Abstract

The propagation of a pulsed light beam through a medium containing absorbing aerosol droplets is considered. A previous analysis of the droplet temperature, including both vaporization and conductivity effects, is used to obtain for a monodisperse distribution of droplet radii the beam intensity and the droplet temperature along the path. For sufficiently long pulses, a vaporization front may be defined by the leading edge of the steady-state droplet temperature regime. The speed of the front is shown to vary for sufficiently large droplets approximately as the inverse fifth power of the droplet radius. Numerical calculations are given for the specific case of beam propagation through a medium containing absorbing water droplets.

© 1984 Optical Society of America

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References

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  1. R. L. Armstrong, Appl. Opt. 23, 148 (1984).
    [CrossRef] [PubMed]
  2. F. A. Williams, Int. J. Heat Mass Transfer 8, 575 (1965).
    [CrossRef]
  3. G. L. Lamb, R. B. Kinney, J. Appl. Phys. 40, 416 (1969).
    [CrossRef]
  4. S. L. Glickler, Appl. Opt. 10, 644 (1971).
    [CrossRef] [PubMed]
  5. R. C. Harney, Appl. Opt. 16, 2974 (1977).
    [CrossRef] [PubMed]
  6. G. W. Sutton, Appl. Opt. 17, 3424 (1978).
    [CrossRef] [PubMed]
  7. C. T. Lee, T. G. Miller, R. W. Jones, Appl. Opt. 21, 428 (1982).
    [CrossRef] [PubMed]
  8. G. E. Caledonia, J. D. Teare, J. Heat Transfer 99, 281 (1977).
    [CrossRef]
  9. L. M. Frantz, J. S. Nodvik, J. Appl. Phys. 34, 2346 (1963).
    [CrossRef]
  10. R. B. Bird, W. E. Stewart, E. N. Lightfoot, Transport Phenomena (Wiley, New York, 1960).
  11. R. W. Schrage, A Theoretical Study of Interphase Mass Transfer (Columbia U.P., New York, 1953).
  12. W. J. Bornhorst, G. N. Hatsopoulus, J. Appl. Mech. 34E, 840 (1967).
    [CrossRef]

1984 (1)

1982 (1)

1978 (1)

1977 (2)

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

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

1971 (1)

1969 (1)

G. L. Lamb, R. B. Kinney, J. Appl. Phys. 40, 416 (1969).
[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]

1963 (1)

L. M. Frantz, J. S. Nodvik, J. Appl. Phys. 34, 2346 (1963).
[CrossRef]

Armstrong, R. L.

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]

Frantz, L. M.

L. M. Frantz, J. S. Nodvik, J. Appl. Phys. 34, 2346 (1963).
[CrossRef]

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 (1969).
[CrossRef]

Lamb, G. L.

G. L. Lamb, R. B. Kinney, J. Appl. Phys. 40, 416 (1969).
[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.

Nodvik, J. S.

L. M. Frantz, J. S. Nodvik, J. Appl. Phys. 34, 2346 (1963).
[CrossRef]

Schrage, R. W.

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

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]

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)

G. L. Lamb, R. B. Kinney, J. Appl. Phys. 40, 416 (1969).
[CrossRef]

L. M. Frantz, J. S. Nodvik, J. Appl. Phys. 34, 2346 (1963).
[CrossRef]

J. Heat Transfer (1)

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

Other (2)

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

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

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Figures (3)

Fig. 1
Fig. 1

Steady-state temperature rise (K) vs range (kM) with α = 103 cm−1 for 0.1-μm droplet: +, I0 = 106 W-cm−2, n0 = 106 cm−3; ×, I0 = 106 W-cm−2, n0 = 107 cm−3; ○, I0 = 5 × 105 W-cm−2, n0 = 106 cm3; Δ, I0 = 5 × 105 W-cm−2, n0 = 107 cm−3.

Fig. 2
Fig. 2

Steady-state temperature rise (K) vs range (kM) with α = 103 cm−1 for 2-μm droplet: +, I0 = 4 × 103 W-cm−2, n0 = 103 cm−3; ×, I0 = 4 × 103 W-cm−2, n0 = 104 cm−3; ○, I0 = 2 × 103 W-cm−2, n0 = 103 cm−3; Δ, I0 = 2 × 103 w-cm−2, n0 = 104 cm−3.

Fig. 3
Fig. 3

Ratio v/cm vs n0 both in logarithmic units for 0.1-, 0.5-, 1-, 2-μm droplet radii, α = 103 cm−1.

Equations (21)

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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 p 2 = α I ,
m = ( D / σ ) ln [ ( 1 - Y 0 ) / ( 1 - Y 0 e λ ) ] , λ = ( L M / R ) [ ( 1 / T 0 ) - ( 1 / T ) ] ,
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 t + c m I Z = - α c m V I ,
x / τ + l 1 x + l 2 x 2 = l 0 ,             l i = ρ l C l i / α ,             i = 0 , 1 , 2 ,
I / ξ = - V I .
I ( ξ , τ ) = I ( 0 , τ ) exp [ - 0 ξ V ( ξ , τ ) d ξ ] ,
I ( 0 , τ ) = I 0 , 0 τ τ p , = 0 , τ < 0 , τ > τ p ,
I ( ξ , τ ) = I 0 exp [ - 0 ξ V ( ξ ) d ξ ] , 0 τ τ p , = 0 , τ < 0 , τ > τ p ,
x p ( Z , t ) = 2 l 0 τ h { 1 - exp [ - ( t - Z / c m ) / τ h ] } ( 1 + l 1 τ h ) + ( 1 - l 1 τ h ) exp [ - ( t - Z / c m ) / τ h ]
x a ( Z , t ) = l 1 x p ( Z , Z / c m + t p ) exp [ - l 1 ( t - t p - Z / c m ) ] l 1 + l 2 x p ( Z , Z / c m + t p ) { 1 - exp [ - l 1 ( t - t p - Z / c m ) ] }
Δ T ( Z ) = Δ T 0 exp ( - Z / Z l ) / ( 1 + { 1 + [ 2 β Γ Δ T 0 / T 0 ( K + Γ ) ] × exp ( - Z / Z l ) } 1 / 2 ) , Δ T 0 = 2 σ 2 α I 0 / 3 ( K + Γ ) ,             Z l = 3 / 4 π σ 3 α n 0 .
T / τ = I ,
D T D t = T t + v T Z ,
v = - T / t T / Z .
v / c m = 1 1 + ρ l C c m V Δ T / I ,
v = I / ρ l C V Δ T ,
T = T 0 + α I τ h ρ l C [ 1 - exp ( - ρ l C τ / α τ h ) ] ,
v / c m = 1 1 + α V c m τ h .
v / c m = 1 1 + G n 0 σ 5 ,             G 4 π α ρ l C c m 9 ( K + Γ ) .

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