The Key Role of Surface Tension in the Theory of BubbleAssisted Explosion/Combustion Triggering 

by Michael Grinfeld 

ARL-TR-4562 September 2008 

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Army Research Laboratory 

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ARL-TR-4562 September 2008 

The Key Role of Surface Tension in the Theory of BubbleAssisted Explosion/Combustion Triggering 

Michael Grinfeld 

Weapons and Materials Research Directorate, ARL 

Approved for public release; distribution is unlimited. 
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The Key Role of Surface Tension in the Theory of Bubble-Assisted 

Explosion/Combustion Triggering 

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Michael Grinfeld 

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14. ABSTRACT 

We have revised the classical and widely accepted theory of (Bowden, F. P.; Yoffe, A. D. The Initiation and Growth of 

Explosion in Liquids and Solids; Cambridge University Press: New York, NY, 1952) explaining the initiation of 

explosion/combustion by means of adiabatic compression of the dissolved gaseous bubbles within condensed liquid substances. 

The main thrust of our study is to explore the role of surface tension at the interface “liquid explosive/gaseous bubble.” The

potential impotence of such a study is associated with smallness of the bubbles. Their smallness causes high overpressure 

within the bubble as compared with the pressure within the surrounding explosive/flammable liquid due to the Laplace excess 

pressure. It is demonstrated that the influence of the surface tension can be indeed quite dramatic. 

15. SUBJECT TERMS

brittle substance, failure wave, brittle fracture 

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Michael Grinfeld 

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iii

Contents 

1. Introduction 1

2. The Thermodynamic Scenario of the Bubble-Generated Ignition 3

3. Analysis of the Scenario for the Case of the Ideal Gas Model 4

4. The Role of Surface Tension in Triggering Combustion/Explosion 6

5. Analysis of the in-Vapor-Ignition and in-Liquid-Ignition Triggering Mechanisms 8

6. Theoretical Analysis of the Bubble-Assisted Triggering for the van der Waals 

Liquid 9

7. Conclusion 10

8. References 11

Distribution List 12 
iv

INTENTIONALLY LEFT BLANK. 
1

1. Introduction 

Triggering (initiating) is one of the key processes in combustion, explosion, and detonation of 

energetic and explosive materials. By controlling triggering, these strong processes can be made 

more probable or to be suppressed if necessary. In order to get such control, one has to 

understand clearly the physical nature of the triggering in different substances and environments. 

Depending on the substance, the effective mechanisms of the triggering can be quite different. 

Explosion/combustion triggering is nothing else but initiation of corresponding chemical 

reactions within substances. As a rule, even relatively modest changes of temperature of the 

potentially explosive/combustible substances are capable of rather big accelerating combustionlike chemical reactions. The combustion is an exothermic chemical reaction accompanied by 

sufficiently big release of energy. Once the combustion is initially triggered, then the 

combustion process becomes self-supporting. It becomes self-supporting because the required 

sufficiently high temperature is maintained due to the energy release accompanying the 

combustion. Thus, the bottleneck for the combustion is the initial triggering of the reaction. 

Various mechanisms of controllable triggering of explosions/combustions deserve serious further 

attention because of the two competing reasons. On one hand, the triggering should be easily 

achievable when we need the explosive/combustible materials to burn or explode. On the other 

hand, we have to be able to prevent these powerful processes when we do not need them, in 

particular, when storing them in hazardous environments. Although there are different 

mechanisms of triggering explosions/combustions, they all share one common feature: the 

reactions are usually triggered in the spatially separated hot spots, i.e., in the spots with 

particularly high temperatures (see figure 1). 

Figure 1. The gas/vapor bubbles with 

gas within liquid energetic 

substances. 

Also, the mechanisms and devices of triggering the explosive and combustible materials are 

based on the processes which are quite different as compared with the spatio-temporal spreading 

of combustion itself. One of the most widespread methods of generating high-temperature spots 

in the explosive/combustible substances is the intensive impacting of these substances. It is 

well-known that short intensive impacts cause adiabatic loading of the substance. In turn, 
2

adiabatic loading is usually accompanied with strong thermal effects, including significant raise 

in temperature. 

The processes of triggering of hot spots due to adiabatic loading of liquid explosive/combustible 

materials have been explored long ago (1, 2). It was observed long ago that gaseous/vapor 

bubbles within condensed explosive/combustible materials can be converted into hot spots by the 

impact-like mechanical loading. Under adiabatic loading, the bubbles become much hotter than 

the surrounding condensed liquids. Thus, they are able to play the role of hot spots. 

Two different mechanisms of triggering by means of gaseous/vapor bubbles should be 

distinguished depending of the nature of the gas inside the bubble. When the gas inside the 

bubble is mostly a flammable vapor of the surrounding flammable liquid, then the 

combustion/explosion begins inside the bubble—this is the in-vapor-ignition mechanism. 

However, if the bubble contains an inflammable, inert gas, then the explosion/combustion starts 

outside the bubble, i.e., within the flammable liquid in close proximity of the bubble—this is the 

in-liquid-ignition mechanism. 

The currently accepted canonical analysis of the bubble-mediated triggering (1) is based on the 

analysis of the adiabata equation of the gas bubble alone, i.e., without the analysis of heating of 

the surrounding condensed phase. Of course, it was clear to the interested authors themselves 

that such an analysis is insufficient: after all, the rate of the chemical reactions within the 

condensed phases depends on the bulk temperature of these phases, not on the temperature of the 

immersed bubbles. However, as the starting point, the analysis (1) was mandatory and 

unavoidable. 

The after-triggering stage of explosion/flame propagation is deeply associated with heat 

conduction, chemical reactions, mass, and momentum exchanges: these important processes 

have been intensively and carefully studied in many classical monographs and textbooks (2–4). 

Much less attention has been paid to the analysis of the process of triggering. This fact can 

create the misleading impression that the triggering processes are already quite clear and 

sufficiently well understood and explored. In fact, the situation is far of being so satisfactory: 

various aspects of triggering are far of being completely clear. For instance, the key formulas (1) 

of triggering by means of adiabatic compression of gaseous bubbles does not depend on the 

bubbles’ sizes. The experiments and observations, however, are indicative of the fact that the 

process of triggering is size-sensitive (5, 6). 

In the following section, we analyze one of the mechanisms that might be responsible for the 

dependence of explosions triggering upon the size of the bubbles. Namely, we take into account 

the surface tension acting at the boundary, separating the bubble from the surrounding condensed 

liquid. Such an analysis seemed to be mandatory because the bubbles are of the size of 10–3 cm. 

For this size range, the effects of the surface-tension-induced Laplace overpressure can be quite 

strong. 
3

Our analysis shows that, indeed, that the bubble-based mechanism of triggering cannot be 

adequately developed without taking into account and understanding of the role of surface 

tension. The influence of the surface tension not only leads to quantitative corrections of the 

main formulas of Bowden and Yoffe (1), but it reveals the necessity of complete revision of the 

canonical theory of the bubble-assisted triggering of explosion/combustion. 

2. The Thermodynamic Scenario of the Bubble-Generated Ignition 

In this report, we analyze one of the simplest scenarios of triggering of combustion/explosion in 

the condensed liquid substance. Namely, we assume that the impact loading can be modeled as a 

sudden jump in the external pressure from the initial value 0

e p to 1e p . Despite the fact that 

impact is a fast process, we assume that the triggering mechanism can be adequately described 

by the methods of classical thermodynamics alone (i.e., without the analysis of the momentum 

and kinetic energy exchange, as well as without any explicit modeling of heat conduction). 

More specifically, we assumed that the triggering process can be split into two different events: 

the starting stage of adiabatic compression of the bubble and the final stage of heating of the 

condensed substance in the small vicinity of each bubble. The previously mentioned mechanism 

of the in-vapor-ignition triggering includes only the starting stage i, whereas the in-liquidignition includes both stages. 

We assume that initially both—the condensed liquid and the gaseous bubble—have the same 

ambient temperature 0 T . Then, the pressure impact causes an adiabatic increase of the 

temperature within both—the liquid and the bubble. However, the temperature increase is much 

more pronounced within the bubble than within the liquid. This not-so-obvious assumption can 

be justified by the fact that the bubble’s substance has much bigger compressibility than the 

condensed liquid. Therefore, the same pressure change is associated with much bigger 

mechanical work exerted on the bubble than on the liquid.* In the lowest order of 

approximation, we can even neglect the temperature change of the liquid during the initial stage 

of ignition. Thus, the starting stage of triggering is nothing else but the adiabatic compression of 

the gas inside compressible bubble. We suppose that the triggering event can start only if the 

temperature of the bubble exceeds the critical value * T . For the in-vapor-ignition mechanism, 

the first stage of triggering is the only mandatory stage. 

For the in-liquid-ignition mechanism to be operational, the first stage of adiabatic temperature 

increase inside the bubble is insufficient for the triggering since the high enough temperature 

should be reached not within the bubble but within the bulk of the liquid. We assume that this 

temperature increase can be achieved by means of heat flux at fixed pressure from the hot bubble 

 *

For instance, pressure applied to an incompressible liquid cannot produce any work on it. 
4

to the initially cool liquid. Thus, the final event is nothing else but the isobaric warming of the 

condensed substance surrounding the hot bubble. Even if the bubble is hot enough at the end of 

the adiabatic compression stage, its potential ability of heating the surrounding liquid can be 

limited because of insufficient amount of the available enthalpy inside the bubble. Thus, the 

bubble should be sufficiently big in size or to reach even higher temperature to carry enough 

enthalpy. In other words, there appears the dependence of the triggering ability upon the size of 

the bubble. 

The full description of the second stage of triggering should be based on the sufficiently detailed 

analysis of the process of heat conduction in the bulk of the bubble and liquid and of the heat 

exchange across the liquid/bubble interface. However, in this report we limit ourselves to the 

simplified model. According to this model, the explosion/combustion triggering becomes 

possible only if the available full enthalpy in the bubble exceeds a certain critical value * H .

Summarizing, we use the following two-elemental criterion of the explosion/combustion 

triggering. The absolute temperature has to exceed the critical value * T and the total available 

enthalpy should exceed the critical value * H .

The main target of our analysis is to find the critical impact overpressure 1 0 / e e p p and of the 

overpressure dependence on the ambient temperature T0 . 

3. Analysis of the Scenario for the Case of the Ideal Gas Model 

The specific internal energy e and enthalpy τ of the ideal gas are given by the following 

formulas: 

 , v e c T const = + (1) 

and 

p τ = c T const + , (2) 

where T is the absolute temperature and v c and p c are specific (constant) heat capacities at 

fixed volume and pressure, respectively. The caloric equation 1 of the ideal gas should be 

amended with the equation of state, connecting the absolute temperature with the pressure p and 

the specific volume v : 

pv RT = , (3) 

where R is a constant. 

The thermodynamic parameters of any two states (v pT 0 00 , , ) and(v pT 1 11 , , ) of any ideal gas, 

belonging to the same adiabata, are connected by the relationships:
5

1 1

1 1

0 0 11 0 0 11 0 0 1 1 p v pv Tv Tv T p T p , ,

γ γ

γ γγ γ γ γ

− −

− − == = , (4) 

where γ is the ratio of the heat capacities: / p v γ ≡ c c . 

The last of the formulas in equation 4 implies the relationship 

1

1

1 1 11

0 0 00

T p pT

T p pT

γ γ

γ γ

−

− ⎛ ⎞ ⎛⎞

= →= ⎜ ⎟ ⎜⎟ ⎝ ⎠ ⎝⎠

. (5) 

Equation 5 leads to the following necessary condition of the successful first stage of triggering: 

* 1

1

0 0

p T

p T

γ

γ − ⎛ ⎞ ≥ ⎜ ⎟ ⎝ ⎠

. (6) 

The jump in the specific enthalpies between two states is given by the formula 

( )( ) 1 /

1 0 1 0 0 10 () / 1 p p c T T cT p p γ γ

τ τ −

−= − = − ⎡ ⎤ ⎣ ⎦ . (7) 

If the bubble has the initial volume V0 , then the total accumulated enthalpy H is equal to 

( )( ) 1 /

1 0 00 / 1

1 H p p pV γ γ γ

γ

−

= − ⎡ ⎤

− ⎣ ⎦ . (8) 

Equation 8 is implied by the following chain: 

( ) ( )( )

( )( ) ( )( )

1 / 0 0

1 000 1 0

0

1/ 1/ 0

1 0 0 1 0 00

/ /1

/ 1 / 1.

1

−

− −

=− = − ⎡ ⎤ ⎣ ⎦

= −= − ⎡ ⎤⎡ ⎤ ⎣ ⎦⎣ ⎦ −

p

p

T V H Vv c pp

v

p c p p V p p pV R

γ γ

γγ γγ

τ τ

γ

γ

 (9) 

Using equation 8, we arrive at the second necessary condition of the in-liquid-ignition during the 

second stage of triggering: 

1

1 00

*

0

1 1

1

p pV

p H

γ

γ γ

γ

− ⎡ ⎤ ⎛ ⎞ ⎢ ⎥ ⎜ ⎟ − ≥ − ⎢ ⎥ ⎝ ⎠ ⎢ ⎥ ⎣ ⎦

. (10) 

In fact, the criterion (equation 10) should be treated as the condition defining the size V0 of the 

bubbles in vicinity of which the in-liquid-ignition mechanism becomes possible.
6

4. The Role of Surface Tension in Triggering Combustion/Explosion 

In the absence of the surface tension at the bubble/liquid interface, equations 6 and 10 would be 

sufficient for the analysis of the bubble-assisted triggering. However, these formulas link the 

parameters of the gas inside the bubble. We need, in fact, the criteria expressed in terms of the 

parameters of the liquid. The pressures inside the bubble are much bigger than the pressures 

inside the liquid in the case of small-size bubbles. 

Let us consider a gaseous bubble inside a liquid. Because of the Laplace excess pressure, we 

now have to distinguish between the pressure in the bubble and in the liquid. Let σ be the 

surface tension at the interface “bubble-liquid.” We assume that σ is a constant, although it is 

known to depend on temperature. Then, let ( )1/3

0 0 R V = 3 /4π and ( )1/31 1 R V = 3 /4π be the radii 

of the bubble when the liquid is under the pressures of 0

e p and 1e p , respectively. Then, because 

of the Laplace excess pressure under curved surfaces, the corresponding pressures 0

b

p and 1

b

p

within the bubble are given by the following formulas: 

1/3

00 0 1/3

0 0

2 32 , 3 −

⎛ ⎞ =+ =+⎜ ⎟ ⎝ ⎠

be e

pp p R V

σ π σ (11) 

and 

1/3

11 1 1/3

1 1

2 32 . 3 −

⎛ ⎞ =+ =+⎜ ⎟ ⎝ ⎠

be e

pp p R V

σ πσ (12) 

Using the third of the adiabata relationships of equation 4, we get 

1/3

1 1

1/3 1/3 1/3 1

1 0 00 0

0

1/3

0 0

32 , 3 1

e

e e

e

p V

T p pV V

T

p V

γ

γ

σ ξ

π ξ σ ξ

−

− − + ⎛ ⎞ ⎛ ⎞ ⎜ ⎟ = ≡ ⎜ ⎟ ⎝ ⎠ ⎝ ⎠ +

, (13) 

implied by the following chain: 

1

1/3

11 1 1 1

1 1/3 1/3 1/3

1 1 1 1 1 1 0 00 0

1 1/3

00 0 0 0 0

1/3

0 0

2 2

2 2 1

e

b e e ee

be e

e

p V

T p p r p v p pV V

Tp p r p v

p V

γ

γ

γγ γ

γγ γ

σ ξ

σ σ

σ σ σ ξ

−

−

−− −

−− −

− −

⎛ ⎞ ⎜ ⎟ + ⎛⎞ ⎛ ⎞ ⎛ ⎞ + + == = = ⎜⎟ ⎜ ⎟ ⎜ ⎟ ⎝⎠ ⎝ ⎠ ⎝ ⎠ + + +

⎝ ⎠

. (14) 

The second of the adiabata relationships of equation 4 implies 

( )

1

1 1/3 3 1

01 0 1

1 1/3

10 1 0

VT V T

VT V T

γ γ

γ

− − − −

− −

⎛ ⎞

=→ = ⎜ ⎟ ⎝ ⎠

. (15)
7

Combining equations 13 and 15, we get 

( )

1

31 1

11 1

1/3 1/3

0 00 0 00 0

1 0

e

ee e

pT T

p pV T pV T

γ

σ σ γ γ

ξ ξ − − ⎛ ⎞ ⎛ ⎞⎛ ⎞

+ −+ = ⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎝ ⎠ ⎝ ⎠⎝ ⎠. (16) 

Introducing the dimensionless variables, 

1 1

1/3

00 0 0

, ,

e

e e

p T

p V pT

ξσ Σ≡ Π≡ Θ≡ , (17) 

we can rewrite equation 16 in the following dimensionless form: 

1

1 1 3( 1)

γ γ

γ γ − − γ − ⎛ ⎞

Π=Θ +Σ Θ −Θ ⎜ ⎟

⎝ ⎠

. (18) 

The first term in equation 18 is equivalent to the result presented by equation 6. Equation 18 can 

be rewritten as follows: 

1

2 1

3( 1)

1 1 1

γ

γ

γ

−

+ −

⎡ ⎛ ⎞⎤

Π=Θ +Σ − ⎢ ⎜ ⎟⎥ ⎢ ⎜ ⎟⎥ ⎢⎣ ⎝ ⎠ Θ ⎥⎦

. (19) 

In view of the inequalities 1, 0,and 1 γ > Σ> Θ> , equation 19 shows that by neglecting the 

surface tension, we can essentially underestimate the impact pressure which can trigger 

explosion/combustion. 

Let us derive the correct generalization of the enthalpy condition (equation 10) for the case of 

non-zero surface tension. For the change of the full enthalpy, we get 

()( ) 0 0 1 1

1

e H pV γ

γ = +Σ Θ− − , (20) 

implied by the following chain: 

( )

0 0 11 1

1 0 0 00 0 0

0 0 0 0 00

1/3

1 1

1/3 00 00

00 0 0

2 () 1 1 1 1

32 1 1 1 1.

13 1 −

⎛ ⎞ ⎛ ⎞ ⎛ ⎞⎛ ⎞

= − = −= −= + − ⎜ ⎟ ⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠⎝ ⎠ −

⎡ ⎤ ⎛ ⎞ ⎛⎞ ⎛⎞ = + − = +Σ − ⎢ ⎥ ⎜ ⎟ ⎜⎟ ⎜⎟ − − ⎣ ⎦ ⎝ ⎠ ⎝⎠ ⎝⎠

p b e

p p

e e

e

V V TT T c

H c T T cT pV p V v v T R T RT

T T pV pV pV T T

γ σ

γ

γ πσ γ

γ γ

 (21) 

Introducing the dimensionless parameterΦ , 

0 0

*

e p V

H

Φ ≡ , (22)
8

we can rewrite equation 20 in the following form: 

( )( ) * 1 1

1

H

H

γ

γ = +Σ Φ Θ− − . (23) 

The dimensionless parameters Σ and Φ are not independent. Using equations 17 and 22, we 

arrive at the following relationship between them: 

( )

3 3

3

2 *

0

ΦΣ = Γ Γ ≡ , where e p H

ξ σ . (24) 

5. Analysis of the in-Vapor-Ignition and in-Liquid-Ignition Triggering 

Mechanisms 

The analysis of the in-vapor-triggering mechanism is the most simple and is based solely on the 

analysis of equation 19. This equation shows that, at fixed parameter Θ of the required 

temperature raise, the parameter of Π diminishes with increase in the parameter Σ . This 

actually means that the smaller the initial volume V0 of the bubble, the smaller the triggering 

overpressure required. 

In other words, by neglecting the surface tension we get bigger values of the overpressure as 

compared with reality. The relative error in the estimation of the critical value of the parameter 

Π by neglecting the surface tension is given by the following formula: 

2 1

3( 1)

1 1

γ + −

⎛ ⎞ ΔΠ ⎜ ⎟ =Σ −

Π ⎜ ⎟

⎝ ⎠ Θ

. (25) 

For example, let us make the estimate ΔΠ Π/ taking the values for the air bubble with the radius 

0 R = 0.1cm within acetone at the external pressure of 1 atm = 106 dyn/cm2

 and the room 

temperature T0 of 20 °C. The surface tension σ is equal to 25 dyn/cm. The ratio of the heat 

capacities / p v γ = c c is approximately equal to 1.4. If for the required temperature raise *

0 Θ = T T/ we accept the value of 1.1, then the formula (equation 24) gives the value 

ΔΠ Π ≈ / 2 . For smaller bubbles, the error can be significantly bigger. 

It is clear that with such high level of discrepancy, the ignition theory without surface energy is 

definitely unacceptable. 
9

6. Theoretical Analysis of the Bubble-Assisted Triggering for the 

van der Waals Liquid 

For the realistic range of thermodynamic parameters the model of the ideal gas does not provide 

sufficient level of numerical accuracy or even of qualitative agreement with observations. A 

much better theoretical and practical agreement with existing data can be achieved by replacing 

the equation of state (equation 3) for the ideal gases with the equation of state of the van der 

Waals substances: 

( ) 2 , RT a p vT vb v = − − , (26) 

where a and b are positive constants, depending on the substance. 

The van der Waals equation of state (equation 26) does not give all the thermodynamic 

information about the substance. For instance, this equation doesn’t anything about the specific 

heat of the substance. However, if the specific heat v c at fixed volume is determined somehow, 

then all the thermodynamic potentials of the substance can, in principle, be derived 

mathematically. Quite often, the assumption of constant v c appears to provide for a qualitatively 

good approximation in wide range of thermodynamic parameters. As we dwell on this 

simplifying assumption, it is worthy to warn of one typical mistake. It concerns the value of the 

heat capacity p c at fixed pressure: for the van der Waals substance, p c depends on the absolute 

temperature even if v c does not. This follows from the identity: 

( )

2 3

2 3 2 p v

R v CC T

Rv T a v b − = − − . (27) 

Looking closely at the analysis of the bubble-assisted triggering of explosion/combustion, one 

can notice that it is based on two sets of formulas. The first set (equation 12) is simply the 

equations expressing the Laplace formula of the tension-induced excess pressure under the 

curved surface. This set remains valid and unchanged for any thermodynamic model of the 

bubble’s gas. 

The second set of formulas (equation 4), on the contrary, is closely dependent upon the equation 

of state. For the van der Waals substance, the equation of adiabatic compression should be 

considerably modified. In particular, in the thermodynamic variables (v T, ) the equation of 

adiabata takes on the following form: 

00 11 ( ) ( )

C C V V

R R T vb T vb

− −

− = − . (28)
10

The equation of adiabata in any other thermodynamic variables can be found by combining 

equation 28 with the equation of state (equation 26). 

Thus, the quantitative and qualitative analysis of the role of surface tension in triggering 

explosion/combustion in non-ideal liquid substances should be based on the system of algebraic 

equations 11, 26, and 28. 

7. Conclusion 

We have re-analyzed the widely accepted theory (1) of initiation of explosion /combustion by 

means of adiabatic compression of the dissolved gaseous bubbles. The main target of our study 

was the role of surface tension at the interface liquid explosive/gaseous bubble. The impotence 

of such a study is associated with smallness of the bubbles. Their smallness causes high 

overpressure within the bubble as compared with pressure within the surrounding 

explosive/flammable liquid due to the Laplace excess pressure. 

We gave the closed algebraic system of the relationships allowing one to analysis the role of the 

surface tension for both the ideal and non-ideal (van der Waals) gas models. The case of the 

ideal gas within the bubbles was explored further. Our results show the Bowden-Yoffe analysis 

(1) that neglects the surface tension always gives the smaller magnitude of power of the 

triggering impact. In fact, in order to initiate explosion/combustion, the impact should be bigger 

than the one predicted by Bowden and Yoffe (1). Moreover, the corrected (for the surface 

tension) theory raises the issue of the validity and realism of the triggering mechanism based on 

adiabatic compression of the dissolved gas bubbles. 
11

8. References 

1. Bowden, F. P.; Yoffe, A. D. The Initiation and Growth of Explosion in Liquids and Solids; 

Cambridge University Press: New York, NY, 1952. 

2. Lewis, B.; Elbe, G. Combustion, Flames, and Explosions of Gases; Academic Press: New 

York, NY, 1987. 

3. Zel’dovich, Y. B.; Raizer, Y. P. Physics of Shock Waves and High-Temperature 

Hydrodynamic Phenomena; Dover Publications: Mineola, NY, 2002. 

4. Landau, L. D.; Lifshits, E. M. Fluid Mechanics; Pergamon Press: Elmsford, NY, 1989. 

5. Bowden, F. P.; Singh, K. Size Effects in the Initiation and Growth of Explosion. Nature

1953, 172, 378–380. 

6. Jones, E. Suppression of Bubble Initiation of Liquid Explosives. Nature 1954, 173, 77–78.
NO. OF 

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 AMSRD SS T 

 6000 6TH ST STE 100 

 FORT BELVOIR VA 22060-5608 

 1 DIRECTOR 

 US ARMY RESEARCH LAB 

 IMNE ALC IMS 

 2800 POWDER MILL RD 

 ADELPHI MD 20783-1197 

 1 DIRECTOR 

 US ARMY RESEARCH LAB 

 AMSRD ARL CI OK TL 

 2800 POWDER MILL RD 

 ADELPHI MD 20783-1197 

 1 DIRECTOR 

 US ARMY RESEARCH LAB 

 AMSRD ARL CI OK T 

 2800 POWDER MILL RD 

 ADELPHI MD 20783-1197 

ABERDEEN PROVING GROUND

 1 DIR USARL 

 AMSRD ARL CI OK TP (BLDG 4600) 
NO. OF 

COPIES ORGANIZATION 

13

ABERDEEN PROVING GROUND

 52 DIR USARL 

 AMSRD ARL CI HC 

 P CHUNG 

 AMSRD ARL SL 

 R COATES 

 AMSRD ARL WM 

 J MCCAULEY 

 T WRIGHT 

 AMSRD ARL WM BD 

 A HORST 

 B RICE 

 AMSRD ARL WM MD 

 C FOUNTZOULAS 

 AMSRD ARL WM T 

 P BAKER 

 AMSRD ARL WM TA 

 C HOPPEL 

 C KRAUTHOUSER 

 B LEAVY 

 S SCHOENFELD 

 AMSRD ARL WM TB 

 S KUKUCK 

 AMSRD ARL WM TC 

 M FERMEN-COKER 

 R MUDD 

 B SCHUSTER 

 S SEGLETES 

 W WALTERS 

 AMSRD ARL WM TD 

 T BJERKE 

 S BILYK 

 D CASEM 

 J CLAYTON 

 T CLINE 

 D DANDEKAR 

 W EDMANSON 

 M GREENFIELD (20 CPS) 

 C GUNNARSON 

 Y HUANG 

 B LOVE 

 M RAFTENBERG 

 E RAPACKI 

 M SCHEIDLER 

 T WEERASOORIYA 
14

INTENTIONALLY LEFT BLANK.