Abstract

Temperature of water-based substances is investigated by aiming a pulsed CO2 laser beam at the water–air surface. This method of controlling temperature is believed to be flexible in medical applications as it avoids the use of thermal devices, which are often cumbersome and generate rather larger temperature swing with time. The control of temperature in this laser method is modeled by the heat conduction equation. In this investigation, it is assumed that the energy delivered by the CO2 laser is confined within a very thin surface layer of roughly 10 μm. It is shown that the temperature can be very well controlled by a CO2 laser at a steady temperature, and we demonstrate that the method can be adapted to work in tandem with another laser beam.

© 2013 Optical Society of America

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References

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  1. W. M. Irvine and J. B. Pollack, “Infrared optical properties of water and ice spheres,” Icarus 8, 324–360 (1968).
    [CrossRef]
  2. G. M. Hale and M. R. Querry, “Optical constants of water in the 200 nm to 200 μm wavelength region,” Appl. Opt. 12, 555–563 (1973).
    [CrossRef]
  3. S. Prahl, “Optical absorption of water,” (2001), http://omlc.ogi.edu/spectra/water/index.html .
  4. S. G. Warren, “Optical constants of ice from the ultraviolet to the microwave,” Appl. Opt. 23, 1206–1225 (1984).
    [CrossRef]
  5. H. G. Tompkins, A User’s Guide to Ellipsometry (Academic, 1993).
  6. A. Katzir, Laser and Optical Fibers in Medicine (Academic, 1993).
  7. B. V. Slaughter, S. S. Khurshid, O. Z. Fisher, A. Khademhosseini, and N. A. Peppas, “Hydrogels in regenerative medicine,” Adv. Mater. 21, 3307–3329 (2009).
    [CrossRef]
  8. Q. Wang, J. L. Mynar, M. Yoshida, E. Lee, M. Lee, K. Okuro, K. Kinbara, and T. Aida, “High-water-content mouldable hydrogels by mixing clay and a dendritic molecular binder,” Nature 463, 339–343 (2010).
    [CrossRef]
  9. J. C. Ion, Laser Processing of Engineering Materials, Principles, Procedures and Industrial Application (Elsevier-Butterworth-Heinemann, 2005), pp. 434–436.
  10. Y. Zhang, T. Gong, W. J. Liu, J. Q. Wei, X. F. Zhang, K. L. Wang, M. L. Zhong, and D. H. Wu, “Angle-dependent light emission from aligned multi-walled carbon nanotubes under CO2 laser irradiation,” Nanotechnology 18, 075710 (2007).
    [CrossRef]
  11. S. Fatimah, M. Ishak, and S. N. Aqida, “CO2 laser cutting of glass fiber reinforced polymer composite,” in Materials Science and Engineering, Vol. 36 of IOP Conference Series (IOP, 2012), 012033.
  12. G. B. Arfken, H. J. Weber, and F. E. Harris, Mathematical Methods for Physicists, 6th ed. (Elsevier Academic, 2005), pp. 611–618.
  13. E. Butkov, Mathematical Physics (Addison-Wesley, 1968), pp. 296–299.
  14. Y. Yener and S. Kakaç, Heat Conduction, 4th Ed. (Taylor & Francis, 2008), pp. 210–212.
  15. M. N. Özişik, Heat Conduction (Wiley, 1980), pp. 276.
  16. K. W. Guan, Y.-Q. Jiang, C.-S. Sun, and H. Yu, “A two-layer model of laser interaction with skin: a photothermal effect analysis,” Opt. Laser Technol. 43, 425–429 (2011).
    [CrossRef]
  17. J. H. Torres, M. Motamedi, J. A. Pearce, and A. J. Welch, “Experimental evaluation of mathematical models for predicting the thermal response of tissue to laser irradiation,” Appl. Opt. 32, 597–606 (1993).
    [CrossRef]
  18. B. Anvari, T. E. Milner, B. S. Tanenbaum, S. Kimmel, L. O. Svaasand, and J. S. Nelson, “Selective cooling of biological tissues: application for thermally mediated therapeutic procedures,” Phys. Med. Biol. 40, 241–252 (1995).
    [CrossRef]
  19. D. Haemmerich, D. J. Schutt, I. dos Santos, J. G. Webster, and D. M. Mahvi, “Measurement of temperature-dependent specific heat of biological tissues,” Physiol. Meas. 26, 59–67 (2005).
    [CrossRef]
  20. Q. Peng, A. Juzeniene, J. Chen, L. O. Svaasand, T. Warloe, K.-E. Giercksky, and J. Moan, “Lasers in medicine,” Rep. Prog. Phys. 71, 056701 (2008).
    [CrossRef]
  21. L. Lévesque and R. G. Sabat, “Thermal lensing investigation on bulk ceramics and thin-film PLZT using visible and far-infrared laser beams,” Opt. Mater. 33, 460–465 (2011).
    [CrossRef]

2011

K. W. Guan, Y.-Q. Jiang, C.-S. Sun, and H. Yu, “A two-layer model of laser interaction with skin: a photothermal effect analysis,” Opt. Laser Technol. 43, 425–429 (2011).
[CrossRef]

L. Lévesque and R. G. Sabat, “Thermal lensing investigation on bulk ceramics and thin-film PLZT using visible and far-infrared laser beams,” Opt. Mater. 33, 460–465 (2011).
[CrossRef]

2010

Q. Wang, J. L. Mynar, M. Yoshida, E. Lee, M. Lee, K. Okuro, K. Kinbara, and T. Aida, “High-water-content mouldable hydrogels by mixing clay and a dendritic molecular binder,” Nature 463, 339–343 (2010).
[CrossRef]

2009

B. V. Slaughter, S. S. Khurshid, O. Z. Fisher, A. Khademhosseini, and N. A. Peppas, “Hydrogels in regenerative medicine,” Adv. Mater. 21, 3307–3329 (2009).
[CrossRef]

2008

Q. Peng, A. Juzeniene, J. Chen, L. O. Svaasand, T. Warloe, K.-E. Giercksky, and J. Moan, “Lasers in medicine,” Rep. Prog. Phys. 71, 056701 (2008).
[CrossRef]

2007

Y. Zhang, T. Gong, W. J. Liu, J. Q. Wei, X. F. Zhang, K. L. Wang, M. L. Zhong, and D. H. Wu, “Angle-dependent light emission from aligned multi-walled carbon nanotubes under CO2 laser irradiation,” Nanotechnology 18, 075710 (2007).
[CrossRef]

2005

D. Haemmerich, D. J. Schutt, I. dos Santos, J. G. Webster, and D. M. Mahvi, “Measurement of temperature-dependent specific heat of biological tissues,” Physiol. Meas. 26, 59–67 (2005).
[CrossRef]

1995

B. Anvari, T. E. Milner, B. S. Tanenbaum, S. Kimmel, L. O. Svaasand, and J. S. Nelson, “Selective cooling of biological tissues: application for thermally mediated therapeutic procedures,” Phys. Med. Biol. 40, 241–252 (1995).
[CrossRef]

1993

1984

1973

1968

W. M. Irvine and J. B. Pollack, “Infrared optical properties of water and ice spheres,” Icarus 8, 324–360 (1968).
[CrossRef]

Aida, T.

Q. Wang, J. L. Mynar, M. Yoshida, E. Lee, M. Lee, K. Okuro, K. Kinbara, and T. Aida, “High-water-content mouldable hydrogels by mixing clay and a dendritic molecular binder,” Nature 463, 339–343 (2010).
[CrossRef]

Anvari, B.

B. Anvari, T. E. Milner, B. S. Tanenbaum, S. Kimmel, L. O. Svaasand, and J. S. Nelson, “Selective cooling of biological tissues: application for thermally mediated therapeutic procedures,” Phys. Med. Biol. 40, 241–252 (1995).
[CrossRef]

Aqida, S. N.

S. Fatimah, M. Ishak, and S. N. Aqida, “CO2 laser cutting of glass fiber reinforced polymer composite,” in Materials Science and Engineering, Vol. 36 of IOP Conference Series (IOP, 2012), 012033.

Arfken, G. B.

G. B. Arfken, H. J. Weber, and F. E. Harris, Mathematical Methods for Physicists, 6th ed. (Elsevier Academic, 2005), pp. 611–618.

Butkov, E.

E. Butkov, Mathematical Physics (Addison-Wesley, 1968), pp. 296–299.

Chen, J.

Q. Peng, A. Juzeniene, J. Chen, L. O. Svaasand, T. Warloe, K.-E. Giercksky, and J. Moan, “Lasers in medicine,” Rep. Prog. Phys. 71, 056701 (2008).
[CrossRef]

dos Santos, I.

D. Haemmerich, D. J. Schutt, I. dos Santos, J. G. Webster, and D. M. Mahvi, “Measurement of temperature-dependent specific heat of biological tissues,” Physiol. Meas. 26, 59–67 (2005).
[CrossRef]

Fatimah, S.

S. Fatimah, M. Ishak, and S. N. Aqida, “CO2 laser cutting of glass fiber reinforced polymer composite,” in Materials Science and Engineering, Vol. 36 of IOP Conference Series (IOP, 2012), 012033.

Fisher, O. Z.

B. V. Slaughter, S. S. Khurshid, O. Z. Fisher, A. Khademhosseini, and N. A. Peppas, “Hydrogels in regenerative medicine,” Adv. Mater. 21, 3307–3329 (2009).
[CrossRef]

Giercksky, K.-E.

Q. Peng, A. Juzeniene, J. Chen, L. O. Svaasand, T. Warloe, K.-E. Giercksky, and J. Moan, “Lasers in medicine,” Rep. Prog. Phys. 71, 056701 (2008).
[CrossRef]

Gong, T.

Y. Zhang, T. Gong, W. J. Liu, J. Q. Wei, X. F. Zhang, K. L. Wang, M. L. Zhong, and D. H. Wu, “Angle-dependent light emission from aligned multi-walled carbon nanotubes under CO2 laser irradiation,” Nanotechnology 18, 075710 (2007).
[CrossRef]

Guan, K. W.

K. W. Guan, Y.-Q. Jiang, C.-S. Sun, and H. Yu, “A two-layer model of laser interaction with skin: a photothermal effect analysis,” Opt. Laser Technol. 43, 425–429 (2011).
[CrossRef]

Haemmerich, D.

D. Haemmerich, D. J. Schutt, I. dos Santos, J. G. Webster, and D. M. Mahvi, “Measurement of temperature-dependent specific heat of biological tissues,” Physiol. Meas. 26, 59–67 (2005).
[CrossRef]

Hale, G. M.

Harris, F. E.

G. B. Arfken, H. J. Weber, and F. E. Harris, Mathematical Methods for Physicists, 6th ed. (Elsevier Academic, 2005), pp. 611–618.

Ion, J. C.

J. C. Ion, Laser Processing of Engineering Materials, Principles, Procedures and Industrial Application (Elsevier-Butterworth-Heinemann, 2005), pp. 434–436.

Irvine, W. M.

W. M. Irvine and J. B. Pollack, “Infrared optical properties of water and ice spheres,” Icarus 8, 324–360 (1968).
[CrossRef]

Ishak, M.

S. Fatimah, M. Ishak, and S. N. Aqida, “CO2 laser cutting of glass fiber reinforced polymer composite,” in Materials Science and Engineering, Vol. 36 of IOP Conference Series (IOP, 2012), 012033.

Jiang, Y.-Q.

K. W. Guan, Y.-Q. Jiang, C.-S. Sun, and H. Yu, “A two-layer model of laser interaction with skin: a photothermal effect analysis,” Opt. Laser Technol. 43, 425–429 (2011).
[CrossRef]

Juzeniene, A.

Q. Peng, A. Juzeniene, J. Chen, L. O. Svaasand, T. Warloe, K.-E. Giercksky, and J. Moan, “Lasers in medicine,” Rep. Prog. Phys. 71, 056701 (2008).
[CrossRef]

Kakaç, S.

Y. Yener and S. Kakaç, Heat Conduction, 4th Ed. (Taylor & Francis, 2008), pp. 210–212.

Katzir, A.

A. Katzir, Laser and Optical Fibers in Medicine (Academic, 1993).

Khademhosseini, A.

B. V. Slaughter, S. S. Khurshid, O. Z. Fisher, A. Khademhosseini, and N. A. Peppas, “Hydrogels in regenerative medicine,” Adv. Mater. 21, 3307–3329 (2009).
[CrossRef]

Khurshid, S. S.

B. V. Slaughter, S. S. Khurshid, O. Z. Fisher, A. Khademhosseini, and N. A. Peppas, “Hydrogels in regenerative medicine,” Adv. Mater. 21, 3307–3329 (2009).
[CrossRef]

Kimmel, S.

B. Anvari, T. E. Milner, B. S. Tanenbaum, S. Kimmel, L. O. Svaasand, and J. S. Nelson, “Selective cooling of biological tissues: application for thermally mediated therapeutic procedures,” Phys. Med. Biol. 40, 241–252 (1995).
[CrossRef]

Kinbara, K.

Q. Wang, J. L. Mynar, M. Yoshida, E. Lee, M. Lee, K. Okuro, K. Kinbara, and T. Aida, “High-water-content mouldable hydrogels by mixing clay and a dendritic molecular binder,” Nature 463, 339–343 (2010).
[CrossRef]

Lee, E.

Q. Wang, J. L. Mynar, M. Yoshida, E. Lee, M. Lee, K. Okuro, K. Kinbara, and T. Aida, “High-water-content mouldable hydrogels by mixing clay and a dendritic molecular binder,” Nature 463, 339–343 (2010).
[CrossRef]

Lee, M.

Q. Wang, J. L. Mynar, M. Yoshida, E. Lee, M. Lee, K. Okuro, K. Kinbara, and T. Aida, “High-water-content mouldable hydrogels by mixing clay and a dendritic molecular binder,” Nature 463, 339–343 (2010).
[CrossRef]

Lévesque, L.

L. Lévesque and R. G. Sabat, “Thermal lensing investigation on bulk ceramics and thin-film PLZT using visible and far-infrared laser beams,” Opt. Mater. 33, 460–465 (2011).
[CrossRef]

Liu, W. J.

Y. Zhang, T. Gong, W. J. Liu, J. Q. Wei, X. F. Zhang, K. L. Wang, M. L. Zhong, and D. H. Wu, “Angle-dependent light emission from aligned multi-walled carbon nanotubes under CO2 laser irradiation,” Nanotechnology 18, 075710 (2007).
[CrossRef]

Mahvi, D. M.

D. Haemmerich, D. J. Schutt, I. dos Santos, J. G. Webster, and D. M. Mahvi, “Measurement of temperature-dependent specific heat of biological tissues,” Physiol. Meas. 26, 59–67 (2005).
[CrossRef]

Milner, T. E.

B. Anvari, T. E. Milner, B. S. Tanenbaum, S. Kimmel, L. O. Svaasand, and J. S. Nelson, “Selective cooling of biological tissues: application for thermally mediated therapeutic procedures,” Phys. Med. Biol. 40, 241–252 (1995).
[CrossRef]

Moan, J.

Q. Peng, A. Juzeniene, J. Chen, L. O. Svaasand, T. Warloe, K.-E. Giercksky, and J. Moan, “Lasers in medicine,” Rep. Prog. Phys. 71, 056701 (2008).
[CrossRef]

Motamedi, M.

Mynar, J. L.

Q. Wang, J. L. Mynar, M. Yoshida, E. Lee, M. Lee, K. Okuro, K. Kinbara, and T. Aida, “High-water-content mouldable hydrogels by mixing clay and a dendritic molecular binder,” Nature 463, 339–343 (2010).
[CrossRef]

Nelson, J. S.

B. Anvari, T. E. Milner, B. S. Tanenbaum, S. Kimmel, L. O. Svaasand, and J. S. Nelson, “Selective cooling of biological tissues: application for thermally mediated therapeutic procedures,” Phys. Med. Biol. 40, 241–252 (1995).
[CrossRef]

Okuro, K.

Q. Wang, J. L. Mynar, M. Yoshida, E. Lee, M. Lee, K. Okuro, K. Kinbara, and T. Aida, “High-water-content mouldable hydrogels by mixing clay and a dendritic molecular binder,” Nature 463, 339–343 (2010).
[CrossRef]

Özisik, M. N.

M. N. Özişik, Heat Conduction (Wiley, 1980), pp. 276.

Pearce, J. A.

Peng, Q.

Q. Peng, A. Juzeniene, J. Chen, L. O. Svaasand, T. Warloe, K.-E. Giercksky, and J. Moan, “Lasers in medicine,” Rep. Prog. Phys. 71, 056701 (2008).
[CrossRef]

Peppas, N. A.

B. V. Slaughter, S. S. Khurshid, O. Z. Fisher, A. Khademhosseini, and N. A. Peppas, “Hydrogels in regenerative medicine,” Adv. Mater. 21, 3307–3329 (2009).
[CrossRef]

Pollack, J. B.

W. M. Irvine and J. B. Pollack, “Infrared optical properties of water and ice spheres,” Icarus 8, 324–360 (1968).
[CrossRef]

Querry, M. R.

Sabat, R. G.

L. Lévesque and R. G. Sabat, “Thermal lensing investigation on bulk ceramics and thin-film PLZT using visible and far-infrared laser beams,” Opt. Mater. 33, 460–465 (2011).
[CrossRef]

Schutt, D. J.

D. Haemmerich, D. J. Schutt, I. dos Santos, J. G. Webster, and D. M. Mahvi, “Measurement of temperature-dependent specific heat of biological tissues,” Physiol. Meas. 26, 59–67 (2005).
[CrossRef]

Slaughter, B. V.

B. V. Slaughter, S. S. Khurshid, O. Z. Fisher, A. Khademhosseini, and N. A. Peppas, “Hydrogels in regenerative medicine,” Adv. Mater. 21, 3307–3329 (2009).
[CrossRef]

Sun, C.-S.

K. W. Guan, Y.-Q. Jiang, C.-S. Sun, and H. Yu, “A two-layer model of laser interaction with skin: a photothermal effect analysis,” Opt. Laser Technol. 43, 425–429 (2011).
[CrossRef]

Svaasand, L. O.

Q. Peng, A. Juzeniene, J. Chen, L. O. Svaasand, T. Warloe, K.-E. Giercksky, and J. Moan, “Lasers in medicine,” Rep. Prog. Phys. 71, 056701 (2008).
[CrossRef]

B. Anvari, T. E. Milner, B. S. Tanenbaum, S. Kimmel, L. O. Svaasand, and J. S. Nelson, “Selective cooling of biological tissues: application for thermally mediated therapeutic procedures,” Phys. Med. Biol. 40, 241–252 (1995).
[CrossRef]

Tanenbaum, B. S.

B. Anvari, T. E. Milner, B. S. Tanenbaum, S. Kimmel, L. O. Svaasand, and J. S. Nelson, “Selective cooling of biological tissues: application for thermally mediated therapeutic procedures,” Phys. Med. Biol. 40, 241–252 (1995).
[CrossRef]

Tompkins, H. G.

H. G. Tompkins, A User’s Guide to Ellipsometry (Academic, 1993).

Torres, J. H.

Wang, K. L.

Y. Zhang, T. Gong, W. J. Liu, J. Q. Wei, X. F. Zhang, K. L. Wang, M. L. Zhong, and D. H. Wu, “Angle-dependent light emission from aligned multi-walled carbon nanotubes under CO2 laser irradiation,” Nanotechnology 18, 075710 (2007).
[CrossRef]

Wang, Q.

Q. Wang, J. L. Mynar, M. Yoshida, E. Lee, M. Lee, K. Okuro, K. Kinbara, and T. Aida, “High-water-content mouldable hydrogels by mixing clay and a dendritic molecular binder,” Nature 463, 339–343 (2010).
[CrossRef]

Warloe, T.

Q. Peng, A. Juzeniene, J. Chen, L. O. Svaasand, T. Warloe, K.-E. Giercksky, and J. Moan, “Lasers in medicine,” Rep. Prog. Phys. 71, 056701 (2008).
[CrossRef]

Warren, S. G.

Weber, H. J.

G. B. Arfken, H. J. Weber, and F. E. Harris, Mathematical Methods for Physicists, 6th ed. (Elsevier Academic, 2005), pp. 611–618.

Webster, J. G.

D. Haemmerich, D. J. Schutt, I. dos Santos, J. G. Webster, and D. M. Mahvi, “Measurement of temperature-dependent specific heat of biological tissues,” Physiol. Meas. 26, 59–67 (2005).
[CrossRef]

Wei, J. Q.

Y. Zhang, T. Gong, W. J. Liu, J. Q. Wei, X. F. Zhang, K. L. Wang, M. L. Zhong, and D. H. Wu, “Angle-dependent light emission from aligned multi-walled carbon nanotubes under CO2 laser irradiation,” Nanotechnology 18, 075710 (2007).
[CrossRef]

Welch, A. J.

Wu, D. H.

Y. Zhang, T. Gong, W. J. Liu, J. Q. Wei, X. F. Zhang, K. L. Wang, M. L. Zhong, and D. H. Wu, “Angle-dependent light emission from aligned multi-walled carbon nanotubes under CO2 laser irradiation,” Nanotechnology 18, 075710 (2007).
[CrossRef]

Yener, Y.

Y. Yener and S. Kakaç, Heat Conduction, 4th Ed. (Taylor & Francis, 2008), pp. 210–212.

Yoshida, M.

Q. Wang, J. L. Mynar, M. Yoshida, E. Lee, M. Lee, K. Okuro, K. Kinbara, and T. Aida, “High-water-content mouldable hydrogels by mixing clay and a dendritic molecular binder,” Nature 463, 339–343 (2010).
[CrossRef]

Yu, H.

K. W. Guan, Y.-Q. Jiang, C.-S. Sun, and H. Yu, “A two-layer model of laser interaction with skin: a photothermal effect analysis,” Opt. Laser Technol. 43, 425–429 (2011).
[CrossRef]

Zhang, X. F.

Y. Zhang, T. Gong, W. J. Liu, J. Q. Wei, X. F. Zhang, K. L. Wang, M. L. Zhong, and D. H. Wu, “Angle-dependent light emission from aligned multi-walled carbon nanotubes under CO2 laser irradiation,” Nanotechnology 18, 075710 (2007).
[CrossRef]

Zhang, Y.

Y. Zhang, T. Gong, W. J. Liu, J. Q. Wei, X. F. Zhang, K. L. Wang, M. L. Zhong, and D. H. Wu, “Angle-dependent light emission from aligned multi-walled carbon nanotubes under CO2 laser irradiation,” Nanotechnology 18, 075710 (2007).
[CrossRef]

Zhong, M. L.

Y. Zhang, T. Gong, W. J. Liu, J. Q. Wei, X. F. Zhang, K. L. Wang, M. L. Zhong, and D. H. Wu, “Angle-dependent light emission from aligned multi-walled carbon nanotubes under CO2 laser irradiation,” Nanotechnology 18, 075710 (2007).
[CrossRef]

Adv. Mater.

B. V. Slaughter, S. S. Khurshid, O. Z. Fisher, A. Khademhosseini, and N. A. Peppas, “Hydrogels in regenerative medicine,” Adv. Mater. 21, 3307–3329 (2009).
[CrossRef]

Appl. Opt.

Icarus

W. M. Irvine and J. B. Pollack, “Infrared optical properties of water and ice spheres,” Icarus 8, 324–360 (1968).
[CrossRef]

Nanotechnology

Y. Zhang, T. Gong, W. J. Liu, J. Q. Wei, X. F. Zhang, K. L. Wang, M. L. Zhong, and D. H. Wu, “Angle-dependent light emission from aligned multi-walled carbon nanotubes under CO2 laser irradiation,” Nanotechnology 18, 075710 (2007).
[CrossRef]

Nature

Q. Wang, J. L. Mynar, M. Yoshida, E. Lee, M. Lee, K. Okuro, K. Kinbara, and T. Aida, “High-water-content mouldable hydrogels by mixing clay and a dendritic molecular binder,” Nature 463, 339–343 (2010).
[CrossRef]

Opt. Laser Technol.

K. W. Guan, Y.-Q. Jiang, C.-S. Sun, and H. Yu, “A two-layer model of laser interaction with skin: a photothermal effect analysis,” Opt. Laser Technol. 43, 425–429 (2011).
[CrossRef]

Opt. Mater.

L. Lévesque and R. G. Sabat, “Thermal lensing investigation on bulk ceramics and thin-film PLZT using visible and far-infrared laser beams,” Opt. Mater. 33, 460–465 (2011).
[CrossRef]

Phys. Med. Biol.

B. Anvari, T. E. Milner, B. S. Tanenbaum, S. Kimmel, L. O. Svaasand, and J. S. Nelson, “Selective cooling of biological tissues: application for thermally mediated therapeutic procedures,” Phys. Med. Biol. 40, 241–252 (1995).
[CrossRef]

Physiol. Meas.

D. Haemmerich, D. J. Schutt, I. dos Santos, J. G. Webster, and D. M. Mahvi, “Measurement of temperature-dependent specific heat of biological tissues,” Physiol. Meas. 26, 59–67 (2005).
[CrossRef]

Rep. Prog. Phys.

Q. Peng, A. Juzeniene, J. Chen, L. O. Svaasand, T. Warloe, K.-E. Giercksky, and J. Moan, “Lasers in medicine,” Rep. Prog. Phys. 71, 056701 (2008).
[CrossRef]

Other

S. Prahl, “Optical absorption of water,” (2001), http://omlc.ogi.edu/spectra/water/index.html .

J. C. Ion, Laser Processing of Engineering Materials, Principles, Procedures and Industrial Application (Elsevier-Butterworth-Heinemann, 2005), pp. 434–436.

H. G. Tompkins, A User’s Guide to Ellipsometry (Academic, 1993).

A. Katzir, Laser and Optical Fibers in Medicine (Academic, 1993).

S. Fatimah, M. Ishak, and S. N. Aqida, “CO2 laser cutting of glass fiber reinforced polymer composite,” in Materials Science and Engineering, Vol. 36 of IOP Conference Series (IOP, 2012), 012033.

G. B. Arfken, H. J. Weber, and F. E. Harris, Mathematical Methods for Physicists, 6th ed. (Elsevier Academic, 2005), pp. 611–618.

E. Butkov, Mathematical Physics (Addison-Wesley, 1968), pp. 296–299.

Y. Yener and S. Kakaç, Heat Conduction, 4th Ed. (Taylor & Francis, 2008), pp. 210–212.

M. N. Özişik, Heat Conduction (Wiley, 1980), pp. 276.

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Figures (7)

Fig. 1.
Fig. 1.

Absorption coefficient of water from the ultraviolet to far-infrared region.

Fig. 2.
Fig. 2.

Temperature of water at z=0.015mm under the surface as a function of time within (a) 1 ms, (b) 10 ms, (c) 100 ms, and (d) 1 s. In this calculation we assumed that K=0.15mm2/s, To=22°C, qo0.0383W/mm2 and k=0.6×103W/mm°C.

Fig. 3.
Fig. 3.

Power profile from the CO2 laser that can be modeled by a rectangular profile of the averaged power within a repetition cycle. Complete period is a sum of two portions, one of which has a rising time T1, while the other has a falling time T2.

Fig. 4.
Fig. 4.

Fluctuation in temperature rise as the laser’s average output power cycles between two values P1 and P2 during: (a) 0.002 s, (b) 0.2 s, (c) 2 s, and (d) 10 s. In this calculation we used z=0.015mm, K=0.15mm2/s, k=6.0×104W/m°C, P1=20W, P2=1.25W, T1=40μs, and T2=160μs.

Fig. 5.
Fig. 5.

Three steps used in the heating procedure at z=0.015mm. Step A: During heating between 0 and 14 s. Data used in Eqs. (10) and (11) were K=0.15mm2/s, k=6.0×104W/m°C, P1=20W, P2=1.25W, T1=40μs, and T2=160μs. Step B: Data used in Eq. (9) were To=22°C, K=0.15mm2/s. TH was the peak value at the end of step A just before the CO2 laser was turned off momentarily for 1 ms. Step C: Temperature is relatively constant. Data used in Eqs. (10) and (11) were K=0.15mm2/s, k=6.0×104W/m°C, P1=6.3W, P2=6.3W, T1=4.5μs and T2=45.5μs.

Fig. 6.
Fig. 6.

Experimental setup used to heat the water sample.

Fig. 7.
Fig. 7.

Temperature as a function of time for a complete heating cycle. Dashed line indicates when the laser is turned off. (a) P5=20% within t=015s, then P20=9% within 1575s; (b) P5=20% within t=015s, then P20=8% within 15135s; (c) P5=30% within t=015s, then P20=11.5% within 15135s; (d) P5=25% within t=015s, then P10=8% within 15195s; (e) P5=25% within t=015s, then P20=9% within 15195s; and (f) P5=25% within t=015s, then P20=13% within 15195s.

Equations (11)

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α=4πλk,
L=1α.
T(z,t)t=K2T(z,t)z2+(z,t)ρc,
2Tz2=1KTt,
kTz=q0,z=0,t>0,
T=To,z,t>0,
T=Toz>0,t=0.
T(z,t)=To+2qokKtπexp(z24Kt)qozkerfc(z4Kt),
T(z,t)=TH(THTo)erfc(z4Kt).
T(z,t)=To+2qo1kKtπexp(z24Kt)qo1zkerfc(z4Kt),0<t<T1.
T(z,t)=To+2qo2kKtπexp(z24Kt)qo2zkerfc(z4Kt),T1<t<T2.

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