Abstract

Approximate analytical and full numerical solutions are obtained for the transient response of both a pure water and solution droplets to both short- and long-time laser heating. The differences in the temperature and size histories between pure water and solution droplets are elucidated. The validity of of the approximate analytical solution, extended from that of Armstrong [“Aerosol Heating and Vaporization by Pulsed Light Beams,” Appl. Opt. 23, 148 ( 1984)] in pure water droplets, is evaluated by comparison to solution of the full governing equations.

© 1984 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).
  2. A. Ashkin, J. M. Dziedzic, “Observations of Optical Resonances of Dielectric Spheres by Light Scattering,” Appl. Opt. 20, 1803 (1981).
    [CrossRef] [PubMed]
  3. G. E. Caledonia, J. D. Teare, J. Heat Transfer 99, 281 (1977).
    [CrossRef]
  4. R. L. Armstrong, “Aerosol Heating and Vaporization by Pulsed Light Beams,” Appl. Opt. 23, 148 (1984).
    [CrossRef] [PubMed]
  5. R. B. Bird, W. E. Stewart, E. N. Lightfoot, Transport Phenomena (Wiley, New York, 1980).
  6. F. A. Williams, “On Vaporization of Mist by Radiation,” Int. J. Heat Mass Transfer 8, 575 (1965).
    [CrossRef]
  7. A. W. Stelson, J. H. Seinfeld, “Relative Humidity and Temperature Dependence of the Ammonium Nitrate Dissociation Constant,” Atmos. Environ. 16, 983 (1982).
    [CrossRef]
  8. S. H. Harned, B. B. Owne, The Physical Chemistry of Electrolytic Solutions (Reinhold, New York, 1958).
  9. W. J. Hamer, Y. C. Wu, “Osmotic Coefficients and Mean Activity Coefficients of Uni-Univalent Electrolytes in Water at 25°C,” J. Phys. Chem. Ref. Data 1, 1047 (1972).
    [CrossRef]
  10. H. F. Gibbard, G. Scatchard, R. A. Rousseau, J. L. Creek, “Liquid-Vapor Equilibrium of Aqueous Sodium Chloride from 298 to 373 K and from 1 to 6 mole kg−1 and Related Properties,” J. Chem. Eng. Data 19, 281 (1974).
    [CrossRef]
  11. L. A. Bromley, A. E. Diamond, E. Salami, D. G. Wilkins, “Heat Capacities and Enthalpies of Sea Salt Solutions to 200°C,” J. Chem. Eng. Data 15, 246 (1970).
    [CrossRef]
  12. M. R. Querry, R. C. Waring, W. A. Holand, G. M. Hale, W. Nijm, “Optical Constants in IR for Aqueous NaCl,” J. Opt. Soc. Am. 62, 849 (1972).
    [CrossRef]

1984 (1)

1982 (1)

A. W. Stelson, J. H. Seinfeld, “Relative Humidity and Temperature Dependence of the Ammonium Nitrate Dissociation Constant,” Atmos. Environ. 16, 983 (1982).
[CrossRef]

1981 (1)

1977 (1)

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

1974 (1)

H. F. Gibbard, G. Scatchard, R. A. Rousseau, J. L. Creek, “Liquid-Vapor Equilibrium of Aqueous Sodium Chloride from 298 to 373 K and from 1 to 6 mole kg−1 and Related Properties,” J. Chem. Eng. Data 19, 281 (1974).
[CrossRef]

1972 (2)

W. J. Hamer, Y. C. Wu, “Osmotic Coefficients and Mean Activity Coefficients of Uni-Univalent Electrolytes in Water at 25°C,” J. Phys. Chem. Ref. Data 1, 1047 (1972).
[CrossRef]

M. R. Querry, R. C. Waring, W. A. Holand, G. M. Hale, W. Nijm, “Optical Constants in IR for Aqueous NaCl,” J. Opt. Soc. Am. 62, 849 (1972).
[CrossRef]

1970 (1)

L. A. Bromley, A. E. Diamond, E. Salami, D. G. Wilkins, “Heat Capacities and Enthalpies of Sea Salt Solutions to 200°C,” J. Chem. Eng. Data 15, 246 (1970).
[CrossRef]

1965 (1)

F. A. Williams, “On Vaporization of Mist by Radiation,” Int. J. Heat Mass Transfer 8, 575 (1965).
[CrossRef]

Armstrong, R. L.

Ashkin, A.

Bird, R. B.

R. B. Bird, W. E. Stewart, E. N. Lightfoot, Transport Phenomena (Wiley, New York, 1980).

Bromley, L. A.

L. A. Bromley, A. E. Diamond, E. Salami, D. G. Wilkins, “Heat Capacities and Enthalpies of Sea Salt Solutions to 200°C,” J. Chem. Eng. Data 15, 246 (1970).
[CrossRef]

Caledonia, G. E.

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

Creek, J. L.

H. F. Gibbard, G. Scatchard, R. A. Rousseau, J. L. Creek, “Liquid-Vapor Equilibrium of Aqueous Sodium Chloride from 298 to 373 K and from 1 to 6 mole kg−1 and Related Properties,” J. Chem. Eng. Data 19, 281 (1974).
[CrossRef]

Diamond, A. E.

L. A. Bromley, A. E. Diamond, E. Salami, D. G. Wilkins, “Heat Capacities and Enthalpies of Sea Salt Solutions to 200°C,” J. Chem. Eng. Data 15, 246 (1970).
[CrossRef]

Dziedzic, J. M.

Gibbard, H. F.

H. F. Gibbard, G. Scatchard, R. A. Rousseau, J. L. Creek, “Liquid-Vapor Equilibrium of Aqueous Sodium Chloride from 298 to 373 K and from 1 to 6 mole kg−1 and Related Properties,” J. Chem. Eng. Data 19, 281 (1974).
[CrossRef]

Hale, G. M.

Hamer, W. J.

W. J. Hamer, Y. C. Wu, “Osmotic Coefficients and Mean Activity Coefficients of Uni-Univalent Electrolytes in Water at 25°C,” J. Phys. Chem. Ref. Data 1, 1047 (1972).
[CrossRef]

Harned, S. H.

S. H. Harned, B. B. Owne, The Physical Chemistry of Electrolytic Solutions (Reinhold, New York, 1958).

Holand, W. A.

Lightfoot, E. N.

R. B. Bird, W. E. Stewart, E. N. Lightfoot, Transport Phenomena (Wiley, New York, 1980).

Nijm, W.

Owne, B. B.

S. H. Harned, B. B. Owne, The Physical Chemistry of Electrolytic Solutions (Reinhold, New York, 1958).

Querry, M. R.

Rousseau, R. A.

H. F. Gibbard, G. Scatchard, R. A. Rousseau, J. L. Creek, “Liquid-Vapor Equilibrium of Aqueous Sodium Chloride from 298 to 373 K and from 1 to 6 mole kg−1 and Related Properties,” J. Chem. Eng. Data 19, 281 (1974).
[CrossRef]

Salami, E.

L. A. Bromley, A. E. Diamond, E. Salami, D. G. Wilkins, “Heat Capacities and Enthalpies of Sea Salt Solutions to 200°C,” J. Chem. Eng. Data 15, 246 (1970).
[CrossRef]

Scatchard, G.

H. F. Gibbard, G. Scatchard, R. A. Rousseau, J. L. Creek, “Liquid-Vapor Equilibrium of Aqueous Sodium Chloride from 298 to 373 K and from 1 to 6 mole kg−1 and Related Properties,” J. Chem. Eng. Data 19, 281 (1974).
[CrossRef]

Seinfeld, J. H.

A. W. Stelson, J. H. Seinfeld, “Relative Humidity and Temperature Dependence of the Ammonium Nitrate Dissociation Constant,” Atmos. Environ. 16, 983 (1982).
[CrossRef]

Stelson, A. W.

A. W. Stelson, J. H. Seinfeld, “Relative Humidity and Temperature Dependence of the Ammonium Nitrate Dissociation Constant,” Atmos. Environ. 16, 983 (1982).
[CrossRef]

Stewart, W. E.

R. B. Bird, W. E. Stewart, E. N. Lightfoot, Transport Phenomena (Wiley, New York, 1980).

Teare, J. D.

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

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).

Waring, R. C.

Wilkins, D. G.

L. A. Bromley, A. E. Diamond, E. Salami, D. G. Wilkins, “Heat Capacities and Enthalpies of Sea Salt Solutions to 200°C,” J. Chem. Eng. Data 15, 246 (1970).
[CrossRef]

Williams, F. A.

F. A. Williams, “On Vaporization of Mist by Radiation,” Int. J. Heat Mass Transfer 8, 575 (1965).
[CrossRef]

Wu, Y. C.

W. J. Hamer, Y. C. Wu, “Osmotic Coefficients and Mean Activity Coefficients of Uni-Univalent Electrolytes in Water at 25°C,” J. Phys. Chem. Ref. Data 1, 1047 (1972).
[CrossRef]

Appl. Opt. (2)

Atmos. Environ. (1)

A. W. Stelson, J. H. Seinfeld, “Relative Humidity and Temperature Dependence of the Ammonium Nitrate Dissociation Constant,” Atmos. Environ. 16, 983 (1982).
[CrossRef]

Int. J. Heat Mass Transfer (1)

F. A. Williams, “On Vaporization of Mist by Radiation,” Int. J. Heat Mass Transfer 8, 575 (1965).
[CrossRef]

J. Chem. Eng. Data (2)

H. F. Gibbard, G. Scatchard, R. A. Rousseau, J. L. Creek, “Liquid-Vapor Equilibrium of Aqueous Sodium Chloride from 298 to 373 K and from 1 to 6 mole kg−1 and Related Properties,” J. Chem. Eng. Data 19, 281 (1974).
[CrossRef]

L. A. Bromley, A. E. Diamond, E. Salami, D. G. Wilkins, “Heat Capacities and Enthalpies of Sea Salt Solutions to 200°C,” J. Chem. Eng. Data 15, 246 (1970).
[CrossRef]

J. Heat Transfer (1)

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

J. Opt. Soc. Am. (1)

J. Phys. Chem. Ref. Data (1)

W. J. Hamer, Y. C. Wu, “Osmotic Coefficients and Mean Activity Coefficients of Uni-Univalent Electrolytes in Water at 25°C,” J. Phys. Chem. Ref. Data 1, 1047 (1972).
[CrossRef]

Other (3)

R. B. Bird, W. E. Stewart, E. N. Lightfoot, Transport Phenomena (Wiley, New York, 1980).

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).

S. H. Harned, B. B. Owne, The Physical Chemistry of Electrolytic Solutions (Reinhold, New York, 1958).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)

Fig. 1
Fig. 1

Temperature rise in a droplet vs dimensionless time at tp = 5 μsec; rs = 0.25, 0.5, 1.0, 2.0 μm, and I0α = 105 W cm−3.

Fig. 2
Fig. 2

Temperature rise in a droplet vs dimensionless time at tp = 5 μsec; rs = 0.10, 0.20, 0.40 μm, and I0α = 108 W cm−3.

Fig. 3
Fig. 3

Contribution of various parameters to the difference between the maximum temperature rise in a solution and that in a pure drop.

Fig. 4
Fig. 4

Discrepancy between the analytical and numerical solutions for the short-time heating of a droplet of m = 3.0 and r = 0.8 μm.

Fig. 5
Fig. 5

Temperature rise vs dimensionless heating time for long-time heating of a droplet of initial radius r0 = 1.0 μm, τd = 0.9435 sec (at I0α = 105 W cm−3), and τd = 0.009435 sec (at I0α = 107 W cm−3).

Fig. 6
Fig. 6

Dimensionless radius vs dimensionless heating time for r0 = 1.0 μm, and 1τd = 0.9435 sec (at I0α = 105 W cm−3).

Tables (1)

Tables Icon

Table I Summary of the Values of Various Physical Constants used in the Calculation (at 298 K)

Equations (28)

Equations on this page are rendered with MathJax. Learn more.

ρ d C d d T d t = I 0 α - 3 r s [ - L D a ( Y r ) r = r a - k a ( T r ) r = r a ] ,
- D a ( Y r ) r = r s = J = D a r s ln ( 1 - Y 1 - Y s ) ,
- k a ( T r ) r = r s = J C a ( T s - T ) L [ exp ( r s J C a k a ) - 1 ] ,
d T d t = I 0 α ρ d C d - 3 J L r s ρ d C d { 1 + C a ( T - T ) L [ exp ( r s J C a k a ) - 1 ] } .
Y s ( T ) a w ( T ) Y 0 ( T ) ,
Y 0 ( T ) = Y 0 ( T ) exp [ - L M w R ( 1 T - 1 T ) ] exp ( 2 v ¯ σ R T r s ) ,
a w ( T ) = exp [ - ν m M w 1000 φ ( T ) ] .
φ ( T ) = 1 + 1 m 0 m m d ln [ γ ( T ) ] .
T ( ln γ 2 ) P = H ¯ i 0 - H ¯ i R T 2 ,
φ ( T ) = φ ( T ) + ( 1 T - 1 T ) 1 m 0 m m m [ ( H ¯ i - H ¯ i 0 ) 2 R ] d m - ( ln T T + T T - 1 ) 1 m 0 m m m [ ( C ¯ i - C ¯ i 0 ) 2 R ] d m ,
δ = 1 m 0 m m m [ ( H ¯ i - H ¯ i 0 ) 2 R ] d m = n = 1 A n ( n n + 2 ) m n / 2 ,
β = 1 m 0 m m m [ ( C ¯ i - C ¯ i 0 ) 2 R ] d m = n = 1 B n ( n n + 2 ) m n / 2 ,
J = D a r s ln [ 1 - Y f ( T ) ] ,
f ( T ) = 1 - Y 0 ( T ) exp { A T - B [ φ T ) + δ ( 1 T - 1 T ) - β ( l n T T + T T - 1 ) ] - C ( 1 T - 1 T ) } ,
A = 2 v ¯ σ R r s ,             B = ν m M w 1000 ,             C = L M w R .
J = D a r s ( X + ψ X 2 ) ,
= ( Y 1 - Y ) ( - A + B δ + C T ) , ψ = [ ( - A + B δ + C ) 2 ( 1 - Y ) T - 1 + B β T 2 ( - A + B δ + C ) ] .
X ( 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 ) ] if t t p , l 1 X ( t p ) exp ( - l 1 t ) l 1 + l 2 X ( t p ) [ 1 - exp ( - l 1 t ) ] if t > t p
l 0 = I 0 α ρ d C d T l 1 = 3 ρ d C d r s 2 ( D a L T + k a ) l 2 = 3 ρ d C d r s 2 ( D a L T ψ - C a D a 2 ) , τ h = ( l 1 2 + 4 l 0 l 2 ) - 1 / 2 .
Φ L = Φ H - Φ H 0 = 458.95 m 1 / 2 - 688.09 m + 241.47 m 3 / 2 - 39.339 m 2 + 4.3245 m 5 / 2 - 0.0449 m 2 ,
Φ C P - Φ C p 0 = 10.291 m 1 / 2 - 3.6538 m + 13.121 m 3 / 2 - 10.638 m 2 + 3.5304 m 5 / 2 - 0.4282 m 3 ,
H ¯ i - H ¯ i 0 = Φ L - m Φ L m .
C P = n w C ¯ w 0 + n 2 Φ C p ,
ρ d = ρ d 0 + c 1000 ( M 2 - Φ V ρ d 0 ) ,
η = T * - T 0 T s - T 0 × 100 % ,
r s t = 1 ρ d J .
τ d = 3 ρ d L ( k a + Γ ) I 0 α Γ ,
Γ = L 2 D a M w Y 0 R ( 1 - Y 0 ) T 2 .

Metrics