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Interferometric determination of the surface profile of a liquid heated by a laser beam
OPTICS COMMUNICATIONS
Volume 42, number 1
1 June 1982
INTERFEROMETRIC DETERMINATION OF THE SURFACE PROFILE OF A LIQUID HEATED BY A LASER BEAM J. CALATRONI Laboratorio de Optica Cuantica, Departamento de Fisica, UniversidadSimon Bohr, A.P. 80659, Curacas, Venezuela
and G. Da COSTA * Laboratoire d’optique, V.E.R. des Sciences, Universitide Limoges, 87060, Limoges Ctfdex, France Received 23 February 1982
A liquid sample (heavy oil) is heated by an argon laser beam in oblique incidence. The sample takes the place of one of the mirrors in a Michelson interferometer. The resulting time-variations of the surface shape are determined by exploration with a He-Ne laser beam. This allows one to determine the mechanical and thermal properties of petroleum samples.
1. Introduction Phenomena occurring during irradiation of heavy oils by a laser beam were described in recent papers [l-6]. The experiment is represented in fig. 1. The * In Sabbatical Year leave from Universidad Simon Bohvar. Issew
beam
Fig. 1. A gaussian laser beam heats a liquid sample. This produces fist a dilatation of the sample. Slmultaneously, a centrifugal liquid-flow grows up in the surface. The depletion of the central region induces the formation of a pit in the top of the hill.
0 030-4018/82/0000-0000/$02.75
0 1982 North-Holland
gaussian power-distribution in a normal section of the laser beam induces the development of a radiallydecreasing, time-growing temperature distribution in the sample. As the surface tension is a decreasing function of the temperature, a centrifugal stress state grows up in the liquid surface. This gives rise in turn to the establishment of a radial liquid flow directed outwards from the laser beam. The depletion of the central region results in the formation of a pit. Simultaneously, the sample expands as a result of the temperature-dependence of the liquid density. The whole phenomenon was first recorded by means of the interferometric technique represented in fig. 2. The details of this experiment are given in refs. [6, 71. The sample takes the place of one of the mirrors in a Michelson interferometer, where it is heated by an argon laser beam at 35 mW (h = 4880 A) and explored by a white-light beam. The white-light source is a 150 Watt xenon lamp. An achromatic lens & forms an image of the sample in the entrance plane (~‘-2’) of a spectroscope. The slit x’ selects the image of a meridian section x of the sample. Polychromatic fringes are obtained at the exit plane (x”, X). Each fringe represents, at a different scale, 5
Volume 42, number 1
1 June 1982
OPTICS COMMUNICATIONS laser
white
Fig. 2. Interferometric technique used to determine the surface-profile in a meridian section of the liquid sample. The surfaceprofile in the direction x appears as a system of polychromatic fringes in the exit-plane (x”, h) of the spectroscope when the sample is explored with a whitsljght beam in a Michelson interferometer.
the surface-profile of the sample in the chosen section. Typical results corresponding to three different time-instants are reproduced in figs. 3-5. The initial dilatation and the formation of the pit are clearly appreciated. This technique allows one to determine in real-time the meridian surface-profile. However, any information regarding the 3D surfaceshape is lost. This is an important drawback when the surface deformations are not axisymmetrical. In the actual paper another optical technique allowing one to display the equal-height curves of the whole surface at any time-instant is used.
Fig. 4. Idem., ri = 11
S, Ah=,
= 5
Mm.
Fig. 5. A pit is now formed in the top of the hill of fig. 4.
2. Coherent interferometric de&&nation of the surface-shape Fig. 3. Surface-profile corresponding to an irradiation time ti = 1 8. The maximum height increase L\h,x is about 1 nm.
6
The experiment is represented in fig. 6. Now the sample is explored by a plane wave coming from
Volume 42, number 1
OPTICS COMMUNICATIONS
Fig. 6. Interferometric technique used to determine the whole 3D shape of the surface of the heated sample. The heating beam Ar is emitted by an argon laser. The sample is explored by a HeNe laser beam. The resulting interference pattern appears in the image of the sample formed by the lens L at the running film F.
1 June 1982
5 mW He-Ne laser beam (h = 6328 A). The argonlaser power is P = 180 mW and the wavelength X = 4880 ,A. An image of the sample and of the reference mirror is formed by the lens L on the photographic film F. The incidence angle of the heating beam is cy= 37”, and the illuminated area is elliptical with axis lengths 2 X 4 mm approximately. A typical photographic sequence is reproduced in figs. 7(a-j). Dark and bright fringes are level (equal-height) curves of the surface, The height-difference Ah corresponding to two contiguous dark-bright fringes is such that 2Ah = h/2 (X = 6328 A, the exploring beam wavelength), so Ah = 1582 b. Fig. 7 shows that the initially unperturbed surface is not perfectly plane. Dilatation takes place until fig. 7(e). It is
Fig. 7a-d.
Fig. 7e-j. Fig. 7. Photographic sequence corresponding to the experiment of fii. 6. The sense of propagation of the laser beam is from South-West to South-East. It coincides with the larger axis of the elliptic pit appearing from fii. 7f to fip. 71.
Volume 42, number 1
OPTICS COMMUNICATIONS
noted that in this kind of experiment it is necessary to observe the direction of circulation of the fringes in order to determine the sign of the height-variations. In photograph 12 a pit is born in the SouthWest point of the top of the expanded region. The new fringes appearing around this point in the following photographs 7(f-j) circulate inwards, while the rest continue to circulate outwards as before. This evidences the formation of an increasingly larger and deeper pit in the top of the ever-expanding hill. Both the hill and the pit follow the elliptical shape of the intersection of the heating beam with the initial surface of the sample.
3. Conclusions The deformations of a liquid sample submitted to inhomogeneous heating are closely related to the thermal and mechanical properties of the material [2]. In particular, the heavy oils studied in our experiments present a great economoical interest. Important wells of these oils exist in Easter Venezuela. However, their exploitation is difficult due to the high viscosity of the samples (about 10 poise). The extractive techniques used in that case (injection of hot water, in situ combustion, etc.) take profit of the fact that the viscosity of heavy oils is a steeply-decreasing function of the temperature. The experiments described in refs. [l-6] showed first that the surface of an inhomogeneously-heated oil behaves as a smooth time-varying mirror. The space-time struc-
1 June 1982
ture of this surface is related to the temperaturedependence of the density, the surface-tension and the viscosity [2]. The coherent interferometric technique used in the actual paper allows one to determine the whole 3D’surface-shape at any time-instant. So it is a valuable tool in the study of physical prop erties of petroleum samples.
Acknowledgement
The experiments described hereup are performed with financial support of the Venezuelan Agencies CONICIT and FONINVES. The authors acknowledge illuminating discussions with Profs. M. Francon (Univ. de Paris VI) and C. Froehly (Univ. de Limoges) on the subject developed in this paper.
References [l] G. Da Costa and J. Calatroni, Appl. Optics 17 (1978) 2381. [2] G. Da Costa and J. Calatroni, Appl. Optics 18 (1979) 233. [ 31 G. Da Costa, Phys. Lett. 80A (1980) 320. [4] G. Da Costa, Phys. Lett. 80A (1980) 323. [S] G. DaCosta, Appl. Optics 19 (1980) 3523. [6] J. Calatroni, G. Da Costa and E. Ruiz, Optical studies of laser-heated petroleum samples, submitted to Appl. Opt. (January 1982) and University Simon Bolivar Preprint. [7] J. Calatroni and E. Ruiz, paper presented at the International Commission for Optics Meeting (I.C.O. 12), Graz, Austria, 1981.
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Volume 42, number 1
1 June 1982
INTERFEROMETRIC DETERMINATION OF THE SURFACE PROFILE OF A LIQUID HEATED BY A LASER BEAM J. CALATRONI Laboratorio de Optica Cuantica, Departamento de Fisica, UniversidadSimon Bohr, A.P. 80659, Curacas, Venezuela
and G. Da COSTA * Laboratoire d’optique, V.E.R. des Sciences, Universitide Limoges, 87060, Limoges Ctfdex, France Received 23 February 1982
A liquid sample (heavy oil) is heated by an argon laser beam in oblique incidence. The sample takes the place of one of the mirrors in a Michelson interferometer. The resulting time-variations of the surface shape are determined by exploration with a He-Ne laser beam. This allows one to determine the mechanical and thermal properties of petroleum samples.
1. Introduction Phenomena occurring during irradiation of heavy oils by a laser beam were described in recent papers [l-6]. The experiment is represented in fig. 1. The * In Sabbatical Year leave from Universidad Simon Bohvar. Issew
beam
Fig. 1. A gaussian laser beam heats a liquid sample. This produces fist a dilatation of the sample. Slmultaneously, a centrifugal liquid-flow grows up in the surface. The depletion of the central region induces the formation of a pit in the top of the hill.
0 030-4018/82/0000-0000/$02.75
0 1982 North-Holland
gaussian power-distribution in a normal section of the laser beam induces the development of a radiallydecreasing, time-growing temperature distribution in the sample. As the surface tension is a decreasing function of the temperature, a centrifugal stress state grows up in the liquid surface. This gives rise in turn to the establishment of a radial liquid flow directed outwards from the laser beam. The depletion of the central region results in the formation of a pit. Simultaneously, the sample expands as a result of the temperature-dependence of the liquid density. The whole phenomenon was first recorded by means of the interferometric technique represented in fig. 2. The details of this experiment are given in refs. [6, 71. The sample takes the place of one of the mirrors in a Michelson interferometer, where it is heated by an argon laser beam at 35 mW (h = 4880 A) and explored by a white-light beam. The white-light source is a 150 Watt xenon lamp. An achromatic lens & forms an image of the sample in the entrance plane (~‘-2’) of a spectroscope. The slit x’ selects the image of a meridian section x of the sample. Polychromatic fringes are obtained at the exit plane (x”, X). Each fringe represents, at a different scale, 5
Volume 42, number 1
1 June 1982
OPTICS COMMUNICATIONS laser
white
Fig. 2. Interferometric technique used to determine the surface-profile in a meridian section of the liquid sample. The surfaceprofile in the direction x appears as a system of polychromatic fringes in the exit-plane (x”, h) of the spectroscope when the sample is explored with a whitsljght beam in a Michelson interferometer.
the surface-profile of the sample in the chosen section. Typical results corresponding to three different time-instants are reproduced in figs. 3-5. The initial dilatation and the formation of the pit are clearly appreciated. This technique allows one to determine in real-time the meridian surface-profile. However, any information regarding the 3D surfaceshape is lost. This is an important drawback when the surface deformations are not axisymmetrical. In the actual paper another optical technique allowing one to display the equal-height curves of the whole surface at any time-instant is used.
Fig. 4. Idem., ri = 11
S, Ah=,
= 5
Mm.
Fig. 5. A pit is now formed in the top of the hill of fig. 4.
2. Coherent interferometric de&&nation of the surface-shape Fig. 3. Surface-profile corresponding to an irradiation time ti = 1 8. The maximum height increase L\h,x is about 1 nm.
6
The experiment is represented in fig. 6. Now the sample is explored by a plane wave coming from
Volume 42, number 1
OPTICS COMMUNICATIONS
Fig. 6. Interferometric technique used to determine the whole 3D shape of the surface of the heated sample. The heating beam Ar is emitted by an argon laser. The sample is explored by a HeNe laser beam. The resulting interference pattern appears in the image of the sample formed by the lens L at the running film F.
1 June 1982
5 mW He-Ne laser beam (h = 6328 A). The argonlaser power is P = 180 mW and the wavelength X = 4880 ,A. An image of the sample and of the reference mirror is formed by the lens L on the photographic film F. The incidence angle of the heating beam is cy= 37”, and the illuminated area is elliptical with axis lengths 2 X 4 mm approximately. A typical photographic sequence is reproduced in figs. 7(a-j). Dark and bright fringes are level (equal-height) curves of the surface, The height-difference Ah corresponding to two contiguous dark-bright fringes is such that 2Ah = h/2 (X = 6328 A, the exploring beam wavelength), so Ah = 1582 b. Fig. 7 shows that the initially unperturbed surface is not perfectly plane. Dilatation takes place until fig. 7(e). It is
Fig. 7a-d.
Fig. 7e-j. Fig. 7. Photographic sequence corresponding to the experiment of fii. 6. The sense of propagation of the laser beam is from South-West to South-East. It coincides with the larger axis of the elliptic pit appearing from fii. 7f to fip. 71.
Volume 42, number 1
OPTICS COMMUNICATIONS
noted that in this kind of experiment it is necessary to observe the direction of circulation of the fringes in order to determine the sign of the height-variations. In photograph 12 a pit is born in the SouthWest point of the top of the expanded region. The new fringes appearing around this point in the following photographs 7(f-j) circulate inwards, while the rest continue to circulate outwards as before. This evidences the formation of an increasingly larger and deeper pit in the top of the ever-expanding hill. Both the hill and the pit follow the elliptical shape of the intersection of the heating beam with the initial surface of the sample.
3. Conclusions The deformations of a liquid sample submitted to inhomogeneous heating are closely related to the thermal and mechanical properties of the material [2]. In particular, the heavy oils studied in our experiments present a great economoical interest. Important wells of these oils exist in Easter Venezuela. However, their exploitation is difficult due to the high viscosity of the samples (about 10 poise). The extractive techniques used in that case (injection of hot water, in situ combustion, etc.) take profit of the fact that the viscosity of heavy oils is a steeply-decreasing function of the temperature. The experiments described in refs. [l-6] showed first that the surface of an inhomogeneously-heated oil behaves as a smooth time-varying mirror. The space-time struc-
1 June 1982
ture of this surface is related to the temperaturedependence of the density, the surface-tension and the viscosity [2]. The coherent interferometric technique used in the actual paper allows one to determine the whole 3D’surface-shape at any time-instant. So it is a valuable tool in the study of physical prop erties of petroleum samples.
Acknowledgement
The experiments described hereup are performed with financial support of the Venezuelan Agencies CONICIT and FONINVES. The authors acknowledge illuminating discussions with Profs. M. Francon (Univ. de Paris VI) and C. Froehly (Univ. de Limoges) on the subject developed in this paper.
References [l] G. Da Costa and J. Calatroni, Appl. Optics 17 (1978) 2381. [2] G. Da Costa and J. Calatroni, Appl. Optics 18 (1979) 233. [ 31 G. Da Costa, Phys. Lett. 80A (1980) 320. [4] G. Da Costa, Phys. Lett. 80A (1980) 323. [S] G. DaCosta, Appl. Optics 19 (1980) 3523. [6] J. Calatroni, G. Da Costa and E. Ruiz, Optical studies of laser-heated petroleum samples, submitted to Appl. Opt. (January 1982) and University Simon Bolivar Preprint. [7] J. Calatroni and E. Ruiz, paper presented at the International Commission for Optics Meeting (I.C.O. 12), Graz, Austria, 1981.
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