Abstract

We show that thermophoresis (particle drift driven by thermal gradients) in aqueous solutions can be measured by using an all-optical thermal-lensing setup, where a temperature gradient is set by a near-infrared laser beam with no need of light-absorbing dyes. After discussing the principles of the method, we study by numerical simulation the nature and extent of parasitic thermal-convection effects, and we describe an optical setup designed to limit them. We finally present preliminary results on thermophoresis in micellar solutions and colloidal dispersions.

© 2004 Optical Society of America

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References

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  1. J. V. Tyrrell, Diffusion and Heat Flow in Liquids (Butterworth, London, 1961).
  2. S. R. De Groot and P. Mazur, Nonequilibrium Thermodynamics (North Holland, Amsterdam, 1962).
  3. A. La Porta and C. M. Surko, “Convective instability in a fluid mixture heated from above,” Phys. Rev. Lett. 80, 3759–3762 (1998).
    [CrossRef]
  4. R. W. Schmitt, “The ocean’s salt fingers,” Sci. Am. 272, 70–75 (1995).
    [CrossRef]
  5. L. L. Zheng, D. J. Larson, Jr., and H. Zhang, “Role of thermotransport (Soret effect) in macrosegregation during eutectic/off-eutectic directional solidification,” J. Cryst. Growth 191, 243–251 (1998).
    [CrossRef]
  6. R. T. Cygan and C. R. Carrigan, “Time-dependent Soret transport: applications to brine and magma,” Chem. Geol. 95, 201–212 (1992).
    [CrossRef]
  7. F. H. Busse, “Fundamentals of thermal convection,” in Mantle Convection: Plate Tectonics and Global Dynamics, W. Peltier, ed. (Gordon and Breach, London, 1989), pp. 23–95.
  8. M. C. Cross and P. C. Honenberg, “Pattern formation outside of equilibrium,” Rev. Mod. Phys. 65, 851–1112 (1993).
    [CrossRef]
  9. A. Vailati and M. Giglio, “Nonequilibrium fluctuations in time-dependent diffusion processes,” Phys. Rev. E 58, 4361–4371 (1998).
    [CrossRef]
  10. D. Braun and A. Libschaber, “Trapping of DNA by thermophoretic depletion and convection,” Phys. Rev. Lett. 89, 188103 (2002).
    [CrossRef] [PubMed]
  11. R. Piazza and A. Guarino, “Soret effect in interacting micellar solutions,” Phys. Rev. Lett. 88, 208302 (2002).
    [CrossRef] [PubMed]
  12. S. Iacopini and R. Piazza, “Thermophoresis in protein solutions,” Europhys. Lett. 63, 247–253 (2003).
    [CrossRef]
  13. M. Giglio and A. Vendramini, “Soret-type motion of macromolecules in solution,” Phys. Rev. Lett. 38, 26–30 (1977).
    [CrossRef]
  14. W. Köhler, “Thermodiffusion in polymer solutions as observed by forced Rayleigh scattering,” J. Chem. Phys. 98, 660–668 (1993).
    [CrossRef]
  15. J. P. Gordon, R. C. C. Leite, R. S. Moore, S. P. S. Porto, and J. R. Whinnery, “Long-transient effects in lasers with inserted liquid samples,” J. Appl. Phys. 36, 3–8 (1965).
    [CrossRef]
  16. J. R. Whinnery, D. T. Miller, and F. Dabby, “Thermal convection and spherical aberration distortion of laser beams in low-loss liquids,” IEEE J. Quantum Electron. 3, 382–383 (1967).
    [CrossRef]
  17. S. E. Bialkowski, Photothermal Spectroscopy Methods for Chemical Analysis (Wiley, New York, 1996).
  18. M. Franko and C. D. Tran, “Analytical thermal lens instrumentation,” Rev. Sci. Instrum. 67, 1–18 (1996).
    [CrossRef]
  19. M. Giglio and A. Vendramini, “Thermal lens effect in a binary liquid mixture: a new effect,” Appl. Phys. Lett. 25, 555–557 (1974).
    [CrossRef]
  20. L. Mistura, “Critical behavior of transport coefficients in multicomponent fluid mixtures,” J. Chem. Phys. 62, 4571–4572 (1975).
    [CrossRef]
  21. S. Alves, A. Bourdon, and A. M. F. Neto, “Generalization of the thermal lens model formalism to account for thermod-iffusion in a single-beam Z-scan experiment: determination of the Soret coefficient,” J. Opt. Soc. Am. B 20, 713–718 (2003).
    [CrossRef]
  22. N. Arnaud and J. Georges, “On the analytical use of the Soret-enhanced thermal lens signal in aqueous solutions,” Anal. Chim. Acta 445, 239–244 (2001).
    [CrossRef]
  23. S. J. Sheldon, L. V. Knight, and J. M. Thorne, “Laser-induced thermal lens effect: a new theoretical model,” Appl. Opt. 21, 1663–1669 (1982).
    [CrossRef] [PubMed]
  24. S. Wu and N. J. Dovichi, “Fresnel diffraction theory for steady-state thermal lens measurements in thin films,” J. Appl. Phys. 67, 1170–1182 (1990).
    [CrossRef]
  25. S. A. Akhmanov, D. P. Krindach, A. V. Migulin, A. P. Sukhorukov, and H. V. Khokhlov, “Thermal self-actions of laser beams,” IEEE J. Quantum Electron. 4, 568–575 (1968).
    [CrossRef]
  26. L. Quartapelle, Numerical Simulations of the Incompressible Navier–Stokes Equations (Birkhauser-Verlag, Berlin, 1993).
  27. C. A. Carter and J. M. Harris, “Comparison of models describing the thermal lens effect,” Appl. Opt. 23, 476–481 (1984).
    [CrossRef] [PubMed]
  28. M. Giglio and A. Vendramini, “Thermal-diffusion measurements near a consolute critical point,” Phys. Rev. Lett. 34, 561–564 (1975).
    [CrossRef]
  29. J. Rauch and W. Köhler, “Diffusion and thermal diffusion in semidilute to concentrated solutions of polystyrene in toluene in the vicinity of the glass transition,” Phys. Rev. Lett. 88, 185901 (2002).
    [CrossRef]

2003 (2)

2002 (3)

J. Rauch and W. Köhler, “Diffusion and thermal diffusion in semidilute to concentrated solutions of polystyrene in toluene in the vicinity of the glass transition,” Phys. Rev. Lett. 88, 185901 (2002).
[CrossRef]

D. Braun and A. Libschaber, “Trapping of DNA by thermophoretic depletion and convection,” Phys. Rev. Lett. 89, 188103 (2002).
[CrossRef] [PubMed]

R. Piazza and A. Guarino, “Soret effect in interacting micellar solutions,” Phys. Rev. Lett. 88, 208302 (2002).
[CrossRef] [PubMed]

2001 (1)

N. Arnaud and J. Georges, “On the analytical use of the Soret-enhanced thermal lens signal in aqueous solutions,” Anal. Chim. Acta 445, 239–244 (2001).
[CrossRef]

1998 (3)

A. Vailati and M. Giglio, “Nonequilibrium fluctuations in time-dependent diffusion processes,” Phys. Rev. E 58, 4361–4371 (1998).
[CrossRef]

A. La Porta and C. M. Surko, “Convective instability in a fluid mixture heated from above,” Phys. Rev. Lett. 80, 3759–3762 (1998).
[CrossRef]

L. L. Zheng, D. J. Larson, Jr., and H. Zhang, “Role of thermotransport (Soret effect) in macrosegregation during eutectic/off-eutectic directional solidification,” J. Cryst. Growth 191, 243–251 (1998).
[CrossRef]

1996 (1)

M. Franko and C. D. Tran, “Analytical thermal lens instrumentation,” Rev. Sci. Instrum. 67, 1–18 (1996).
[CrossRef]

1995 (1)

R. W. Schmitt, “The ocean’s salt fingers,” Sci. Am. 272, 70–75 (1995).
[CrossRef]

1993 (2)

M. C. Cross and P. C. Honenberg, “Pattern formation outside of equilibrium,” Rev. Mod. Phys. 65, 851–1112 (1993).
[CrossRef]

W. Köhler, “Thermodiffusion in polymer solutions as observed by forced Rayleigh scattering,” J. Chem. Phys. 98, 660–668 (1993).
[CrossRef]

1992 (1)

R. T. Cygan and C. R. Carrigan, “Time-dependent Soret transport: applications to brine and magma,” Chem. Geol. 95, 201–212 (1992).
[CrossRef]

1990 (1)

S. Wu and N. J. Dovichi, “Fresnel diffraction theory for steady-state thermal lens measurements in thin films,” J. Appl. Phys. 67, 1170–1182 (1990).
[CrossRef]

1984 (1)

1982 (1)

1977 (1)

M. Giglio and A. Vendramini, “Soret-type motion of macromolecules in solution,” Phys. Rev. Lett. 38, 26–30 (1977).
[CrossRef]

1975 (2)

L. Mistura, “Critical behavior of transport coefficients in multicomponent fluid mixtures,” J. Chem. Phys. 62, 4571–4572 (1975).
[CrossRef]

M. Giglio and A. Vendramini, “Thermal-diffusion measurements near a consolute critical point,” Phys. Rev. Lett. 34, 561–564 (1975).
[CrossRef]

1974 (1)

M. Giglio and A. Vendramini, “Thermal lens effect in a binary liquid mixture: a new effect,” Appl. Phys. Lett. 25, 555–557 (1974).
[CrossRef]

1968 (1)

S. A. Akhmanov, D. P. Krindach, A. V. Migulin, A. P. Sukhorukov, and H. V. Khokhlov, “Thermal self-actions of laser beams,” IEEE J. Quantum Electron. 4, 568–575 (1968).
[CrossRef]

1967 (1)

J. R. Whinnery, D. T. Miller, and F. Dabby, “Thermal convection and spherical aberration distortion of laser beams in low-loss liquids,” IEEE J. Quantum Electron. 3, 382–383 (1967).
[CrossRef]

1965 (1)

J. P. Gordon, R. C. C. Leite, R. S. Moore, S. P. S. Porto, and J. R. Whinnery, “Long-transient effects in lasers with inserted liquid samples,” J. Appl. Phys. 36, 3–8 (1965).
[CrossRef]

Akhmanov, S. A.

S. A. Akhmanov, D. P. Krindach, A. V. Migulin, A. P. Sukhorukov, and H. V. Khokhlov, “Thermal self-actions of laser beams,” IEEE J. Quantum Electron. 4, 568–575 (1968).
[CrossRef]

Alves, S.

Arnaud, N.

N. Arnaud and J. Georges, “On the analytical use of the Soret-enhanced thermal lens signal in aqueous solutions,” Anal. Chim. Acta 445, 239–244 (2001).
[CrossRef]

Bourdon, A.

Braun, D.

D. Braun and A. Libschaber, “Trapping of DNA by thermophoretic depletion and convection,” Phys. Rev. Lett. 89, 188103 (2002).
[CrossRef] [PubMed]

Carrigan, C. R.

R. T. Cygan and C. R. Carrigan, “Time-dependent Soret transport: applications to brine and magma,” Chem. Geol. 95, 201–212 (1992).
[CrossRef]

Carter, C. A.

Cross, M. C.

M. C. Cross and P. C. Honenberg, “Pattern formation outside of equilibrium,” Rev. Mod. Phys. 65, 851–1112 (1993).
[CrossRef]

Cygan, R. T.

R. T. Cygan and C. R. Carrigan, “Time-dependent Soret transport: applications to brine and magma,” Chem. Geol. 95, 201–212 (1992).
[CrossRef]

Dabby, F.

J. R. Whinnery, D. T. Miller, and F. Dabby, “Thermal convection and spherical aberration distortion of laser beams in low-loss liquids,” IEEE J. Quantum Electron. 3, 382–383 (1967).
[CrossRef]

Dovichi, N. J.

S. Wu and N. J. Dovichi, “Fresnel diffraction theory for steady-state thermal lens measurements in thin films,” J. Appl. Phys. 67, 1170–1182 (1990).
[CrossRef]

Franko, M.

M. Franko and C. D. Tran, “Analytical thermal lens instrumentation,” Rev. Sci. Instrum. 67, 1–18 (1996).
[CrossRef]

Georges, J.

N. Arnaud and J. Georges, “On the analytical use of the Soret-enhanced thermal lens signal in aqueous solutions,” Anal. Chim. Acta 445, 239–244 (2001).
[CrossRef]

Giglio, M.

A. Vailati and M. Giglio, “Nonequilibrium fluctuations in time-dependent diffusion processes,” Phys. Rev. E 58, 4361–4371 (1998).
[CrossRef]

M. Giglio and A. Vendramini, “Soret-type motion of macromolecules in solution,” Phys. Rev. Lett. 38, 26–30 (1977).
[CrossRef]

M. Giglio and A. Vendramini, “Thermal-diffusion measurements near a consolute critical point,” Phys. Rev. Lett. 34, 561–564 (1975).
[CrossRef]

M. Giglio and A. Vendramini, “Thermal lens effect in a binary liquid mixture: a new effect,” Appl. Phys. Lett. 25, 555–557 (1974).
[CrossRef]

Gordon, J. P.

J. P. Gordon, R. C. C. Leite, R. S. Moore, S. P. S. Porto, and J. R. Whinnery, “Long-transient effects in lasers with inserted liquid samples,” J. Appl. Phys. 36, 3–8 (1965).
[CrossRef]

Guarino, A.

R. Piazza and A. Guarino, “Soret effect in interacting micellar solutions,” Phys. Rev. Lett. 88, 208302 (2002).
[CrossRef] [PubMed]

Harris, J. M.

Honenberg, P. C.

M. C. Cross and P. C. Honenberg, “Pattern formation outside of equilibrium,” Rev. Mod. Phys. 65, 851–1112 (1993).
[CrossRef]

Iacopini, S.

S. Iacopini and R. Piazza, “Thermophoresis in protein solutions,” Europhys. Lett. 63, 247–253 (2003).
[CrossRef]

Khokhlov, H. V.

S. A. Akhmanov, D. P. Krindach, A. V. Migulin, A. P. Sukhorukov, and H. V. Khokhlov, “Thermal self-actions of laser beams,” IEEE J. Quantum Electron. 4, 568–575 (1968).
[CrossRef]

Knight, L. V.

Köhler, W.

J. Rauch and W. Köhler, “Diffusion and thermal diffusion in semidilute to concentrated solutions of polystyrene in toluene in the vicinity of the glass transition,” Phys. Rev. Lett. 88, 185901 (2002).
[CrossRef]

W. Köhler, “Thermodiffusion in polymer solutions as observed by forced Rayleigh scattering,” J. Chem. Phys. 98, 660–668 (1993).
[CrossRef]

Krindach, D. P.

S. A. Akhmanov, D. P. Krindach, A. V. Migulin, A. P. Sukhorukov, and H. V. Khokhlov, “Thermal self-actions of laser beams,” IEEE J. Quantum Electron. 4, 568–575 (1968).
[CrossRef]

La Porta, A.

A. La Porta and C. M. Surko, “Convective instability in a fluid mixture heated from above,” Phys. Rev. Lett. 80, 3759–3762 (1998).
[CrossRef]

Larson Jr., D. J.

L. L. Zheng, D. J. Larson, Jr., and H. Zhang, “Role of thermotransport (Soret effect) in macrosegregation during eutectic/off-eutectic directional solidification,” J. Cryst. Growth 191, 243–251 (1998).
[CrossRef]

Leite, R. C. C.

J. P. Gordon, R. C. C. Leite, R. S. Moore, S. P. S. Porto, and J. R. Whinnery, “Long-transient effects in lasers with inserted liquid samples,” J. Appl. Phys. 36, 3–8 (1965).
[CrossRef]

Libschaber, A.

D. Braun and A. Libschaber, “Trapping of DNA by thermophoretic depletion and convection,” Phys. Rev. Lett. 89, 188103 (2002).
[CrossRef] [PubMed]

Migulin, A. V.

S. A. Akhmanov, D. P. Krindach, A. V. Migulin, A. P. Sukhorukov, and H. V. Khokhlov, “Thermal self-actions of laser beams,” IEEE J. Quantum Electron. 4, 568–575 (1968).
[CrossRef]

Miller, D. T.

J. R. Whinnery, D. T. Miller, and F. Dabby, “Thermal convection and spherical aberration distortion of laser beams in low-loss liquids,” IEEE J. Quantum Electron. 3, 382–383 (1967).
[CrossRef]

Mistura, L.

L. Mistura, “Critical behavior of transport coefficients in multicomponent fluid mixtures,” J. Chem. Phys. 62, 4571–4572 (1975).
[CrossRef]

Moore, R. S.

J. P. Gordon, R. C. C. Leite, R. S. Moore, S. P. S. Porto, and J. R. Whinnery, “Long-transient effects in lasers with inserted liquid samples,” J. Appl. Phys. 36, 3–8 (1965).
[CrossRef]

Neto, A. M. F.

Piazza, R.

S. Iacopini and R. Piazza, “Thermophoresis in protein solutions,” Europhys. Lett. 63, 247–253 (2003).
[CrossRef]

R. Piazza and A. Guarino, “Soret effect in interacting micellar solutions,” Phys. Rev. Lett. 88, 208302 (2002).
[CrossRef] [PubMed]

Porto, S. P. S.

J. P. Gordon, R. C. C. Leite, R. S. Moore, S. P. S. Porto, and J. R. Whinnery, “Long-transient effects in lasers with inserted liquid samples,” J. Appl. Phys. 36, 3–8 (1965).
[CrossRef]

Rauch, J.

J. Rauch and W. Köhler, “Diffusion and thermal diffusion in semidilute to concentrated solutions of polystyrene in toluene in the vicinity of the glass transition,” Phys. Rev. Lett. 88, 185901 (2002).
[CrossRef]

Schmitt, R. W.

R. W. Schmitt, “The ocean’s salt fingers,” Sci. Am. 272, 70–75 (1995).
[CrossRef]

Sheldon, S. J.

Sukhorukov, A. P.

S. A. Akhmanov, D. P. Krindach, A. V. Migulin, A. P. Sukhorukov, and H. V. Khokhlov, “Thermal self-actions of laser beams,” IEEE J. Quantum Electron. 4, 568–575 (1968).
[CrossRef]

Surko, C. M.

A. La Porta and C. M. Surko, “Convective instability in a fluid mixture heated from above,” Phys. Rev. Lett. 80, 3759–3762 (1998).
[CrossRef]

Thorne, J. M.

Tran, C. D.

M. Franko and C. D. Tran, “Analytical thermal lens instrumentation,” Rev. Sci. Instrum. 67, 1–18 (1996).
[CrossRef]

Vailati, A.

A. Vailati and M. Giglio, “Nonequilibrium fluctuations in time-dependent diffusion processes,” Phys. Rev. E 58, 4361–4371 (1998).
[CrossRef]

Vendramini, A.

M. Giglio and A. Vendramini, “Soret-type motion of macromolecules in solution,” Phys. Rev. Lett. 38, 26–30 (1977).
[CrossRef]

M. Giglio and A. Vendramini, “Thermal-diffusion measurements near a consolute critical point,” Phys. Rev. Lett. 34, 561–564 (1975).
[CrossRef]

M. Giglio and A. Vendramini, “Thermal lens effect in a binary liquid mixture: a new effect,” Appl. Phys. Lett. 25, 555–557 (1974).
[CrossRef]

Whinnery, J. R.

J. R. Whinnery, D. T. Miller, and F. Dabby, “Thermal convection and spherical aberration distortion of laser beams in low-loss liquids,” IEEE J. Quantum Electron. 3, 382–383 (1967).
[CrossRef]

J. P. Gordon, R. C. C. Leite, R. S. Moore, S. P. S. Porto, and J. R. Whinnery, “Long-transient effects in lasers with inserted liquid samples,” J. Appl. Phys. 36, 3–8 (1965).
[CrossRef]

Wu, S.

S. Wu and N. J. Dovichi, “Fresnel diffraction theory for steady-state thermal lens measurements in thin films,” J. Appl. Phys. 67, 1170–1182 (1990).
[CrossRef]

Zhang, H.

L. L. Zheng, D. J. Larson, Jr., and H. Zhang, “Role of thermotransport (Soret effect) in macrosegregation during eutectic/off-eutectic directional solidification,” J. Cryst. Growth 191, 243–251 (1998).
[CrossRef]

Zheng, L. L.

L. L. Zheng, D. J. Larson, Jr., and H. Zhang, “Role of thermotransport (Soret effect) in macrosegregation during eutectic/off-eutectic directional solidification,” J. Cryst. Growth 191, 243–251 (1998).
[CrossRef]

Anal. Chim. Acta (1)

N. Arnaud and J. Georges, “On the analytical use of the Soret-enhanced thermal lens signal in aqueous solutions,” Anal. Chim. Acta 445, 239–244 (2001).
[CrossRef]

Appl. Opt. (2)

Appl. Phys. Lett. (1)

M. Giglio and A. Vendramini, “Thermal lens effect in a binary liquid mixture: a new effect,” Appl. Phys. Lett. 25, 555–557 (1974).
[CrossRef]

Chem. Geol. (1)

R. T. Cygan and C. R. Carrigan, “Time-dependent Soret transport: applications to brine and magma,” Chem. Geol. 95, 201–212 (1992).
[CrossRef]

Europhys. Lett. (1)

S. Iacopini and R. Piazza, “Thermophoresis in protein solutions,” Europhys. Lett. 63, 247–253 (2003).
[CrossRef]

IEEE J. Quantum Electron. (2)

J. R. Whinnery, D. T. Miller, and F. Dabby, “Thermal convection and spherical aberration distortion of laser beams in low-loss liquids,” IEEE J. Quantum Electron. 3, 382–383 (1967).
[CrossRef]

S. A. Akhmanov, D. P. Krindach, A. V. Migulin, A. P. Sukhorukov, and H. V. Khokhlov, “Thermal self-actions of laser beams,” IEEE J. Quantum Electron. 4, 568–575 (1968).
[CrossRef]

J. Appl. Phys. (2)

S. Wu and N. J. Dovichi, “Fresnel diffraction theory for steady-state thermal lens measurements in thin films,” J. Appl. Phys. 67, 1170–1182 (1990).
[CrossRef]

J. P. Gordon, R. C. C. Leite, R. S. Moore, S. P. S. Porto, and J. R. Whinnery, “Long-transient effects in lasers with inserted liquid samples,” J. Appl. Phys. 36, 3–8 (1965).
[CrossRef]

J. Chem. Phys. (2)

W. Köhler, “Thermodiffusion in polymer solutions as observed by forced Rayleigh scattering,” J. Chem. Phys. 98, 660–668 (1993).
[CrossRef]

L. Mistura, “Critical behavior of transport coefficients in multicomponent fluid mixtures,” J. Chem. Phys. 62, 4571–4572 (1975).
[CrossRef]

J. Cryst. Growth (1)

L. L. Zheng, D. J. Larson, Jr., and H. Zhang, “Role of thermotransport (Soret effect) in macrosegregation during eutectic/off-eutectic directional solidification,” J. Cryst. Growth 191, 243–251 (1998).
[CrossRef]

J. Opt. Soc. Am. B (1)

Phys. Rev. E (1)

A. Vailati and M. Giglio, “Nonequilibrium fluctuations in time-dependent diffusion processes,” Phys. Rev. E 58, 4361–4371 (1998).
[CrossRef]

Phys. Rev. Lett. (6)

D. Braun and A. Libschaber, “Trapping of DNA by thermophoretic depletion and convection,” Phys. Rev. Lett. 89, 188103 (2002).
[CrossRef] [PubMed]

R. Piazza and A. Guarino, “Soret effect in interacting micellar solutions,” Phys. Rev. Lett. 88, 208302 (2002).
[CrossRef] [PubMed]

M. Giglio and A. Vendramini, “Soret-type motion of macromolecules in solution,” Phys. Rev. Lett. 38, 26–30 (1977).
[CrossRef]

A. La Porta and C. M. Surko, “Convective instability in a fluid mixture heated from above,” Phys. Rev. Lett. 80, 3759–3762 (1998).
[CrossRef]

M. Giglio and A. Vendramini, “Thermal-diffusion measurements near a consolute critical point,” Phys. Rev. Lett. 34, 561–564 (1975).
[CrossRef]

J. Rauch and W. Köhler, “Diffusion and thermal diffusion in semidilute to concentrated solutions of polystyrene in toluene in the vicinity of the glass transition,” Phys. Rev. Lett. 88, 185901 (2002).
[CrossRef]

Rev. Mod. Phys. (1)

M. C. Cross and P. C. Honenberg, “Pattern formation outside of equilibrium,” Rev. Mod. Phys. 65, 851–1112 (1993).
[CrossRef]

Rev. Sci. Instrum. (1)

M. Franko and C. D. Tran, “Analytical thermal lens instrumentation,” Rev. Sci. Instrum. 67, 1–18 (1996).
[CrossRef]

Sci. Am. (1)

R. W. Schmitt, “The ocean’s salt fingers,” Sci. Am. 272, 70–75 (1995).
[CrossRef]

Other (5)

J. V. Tyrrell, Diffusion and Heat Flow in Liquids (Butterworth, London, 1961).

S. R. De Groot and P. Mazur, Nonequilibrium Thermodynamics (North Holland, Amsterdam, 1962).

F. H. Busse, “Fundamentals of thermal convection,” in Mantle Convection: Plate Tectonics and Global Dynamics, W. Peltier, ed. (Gordon and Breach, London, 1989), pp. 23–95.

S. E. Bialkowski, Photothermal Spectroscopy Methods for Chemical Analysis (Wiley, New York, 1996).

L. Quartapelle, Numerical Simulations of the Incompressible Navier–Stokes Equations (Birkhauser-Verlag, Berlin, 1993).

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Figures (11)

Fig. 1
Fig. 1

Fractional change of the central-beam intensity as a function of the distance z from the cell entrance window to the beam waist, calculated according to the text for different values of P and l, but constant Pl, compared with the analytical 2-D expression (10) (solid curve).

Fig. 2
Fig. 2

Numerical results for the convection velocity at the center of the cell, normalized to χ/w, as a function of the cell thickness, for w0=60µm, P=20 mW. Values obtained for l1 mm are fitted with a parabola in the inset.

Fig. 3
Fig. 3

Thermal convection patterns in a cylindrical cell of diameter d=9 mm and optical path length l=0.5 mm, in horizontal (top) and upright (bottom) optical axis configurations, with axes units in millimeters. Arrows indicate the flow direction in the convective rolls.

Fig. 4
Fig. 4

Numerical results for the temperature profile in a cylindrical cell of diameter d=9 mm and optical path length l=0.5 mm, in an upright optical axis configuration, for an incident beam power of 0.5 (●), 10 (○), and 20 (■) W, focused to a minimal spot size w0=45µm. The solid curve is the thermal profile in the absence of convective motion.

Fig. 5
Fig. 5

Main body: Numerical results for concentration profiles, normalized to Δc0STc(1-c)Pb/κ, obtained for ξ=0.01 (●), 0.1 (○), 1 (□), and 10 (■). The solid curve is the profile in the absence of convection. Inset: Velocity profiles for a solute with β=0.15 and ST=+0.02 K-1 (●) or -0.02 K-1 (□). Open symbols refer to simulations made for β=0 (○) and α0=0 (□).

Fig. 6
Fig. 6

Layout (left) and picture (right) of the thermal-lensing apparatus in an upright configuration.

Fig. 7
Fig. 7

Measured TL effects in water, as a function of the cell distance from the beam waist, for P=50 mW, l=0.02 cm, T=26 °C (○), and P=18 mW, l=0.5 cm, T=20 °C (●). The solid curves are fits using Eqs. (10) and (26), respectively. Inset: Thermal-lens number for D2O solutions, normalized to its value ϑw for water.

Fig. 8
Fig. 8

TL signal for a 25-g/l water solution of sodium dodecyl sulfate in the presence of 20-mM NaCl. The inset shows the buildup of the initial thermal effect, taking place in a very short time. Transients are fitted using the buildup functions f(t; τD; 3) and f(t; τth; 3), respectively.

Fig. 9
Fig. 9

Soret coefficient of SDS micellar solutions as a function of surfactant concentration, in the presence of 10-mM (circles) and 20-mM (squares) NaCl, using the TL (full symbols) and beam-deflection (open symbols) methods. Inset: Thermal-lens number ϑ versus incident power P for pure water (○) and for a 10-g/l SDS solution (●).

Fig. 10
Fig. 10

Inset: TL signal for a c=10% Triton X100 solution at room temperature. Main body: Soret coefficient for Triton solutions as a function of surfactant concentration. A vertical broken line is drawn in correspondence to the experimental c* value for Triton in the 60% D2O mixture we have used.

Fig. 11
Fig. 11

Inset: Negative TL signal for a c=2.5% Ludox TMA suspension. Main body: Soret coefficient for Ludox TMA suspensions as a function of added salt concentration.

Equations (26)

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Jm=-Dc-c¯(1-c¯)DTT,
ST=DTD=-1c¯(1-c¯) dcdT.
(ΔT(r, t))t=χQ˙κ+χ2(ΔT(r, t)),
Q˙=2Plπw2 exp-2r2w2,
ΔT(r, t)=Pb4πκ C(t; τth)-φ(t; τth) 2r2w2,
n(0, t)-n(r, t)=Pb2κ nTφ(t; τth) r2πw2,
1fth=-ϑth λπw2φ(t; τth),
ϑth=-Pblκλ nT.
ΔIII(0)-I()I()=-ϑth 2z˜1+z˜2,
ΔII=-1+1-ϑth arctan2z˜3+z˜2-1,
f(t; τth; z˜)=arctan2z˜3+z˜2+(9+z˜2)τth/2t.
(Δc(r, t))t=D2(Δc(r, t))+STc¯(1-c¯)2(ΔT(r, t)).
(Δc(r, t))t=D2(Δc(r, t))-STc¯(1-c¯)DQ˙κ,
Δc(r, t)=-PbSTc¯(1-c¯)4πκ C(t; τD)-φ(t; τD) 2r2w2,
1fS=-ϑS λπw2φ(t, τD),
ϑS=Pblκλ ncSTc¯(1-c¯).
ϑ=Pblκλ nTφ(t; τth)-STc¯(1-c¯) ncφ(t; τD).
ϑSϑth=-STc¯(1-c¯) n/cn/T,
ΔIS+thΔIth=1-STc¯(1-c¯) n/cn/T,
U˜gα0g2ΔT/ν,
wg24νχgα0ΔT.
wg24νDgαΔT,
α=α0+βc(1-c)ST,
·(p/ρ)=·f-·(U·)U,
·(p/ρ)=·f-·(U·)U+δ·U,
ΔII=-1+1-ϑthf(z˜)+ϑth24[f2(z˜)+g2(z˜)]-1,

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