Abstract

Heavy hydrocarbons are irradiated with a Gaussian laser beam. The time-varying temperature distribution induced in the fluid gives rise to a surface-tension distribution. The later gives rise in turn to an accompanying liquid flow and surface-height distribution. In this paper, the time-varying shape of the induced depression is calculated as a function of the power distribution in the laser beam and of the thermal and mechanical properties of the material. The intensity distribution in the laser beam reflected from the depression is also calculated. Good agreement is found with previous experimental results.

© 1979 Optical Society of America

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References

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  1. G. Da Costa, J. Calatroni, Appl. Opt. 17, 2381 (1978).
    [CrossRef]
  2. V. G. Levich, Physicochemical Hydrodynamics (Prentice Hall, Englewood Cliffs, N.J., 1962), pp. 384–390.
  3. L. Landau, E. Lifschitz, Mechanics of Fluids (Addison-Wesley, New York, 1959; Mir, Moscow, 1971), pp. 296–297.
  4. M. I. Cohen, in Laser Handbook, F. T. Arecchi, E. O. DuBois, Eds. (North Holland, Amsterdam1972), pp. 1586–1587.

1978

Calatroni, J.

Cohen, M. I.

M. I. Cohen, in Laser Handbook, F. T. Arecchi, E. O. DuBois, Eds. (North Holland, Amsterdam1972), pp. 1586–1587.

Da Costa, G.

Landau, L.

L. Landau, E. Lifschitz, Mechanics of Fluids (Addison-Wesley, New York, 1959; Mir, Moscow, 1971), pp. 296–297.

Levich, V. G.

V. G. Levich, Physicochemical Hydrodynamics (Prentice Hall, Englewood Cliffs, N.J., 1962), pp. 384–390.

Lifschitz, E.

L. Landau, E. Lifschitz, Mechanics of Fluids (Addison-Wesley, New York, 1959; Mir, Moscow, 1971), pp. 296–297.

Appl. Opt.

Other

V. G. Levich, Physicochemical Hydrodynamics (Prentice Hall, Englewood Cliffs, N.J., 1962), pp. 384–390.

L. Landau, E. Lifschitz, Mechanics of Fluids (Addison-Wesley, New York, 1959; Mir, Moscow, 1971), pp. 296–297.

M. I. Cohen, in Laser Handbook, F. T. Arecchi, E. O. DuBois, Eds. (North Holland, Amsterdam1972), pp. 1586–1587.

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Figures (6)

Fig. 1
Fig. 1

A thin liquid slab (height y0) is illuminated by a Gaussian laser beam. A depression is then induced in the surface of the sample.

Fig. 2
Fig. 2

Computer-calculated values of the relative height of the depression (y/y0) for different values of the intensity-dependent parameter b and the time-dependent parameter γ. The ordinates of the minima are equal to y/y0 = 0.999 (γ = 0.01), y/y0 = 0.995 (γ= 0.1), y/y0 = 0.964 (γ= 1).

Fig. 3
Fig. 3

Idem.: y/y0 = 0.995 (γ = 0.01), y/y0 = 0.951 (γ= 0.1), y/y0 = 0.556 (γ = 1).

Fig. 4
Fig. 4

Idem.: y/y0 = 0.949 (γ = 0.01), y/y0 = 0.215 (γ = 0.1).

Fig. 5
Fig. 5

Experimental intensity distribution in the light field reflected from the deformed surface (from Ref. 1).

Fig. 6
Fig. 6

Computer-calculated family of light rays reflected from the deformed surface corresponding to b = 10, γ = 0.01. Due to the small value chosen for the vertical scale, the liquid surface appears superposed to the horizontal axis. The light rays appear as coming from a point source F2 and from a ring source passing by F1 and F 1 . This gives rise to the interference pattern of Fig. 5.

Equations (7)

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y ( α ) = [ y 0 2 ( ρ 0 ρ ) 3 / 4 + 3 ρ g ( α - α 0 ) ] 1 / 2 .
α ( T ) = α 0 + c ( T - T 0 ) .
y ( T ) y 0 = ( 1 - T - T 0 T α ) 1 / 2 .
T α = - [ ( ρ g y 0 2 ) / ( 3 c ) ] .
T - T 0 = H 0 a 2 4 k y 0 { - E i [ - ( x a ) 2 1 + 4 κ t a 2 ] + E i [ - ( x a ) 2 ] ,
y / y 0 = [ 1 + b f ( β , γ ) ] 1 / 2 .
b = 3 4 π · c P ρ g k y 0 3             γ = t / t 0 t 0 = a 2 / 4 κ β = x / a f ( β , γ ) = β 2 / 1 + γ β 2 d θ θ e θ .

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