Abstract

The interaction of absorbing aerosols with pulsed light beams is considered. Approximate energy and mass conservation equations are developed which admit of analytic solutions for the aerosol temperature and vaporization state within a limited domain of values for the aerosol mass flux. Numerical solutions are obtained for the particular case of absorbing water droplets in an intense pulsed light beam, and the validity of these solutions is examined. A number of recommendations are made for future work on this problem.

© 1984 Optical Society of America

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References

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  1. F. G. Gebhardt, Appl. Opt. 15, 1479 (1976).
    [CrossRef] [PubMed]
  2. G. L. Lamb, R. B. Kinney, J. Appl. Phys. 40, 416 (1968).
    [CrossRef]
  3. S. L. Glickler, Appl. Opt. 10, 644 (1971).
    [CrossRef] [PubMed]
  4. R. C. Harney, Appl. Opt. 16, 2974 (1977).
    [CrossRef] [PubMed]
  5. G. W. Sutton, Appl. Opt. 17, 3424 (1978).
    [CrossRef] [PubMed]
  6. C. T. Lee, T. G. Miller, R. W. Jones, Appl. Opt. 21, 428 (1982).
    [CrossRef] [PubMed]
  7. R. B. Bird, W. E. Stewart, E. N. Lightfoot, Transport Phenomena (Wiley, New York, 1960).
  8. D. C. Smith, J. Appl. Phys. 48, 2217 (1977).
    [CrossRef]
  9. F. A. Williams, Int. J. Heat Mass Transfer 8, 575 (1965).
    [CrossRef]
  10. R. W. Schrage, A Theoretical Study of Interface Mass Transfer (Columbia U. P., New York, 1953).
  11. W. J. Bornhorst, G. N. Hatsopoulus, J. Appl. Mech. 34E, 840 (1967).
    [CrossRef]
  12. G. E. Caledonia, J. D. Teare, J. Heat Transfer 99, 281 (1977).
    [CrossRef]
  13. J. Wallace, “Formulation of the Analysis for Nonlinear Aerosol Thermal Blooming,” U.S. Army Missile Command Final Report, contract DAAH01-81-C-A810 (Oct.1981).
  14. S. C. Chen, J. Atmos. Sci. 31, 845 (1974).
    [CrossRef]
  15. N. Chodes, J. Warner, A. Gayin, J. Atmos. Sci. 31, 1351 (1974).
    [CrossRef]

1982 (1)

1978 (1)

1977 (3)

R. C. Harney, Appl. Opt. 16, 2974 (1977).
[CrossRef] [PubMed]

D. C. Smith, J. Appl. Phys. 48, 2217 (1977).
[CrossRef]

G. E. Caledonia, J. D. Teare, J. Heat Transfer 99, 281 (1977).
[CrossRef]

1976 (1)

1974 (2)

S. C. Chen, J. Atmos. Sci. 31, 845 (1974).
[CrossRef]

N. Chodes, J. Warner, A. Gayin, J. Atmos. Sci. 31, 1351 (1974).
[CrossRef]

1971 (1)

1968 (1)

G. L. Lamb, R. B. Kinney, J. Appl. Phys. 40, 416 (1968).
[CrossRef]

1967 (1)

W. J. Bornhorst, G. N. Hatsopoulus, J. Appl. Mech. 34E, 840 (1967).
[CrossRef]

1965 (1)

F. A. Williams, Int. J. Heat Mass Transfer 8, 575 (1965).
[CrossRef]

Bird, R. B.

R. B. Bird, W. E. Stewart, E. N. Lightfoot, Transport Phenomena (Wiley, New York, 1960).

Bornhorst, W. J.

W. J. Bornhorst, G. N. Hatsopoulus, J. Appl. Mech. 34E, 840 (1967).
[CrossRef]

Caledonia, G. E.

G. E. Caledonia, J. D. Teare, J. Heat Transfer 99, 281 (1977).
[CrossRef]

Chen, S. C.

S. C. Chen, J. Atmos. Sci. 31, 845 (1974).
[CrossRef]

Chodes, N.

N. Chodes, J. Warner, A. Gayin, J. Atmos. Sci. 31, 1351 (1974).
[CrossRef]

Gayin, A.

N. Chodes, J. Warner, A. Gayin, J. Atmos. Sci. 31, 1351 (1974).
[CrossRef]

Gebhardt, F. G.

Glickler, S. L.

Harney, R. C.

Hatsopoulus, G. N.

W. J. Bornhorst, G. N. Hatsopoulus, J. Appl. Mech. 34E, 840 (1967).
[CrossRef]

Jones, R. W.

Kinney, R. B.

G. L. Lamb, R. B. Kinney, J. Appl. Phys. 40, 416 (1968).
[CrossRef]

Lamb, G. L.

G. L. Lamb, R. B. Kinney, J. Appl. Phys. 40, 416 (1968).
[CrossRef]

Lee, C. T.

Lightfoot, E. N.

R. B. Bird, W. E. Stewart, E. N. Lightfoot, Transport Phenomena (Wiley, New York, 1960).

Miller, T. G.

Schrage, R. W.

R. W. Schrage, A Theoretical Study of Interface Mass Transfer (Columbia U. P., New York, 1953).

Smith, D. C.

D. C. Smith, J. Appl. Phys. 48, 2217 (1977).
[CrossRef]

Stewart, W. E.

R. B. Bird, W. E. Stewart, E. N. Lightfoot, Transport Phenomena (Wiley, New York, 1960).

Sutton, G. W.

Teare, J. D.

G. E. Caledonia, J. D. Teare, J. Heat Transfer 99, 281 (1977).
[CrossRef]

Wallace, J.

J. Wallace, “Formulation of the Analysis for Nonlinear Aerosol Thermal Blooming,” U.S. Army Missile Command Final Report, contract DAAH01-81-C-A810 (Oct.1981).

Warner, J.

N. Chodes, J. Warner, A. Gayin, J. Atmos. Sci. 31, 1351 (1974).
[CrossRef]

Williams, F. A.

F. A. Williams, Int. J. Heat Mass Transfer 8, 575 (1965).
[CrossRef]

Appl. Opt. (5)

Int. J. Heat Mass Transfer (1)

F. A. Williams, Int. J. Heat Mass Transfer 8, 575 (1965).
[CrossRef]

J. Appl. Mech. (1)

W. J. Bornhorst, G. N. Hatsopoulus, J. Appl. Mech. 34E, 840 (1967).
[CrossRef]

J. Appl. Phys. (2)

D. C. Smith, J. Appl. Phys. 48, 2217 (1977).
[CrossRef]

G. L. Lamb, R. B. Kinney, J. Appl. Phys. 40, 416 (1968).
[CrossRef]

J. Atmos. Sci. (2)

S. C. Chen, J. Atmos. Sci. 31, 845 (1974).
[CrossRef]

N. Chodes, J. Warner, A. Gayin, J. Atmos. Sci. 31, 1351 (1974).
[CrossRef]

J. Heat Transfer (1)

G. E. Caledonia, J. D. Teare, J. Heat Transfer 99, 281 (1977).
[CrossRef]

Other (3)

J. Wallace, “Formulation of the Analysis for Nonlinear Aerosol Thermal Blooming,” U.S. Army Missile Command Final Report, contract DAAH01-81-C-A810 (Oct.1981).

R. B. Bird, W. E. Stewart, E. N. Lightfoot, Transport Phenomena (Wiley, New York, 1960).

R. W. Schrage, A Theoretical Study of Interface Mass Transfer (Columbia U. P., New York, 1953).

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Figures (9)

Fig. 1
Fig. 1

Mass flux vs droplet temperature rise ΔT(K); exact curve from Eq. (5); second-order curve from Eq. (6).

Fig. 2
Fig. 2

Droplet temperature rise ΔT(K) vs time (t/tp) for pulse length tp = 5 sec; droplet radii 0.1, 0.5, 1, 2 μm; (αI) = 104 W/cm3.

Fig. 3
Fig. 3

Same as Fig. 2 except droplet radii 0.1, 0.2, 0.4 μm, (αI) = 108 W/cm3.

Fig. 4
Fig. 4

Droplet radius (microns) vs time (t/τd) for τd = 0.964 sec, αI = 104 W/cm3.

Fig. 5
Fig. 5

Same as Fig. 4 except τd = 96.4 μsec, αI = 108 W/cm3.

Fig. 6
Fig. 6

Energy ratios vs time (tp/τh) for τh = 0.189 μsec, radius = 0.1 μm,αI = 104 W/cm3.

Fig. 7
Fig. 7

Same as Fig. 6 except τh = 20.2 μsec, radius = 2 μm, αI = 107 W/cm3.

Fig. 9
Fig. 9

Same as Fig. 6 except τh = 20.2 μsec, radius = 2 μm, αI = 107 W/cm3.

Tables (1)

Tables Icon

Table I Physical Constants for Water Droplet–Air System

Equations (35)

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t ρ ( U + ½ v 2 ) + · ρ v ( H + ½ v 2 ) + · ( - K T ) = W ,
4 π σ 3 3 ρ l C T t + 4 π σ 2 [ m L - K ( T r ) σ + m 3 2 ρ 2 ] = π σ 2 Q I ,
Y t + v Y r = D ρ r 2 r ( r 2 Y r ) ,
T t + v T r = K C p r 2 r ( r 2 T r ) ,
R ~ ( Δ r / Δ t ) / v ,
m = ( D / σ ) ln [ ( 1 - Y 0 ) / ( 1 - Y 0 e λ ) ] , λ = ( L M / R ) [ ( 1 / T 0 ) - ( 1 / T ) ] ,
K ( T r ) σ = - m C p ( T - T 0 ) [ exp ( σ m C p / K ) - 1 ] - 1 ,
ρ l C T t + 3 m L σ { 1 + C p ( T - T 0 ) L [ exp ( σ m C p / K ) - 1 ] } + 3 m 3 2 σ ρ 2 = α I .
σ m D = [ L M Y 0 R T 0 ( 1 - Y 0 ) ] x + { L M Y 0 2 R T 0 ( 1 - Y 0 ) 2 × [ L M R T 0 - 2 ( 1 - Y 0 ) ] } x 2 + ,
x t + l 1 x + l 2 x 2 + = l 0 ,
l 0 = α I / ρ l C T 0 , l 1 = 3 ( Γ + K ) / ρ l C σ 2 ,             l 2 = 3 Γ β / ρ l C σ 2 , Γ = L 2 D M Y 0 / R T 0 2 ( 1 - Y 0 ) , β = [ L M / 2 R T 0 ( 1 - Y 0 ) ] - [ C p T 0 / 2 L ) - 1.
I = I 0 , 0 t t p , = 0 , t < 0 , t > t p
x t t p ( t ) = 2 l 0 τ h [ 1 - exp ( - t / τ h ) ] 1 + l 1 τ h + ( 1 - l 1 τ h ) exp ( - t / τ h ) , x t > t p ( t ) = l 1 x t t p ( t p ) exp [ - l 1 ( t - t p ) ] l 1 + l 2 x t t p ( t p ) { 1 - exp [ - l 1 ( t - t p ) ] } ,
τ h = ( l 1 2 + 4 l 0 l 2 ) - 1 / 2 .
x s = 2 l 0 τ h / ( 1 + l 1 τ h ) .
x s ( l 0 / l 1 ) ( 1 - l 0 l 2 / l 1 2 )
m = ρ l σ / τ d + [ Γ ( α I ) 2 σ 3 / 9 L T 0 ( K + Γ ) 2 ] [ K β / ( K + Γ ) - C p T 0 / L ] ,
τ d = 3 ρ l L ( K + Γ ) / α I Γ .
σ ( t ) = σ ( 0 ) exp ( - t / τ d ) { 1 + α I σ 0 2 3 T 0 ( K + Γ ) ( K K + Γ β - C p T 0 L ) × [ 1 - exp ( - 2 t / τ d ] } - 1 / 2
p l C T t + 3 m L σ + 3 K ( T - T 0 ) σ 2 = α I .
4 π ρ l C T 0 3 0 t p σ 3 x t d t + 4 π L 0 t p σ 2 m d t + 4 π K T 0 0 t p σ x d t = 4 π α I 3 0 t p σ 3 d t ,
E H + E V + E C = E T .
Q H = E H / E T ,             Q V = E V / E T ,             Q C = E C / E T ,
Q H = ( ρ l C T 0 / α I t p ) 0 t p x t d t ,
Q C = ( 3 K T 0 / σ 2 α I t p ) 0 t p x d t .
0 t p x t d t = x ( t p ) = 2 l 0 τ h [ 1 - exp ( - t p / τ h ) ] 1 + l 1 τ h + ( 1 - l 1 τ h ) exp ( - t p / τ h ) , 0 t p x d t = 2 l 0 τ h { t p 1 + l 1 τ h + 2 τ h 1 - ( l 1 τ h ) 2 × ln [ 1 + l 1 τ h + ( 1 - l 1 τ h ) exp ( - t p / τ h ) 2 ] } ,
Q H 0 , Q C 6 K T 0 l 0 τ h σ 2 α I ( 1 + l 1 τ h ) .
1 / τ h = l 1 ( 1 + 4 l 0 l 2 l 1 2 ) 1 / 2 ,
4 l 0 l 2 l 1 2 = 4 σ 2 α I Γ β / 3 T 0 ( K + Γ ) 2 .
4 l 0 l 2 l 1 2 = σ 2 α I / J ,
σ 2 α I J [ here τ h 1 / l 1 = ρ l C σ 2 / 3 ( Γ + K ) ] , Q C K / ( K + Γ ) , Q V 1 - Q C ;
σ 2 α I J ( here τ h 1 / ( 4 l 0 l 2 ) 1 / 2 ) = [ ρ l C σ / 2 ) ( T 0 / 3 Γ β α I ) 1 / 2 ] , Q C ( K / K + Γ ) ( 4 J / σ 2 α I ) 1 / 2 , Q V 1 - Q C .
( σ 2 α I / 4 J ) 1 / 2 1 ,
x t = l 0 ,
Δ T = T - T 0 = α I t p / ρ l C ,

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