

0<r<T,

r>T.

(52)

Maximum stress values of

•m,•= (C•Zo/2J$)E•--e-"C•5 (53)

appear at r=0 and r= T and approach a limiting value of CfiIo/2JS for aCT>>I.

CW(l_e-8•)e-CX/C)8 0.8

•Eu (•,t) • = - •(s'•-•C '•) ..... (45) q c•w (•- e-•)e-•': • o.•

s•(s,•_a•C,•) ' We take the inverse to get (x,t) and solve for • I I •-

•(x,t) as before, to get-- • I-g.t -o[, } [ f• _,

•) fi[o I sinhaCt sinhaC(t- _

.c r (46) 0.8

• (x,t) = (CfiIo/JS) { sinhaCt (1-- cosh,Cr) Fro. 2. Computed stress • water as a function of reduced time,

+coshaCt sinhaCT}•"x; (47) free surface. C and T as • Fig. 1.



13:58:55

L. S. GOURNAY

It is clear that the stress undergoes an abrupt change from compression to tension during the time T (over a distance CT) and large pressure gradients are predicted. For example, a 100-MW, 30-nsec laser pulse on water with a=100 is expected to produce peak stresses of +20 arm. Over the distance CT= 15 t• the total stress change should be 40 arm.

Equation 52 was solved for various values of a and results are plotted in Fig. 2.

D. Efficiency of Energy Conversion

We define conversion efficiency as the ratio

(54)

where Ea is the energy of the propagated elastic wave and Ee is the energy of the incident electromagnetic wave.

Elastic wave energy is given by

Aaf Aa( CfiEe •2 E a = ;• (r•d t = • X oc \2]-•Tr/

1. Free Surface

(55)

where Aa is the area through which the elastic wave is propagated and Ae is the area over which the electromagnetic wave is incident. We perform the integrations of Eq. 55, let Aa= Ae, and obtain

N= (Cfi•to/2oS•J•')Fx (aCT), (56) where

F x (acr) = (1-- e-•Cv--aCre-•e•') /acr. (57)

I0 is in watts per square centimeter, and the remaining quantities are in cgs (centimeter-gram-second) units. The function Fx(aCT) is plotted in Fig. 3 for various values of its argument; its maximum value is 0.3 when aCT= 2.0. To illustrate the dependence of efficiency on properties of the medium, we compare water and carbon tetrachloride and obtain numerically

Nu=o = 1.83 X 10-11IoFl(•Cr), (58)

Nee,,= 6.14X l•'I•½cr), (59)

where I0 is in watts per square centimeter. For comparable input energy, •e latter liquid is considerably more efficient.

io o

o-•

I I I I

I i i i 10-2 I0-1 I0 0 I01 10 2

e CT

Fro. 3. Free-surface efficiency function.



13:58:55


2. Constrained Surface

Under these conditions, the elastic-wave energy is

•' e•C•(1--2e-•C•+e-2•C•)dr Ea= pC \'2J-•T/ X' -• [4-½e-2•c•-ke•C<•-•)--4e-•C•--4e•C<•-•)-½ 2e-•C•--]dr

-• f• e -•c • (e •c•-- 2e•C•-• 1)dr.

t60)

After integrating and regrouping, we have

N= (Cl•Io/2pJ•S•)F2 (aCT), where

II. EXPERIMENTAL RESULTS

(61) A. Apparatus

F•(aCT)= (aCTe-•C•+3e-•C*+ 2aCT--3)/aCT. (62)

The last function, plotted in Fig. 4, approaches a maximum value of 2.0 for large values of aCT. For comparison, Expressions 58 and 59 hold for a constrained surface if F2(aCT) is used instead.

Naively taken, the preceeding expressions would indicate that efficiency can be increased without limit as I0 is increased. Instead, they show where the assumed model of stress generation is no longer applicable and must be replaced by another. We cite several limitations of this model. (1) Thermal characteristics of the medium impose limits on intensity; e.g., liquids boil, solids melt and vaporize. Stresses continue to be generated but by different processes, (2) Even before phase changes are reached, temperature dependence of thermal and elastic properties become evident and so cause deviations from the formulas at high intensities, (3) As efficiency becomes significant, the temperature distribution is no longer correct because of the appreci- able fraction of input energy that is radiated away in the form of elastic waves.

Stress transients were investigated in several absorbing liquids with the experimental arrangement sketched in Fig. 5. Liquids were used because of the relative ease of controlling absorption, the wide available range of parameters such as expansion coefficient, the occurrence of a phase change at a modest temperature rise, and the ease with which boundary conditions could be changed. Distilled water, acetone, methanol and carbon tetracholoride were used at an initial

temperature of 23øC. Their pertinent characteristics are listed in Table I.

Absorption coefficient was controlled by the introduction of a soluble dye in the liquid. Dyes used were Eastman Kodak toluidine blue and National Aniline

malichite green. Absorption of each solution was measured independently using standard optical techniques.

In the course of these experiments, two different ruby lasers were employed as energy sources. The first utilized a bleachable filter to achieve a single, high- intensity pulse of 60-nsec length. Power was limited, however, to a maximum of 12 MW. The second laser used a bleachable filter in conjunction with a rotating prism for Q switching and delivered a maximum of 2 J

Fro. 4. Constrained-surface efficiency function.

io I

•0 0 --

iO -I __

10 -2

I i I I

I I I I I0-I i0 0 i01 i0 2 i0 3

aCT



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I.. s. GOURNAY

,,,

LASER

SCOPE SIGNAL SYNC

'] LIGHT MONITOR

•ClLLO-• SCOPE /

r• PRISM Illin

TRANSDUCER

Fro. 5. Schematic of experimental setup for stress generation and measurement.

of energy in 20 nsec for a power output of 100 MW. This arrangement allowed some measurements to be made at a different T and thus varied another parameter in the equations. Total energy in the light pulse was measured with a Korad model KJ laser calorimeter and microvoltmeter. When in use, the calorimeter inter- cepted all the light and hence excluded simultaneous light energy and stress measurements. However, it was found that energy output was reproducible to 4-5% between consecutive laser shots, so energy measurements were only made before and after a series of stress measurements.

Stresses were generated under three surface conditions described as follows: (a) free surface where a simple liquid-air interface was present; (b) a constrained liquid surface achieved by transmitting the laser beam through a glass plate that rested on the liquid surface. Because the acoustic impedance of glass is much greater than that of the liquids tested, a constrained liquid surface is closely approximated. To examine the threshold of vaporization and its elastic effects, the cell was modified as in Fig. 6. The liquid above and below a 1-mil Saran © diaphragm was the same, except that the liquid below contained a dye whereas that above was transparent. The result of this arrangement was to delay the second half of the elastic transient and permit undisturbed observations of vaporization effects.

Stress transients generated at the liquid surface were detected by a piezoceramic transducer (Clevite PZT-4), located a known distance below the surface. The transducer was capable of being positioned any- where in the horizontal plane and could thereby probe

IQUlD WITH DY

TO SCOPE •TRANSDUCER

Fro. 6. Modified cell.

TABLE I. Physical properties of liquids investigated.

C (cm/sec) fi (deg -•) S (cal/g.øC) Cfi/S

Water 1.48 X 105 6.90 X 10 -5 1.00 10.2 Acetone 1.17X105 4.95X10 -4 0.529 110 Methanol 1.14X105 3.74X10 -4 0.580 70.3 CC14 0.926 X 105 4.12 X 10 -4 0.202 189

horizontal distribution of stress. Transducer output was displayed and photographed on a Tektronic 555 dual-beam oscilloscope with a rise time of 10 nsec. Trigger for the scope trace was provided by a fast-rise detector (silicon epitaxial diode) that viewed a small fraction of light reflected from the prism face. This trigger signal could also be displayed for determination of pulse width and relative pulse height.

B. Data and Discussion

A typical stress-time relationship observed in water with a= 32 cm -• is shown in Fig. 7. These results were obtained in the modified cell that displaced the reflected wave in time. The semilog plot demonstrates the exponential rise predicted by Eq. 52. The time scale in Fig. 7 begins with laser firing; hence, the 5.2-t•sec travel time shown agrees well with the measured transducer-surface distance of 8 mm. These data, when replotted on linear scales in Fig. 8, make evident the very short decay time of the acoustic pulse.

Figure 9 is typical of a propagated stress wave in water (a= 160 cm -1) with a constrained surface. Note the shorter acoustic pulse length that restfits from increasing a. Pulse shape closely approximates that predicted by the theory.

Peak stress was measured in the four liquids under different conditions of absorption, intensity of input,

6.0

4.0

/ •, o

o/

•' o /

_

« - /

_ o / _ /

/ /

-- / -

/ /

20

I0

2.0

1.0 -0.8 -0.6 -0.4 -0.2 0 0.2

1' (MICROSEC,)

Fro. 7. Stress in water as a function of time (free surface).



13:58:55


and boundary conditions, at a distance of 3 cm from the :surface. The measured peak stress is compared in Fig. 10 with that calculated using Eqs. 36 and 52. The agree- ment observed over this wide range of stress and physical properties of media is indicative of the general validity of our model of stress generation.

Rupture of the liquids occurred consistently under conditions of large tension at a free surface. This is not surprising in view of the fact that tensile stresses of the order of hundreds of pounds per square inch were present. When rupture occurred under tensile stress, tentative results indicate that liquid was ejected from the cell with velocities exceeding Mach 1.0 in air. This phenomena was often accompanied by the sharp crack of a shock wave in air.

Angular divergence of the acoustic transient was examined in water for two values of absorption coefficient. The transducer was maintained at a fixed distance

of 5 cm from the surface and moved horizontally to a new position for each laser shot. A cross-sectional scan of the acoustic beam amplitude was thus obtained and is reproduced in Fig. 11. These data correspond to

'" 60

z :3 50

>.. 13:: ,(• 40 13::

13:: 30

U') 20

I-- IO

-.12 -.08 -.04 0 .04 .08 .12 .16 .20 .24

'r (MICROSEC)

Fro. 9. Stress in water as a function of time (constrained surface).

..., io 8

z

ß .-, io 7

b.I io 6

i i // /

p/ /

/ /

- / x -

/ x/ /

/ o

/• oAO /

/ x -

/ ,,.

tu

::) (/)

• // o • 10 5

105 106 107 I O 8 CALCULATED PEAK STRESS (DYNES/CM ::))

Fro. 10. Comparison of measured and calculated values of peak stress. 100 dyn/cm•= 1 atm. O, water; X, methanol; F1, actone; a, CCI•.

:50' 20* I0' 0 I0 ø 20 •

Fro. 11. Normalized acoustic amplitude in water as a function of angie from normal. o,a--61 crn-•; X,a- 12 cm-L

radiation from a diffraction limited source and justify the assumptions made earlier regarding a plane-wave structure. As might be expected from such a source, those acoustic pulses derived from the larger absorption coefficient have components of higher frequency and therefore less angular divergence for a fixed-source aperture. This trend is evident in the radiation patterns of Fig. 11.

The equations of stress that have been derived rest on the assumption of thermal expansion and do not consider the occurrence of a phase change. If a liquid is brought to its boiling point, expansion of the vapor phase should give rise to secondary acoustic radiation. 6 Furthermore, Eq. 13 should define the minimum value of (aloT) required to initiate a phase change at X=0. The surface of methyl alcohol, for example, would be raised from 25øC to its boiling point with an (aloT)

6R. H. Cole, Underwater Explosions (Princeton University Press, Princeton, N.J., 1948).



13:58:55

L. S. GOURNAY

_,.120 Z

I00

• 8O

IZ: 60

U3 40

U3 20

140 •--

x

0

-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 ß r (MICROSEC)

FIG. 12. Stress in methyl alcohol with odoT as a parameter. Values of aloT: r-I, 16; a, 37; o, 58; x, 120.

of 77 J/cm 3 at X-0. Energy densities greater than this value should initiate vaporization at larger distances from the surface.

Acoustic radiation from vapor expansion was observed in all liquids in the modified cell. An example of the onset of this effect is shown in Fig. 12. The stress transient was observed at a distance of 5 cm from a methanol surface as a was progressively increased between shots. We interpret the stress during r<0 to be due to thermal expansion of the liquid phase. Hence, for small a, the stress drops rapidly to zero at r>0 and shows no further change. As (a10T) approaches 60 J/cm 3, a second well-defined transient appears at r>0, and we interpret this one as due to expansion of the vapor phase. As a is further increased, the stress during r < 0 becomes shorter and approaches a limiting peak value as predicted; whereas, the vapor expansion stress increases in magnitude and time duration.

Surface-heating effects as described here appear to have some application as a source of acoustic energy in liquids. Peak pressures of several hundred pounds per square inch over a time interval of approximately 1 t•sec were generated in CC14 for example. As long as surface temperature was held below the boiling point, the frequency power spectrum of acoustic energy was variable through a and T. It follows also that much of the acoustic power of these short pulses is in the megacycle-per-second frequency region. Cavitation effects should be pronounced in stress waves that originate at a free surface, since extremes of com- pressire and tensile stress are present.

ACKNOWLEDGMENTS

The author thanks Dr. Franz Selig and Dr. Richard Wood for helpful discussions in the course of this work.



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conversion of electromagnetic to acoustic energy by surface heating

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