Abstract

We optically manipulated a metal particle in borosilicate glass. The glass in the neighborhood of the laser-heated metal particle softened; hence, the metal particle was able to migrate in the glass. In this letter, the driving force of the metal particle toward the light source in the glass provided by laser illumination was investigated. The variation in the surface tension of the glass at the interface between the glass and the metal particle induced by the temperature gradient was calculated via a numerical temperature calculation. It was found that the temperature at the laser-illuminated surface of a stainless-steel particle with a radius of 40 μm was ~320 K higher than that on the nonilluminated side. The force applied to the metal particle from the surrounding glass was calculated to be ~100 μN, which was approximately equal to the viscous resistance force. In addition, the experimental and numerically calculated speeds of the moving particle, which was measured while varying the laser power, are discussed.

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Errata

Hirofumi Hidai, Makoto Matsushita, Souta Matsusaka, Akira Chiba, and Noboru Morita, "Moving force of metal particle migration induced by laser irradiation in borosilicate glass: erratum," Opt. Express 22, 25194-25195 (2014)
https://www.osapublishing.org/oe/abstract.cfm?uri=oe-22-21-25194

References

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  1. K. T. Kotz, K. A. Noble, and G. W. Faris, “Optical microfluidics,” Appl. Phys. Lett.85(13), 2658–2660 (2004).
    [CrossRef]
  2. N. O. Young, J. S. Goldstein, and M. J. Block, “The motion of bubbles in a vertical temperature gradient,” J. Fluid Mech.6(03), 350–356 (1959).
    [CrossRef]
  3. A. Ashkin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett.24(4), 156–159 (1970).
    [CrossRef]
  4. M. Sitarski and M. Kerker, “Monte Carlo simulation of photophoresis of submicron aerosol particles,” J. Atmos. Sci.41(14), 2250–2262 (1984).
    [CrossRef]
  5. F. M. Weinert and D. Braun, “Optically driven fluid flow along arbitrary microscale patterns using thermoviscous expansion,” J. Appl. Phys.104(10), 104701 (2008).
    [CrossRef]
  6. H. Hidai, T. Yamazaki, S. Itoh, K. Hiromatsu, and H. Tokura, “Metal particle manipulation by laser irradiation in borosilicate glass,” Opt. Express18(19), 20313–20320 (2010).
    [CrossRef] [PubMed]
  7. S. Maeda, “Kihou no seisei to undou” Chem. Eng. J.31, 438–443 (1967) (in Japanese).
  8. C. W. Parmelee, K. C. Lyon, and C. G. Harman, “The surface tensions of molten glass,” Univ. Illinois Eng. Exp. Station Bull.36, 5–50 (1939).
  9. . Liu, J. Shang, J. Tang, and Q.-A. Huang, “Micromachining of Pyrex 7740 glass by silicon molding and vacuum anodic bonding,” J. Microelectromech. Syst.20(4), 909–915 (2011).
    [CrossRef]
  10. H. Hidai, M. Yoshioka, K. Hiromatsu, and H. Tokura, “Glass modification by continuous-wave laser backside irradiation (CW-LBI),” Appl. Phys., A Mater. Sci. Process.96(4), 869–872 (2009).
    [CrossRef]
  11. H. Hidai, M. Yoshioka, K. Hiromatsu, and H. Tokura, “Structural changes in silica glass by continuous-wave laser backside irradiation,” J. Am. Ceram. Soc.93, 1597–1601 (2010).

2011

. Liu, J. Shang, J. Tang, and Q.-A. Huang, “Micromachining of Pyrex 7740 glass by silicon molding and vacuum anodic bonding,” J. Microelectromech. Syst.20(4), 909–915 (2011).
[CrossRef]

2010

H. Hidai, T. Yamazaki, S. Itoh, K. Hiromatsu, and H. Tokura, “Metal particle manipulation by laser irradiation in borosilicate glass,” Opt. Express18(19), 20313–20320 (2010).
[CrossRef] [PubMed]

H. Hidai, M. Yoshioka, K. Hiromatsu, and H. Tokura, “Structural changes in silica glass by continuous-wave laser backside irradiation,” J. Am. Ceram. Soc.93, 1597–1601 (2010).

2009

H. Hidai, M. Yoshioka, K. Hiromatsu, and H. Tokura, “Glass modification by continuous-wave laser backside irradiation (CW-LBI),” Appl. Phys., A Mater. Sci. Process.96(4), 869–872 (2009).
[CrossRef]

2008

F. M. Weinert and D. Braun, “Optically driven fluid flow along arbitrary microscale patterns using thermoviscous expansion,” J. Appl. Phys.104(10), 104701 (2008).
[CrossRef]

2004

K. T. Kotz, K. A. Noble, and G. W. Faris, “Optical microfluidics,” Appl. Phys. Lett.85(13), 2658–2660 (2004).
[CrossRef]

1984

M. Sitarski and M. Kerker, “Monte Carlo simulation of photophoresis of submicron aerosol particles,” J. Atmos. Sci.41(14), 2250–2262 (1984).
[CrossRef]

1970

A. Ashkin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett.24(4), 156–159 (1970).
[CrossRef]

1967

S. Maeda, “Kihou no seisei to undou” Chem. Eng. J.31, 438–443 (1967) (in Japanese).

1959

N. O. Young, J. S. Goldstein, and M. J. Block, “The motion of bubbles in a vertical temperature gradient,” J. Fluid Mech.6(03), 350–356 (1959).
[CrossRef]

1939

C. W. Parmelee, K. C. Lyon, and C. G. Harman, “The surface tensions of molten glass,” Univ. Illinois Eng. Exp. Station Bull.36, 5–50 (1939).

Ashkin, A.

A. Ashkin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett.24(4), 156–159 (1970).
[CrossRef]

Block, M. J.

N. O. Young, J. S. Goldstein, and M. J. Block, “The motion of bubbles in a vertical temperature gradient,” J. Fluid Mech.6(03), 350–356 (1959).
[CrossRef]

Braun, D.

F. M. Weinert and D. Braun, “Optically driven fluid flow along arbitrary microscale patterns using thermoviscous expansion,” J. Appl. Phys.104(10), 104701 (2008).
[CrossRef]

Faris, G. W.

K. T. Kotz, K. A. Noble, and G. W. Faris, “Optical microfluidics,” Appl. Phys. Lett.85(13), 2658–2660 (2004).
[CrossRef]

Goldstein, J. S.

N. O. Young, J. S. Goldstein, and M. J. Block, “The motion of bubbles in a vertical temperature gradient,” J. Fluid Mech.6(03), 350–356 (1959).
[CrossRef]

Harman, C. G.

C. W. Parmelee, K. C. Lyon, and C. G. Harman, “The surface tensions of molten glass,” Univ. Illinois Eng. Exp. Station Bull.36, 5–50 (1939).

Hidai, H.

H. Hidai, M. Yoshioka, K. Hiromatsu, and H. Tokura, “Structural changes in silica glass by continuous-wave laser backside irradiation,” J. Am. Ceram. Soc.93, 1597–1601 (2010).

H. Hidai, T. Yamazaki, S. Itoh, K. Hiromatsu, and H. Tokura, “Metal particle manipulation by laser irradiation in borosilicate glass,” Opt. Express18(19), 20313–20320 (2010).
[CrossRef] [PubMed]

H. Hidai, M. Yoshioka, K. Hiromatsu, and H. Tokura, “Glass modification by continuous-wave laser backside irradiation (CW-LBI),” Appl. Phys., A Mater. Sci. Process.96(4), 869–872 (2009).
[CrossRef]

Hiromatsu, K.

H. Hidai, M. Yoshioka, K. Hiromatsu, and H. Tokura, “Structural changes in silica glass by continuous-wave laser backside irradiation,” J. Am. Ceram. Soc.93, 1597–1601 (2010).

H. Hidai, T. Yamazaki, S. Itoh, K. Hiromatsu, and H. Tokura, “Metal particle manipulation by laser irradiation in borosilicate glass,” Opt. Express18(19), 20313–20320 (2010).
[CrossRef] [PubMed]

H. Hidai, M. Yoshioka, K. Hiromatsu, and H. Tokura, “Glass modification by continuous-wave laser backside irradiation (CW-LBI),” Appl. Phys., A Mater. Sci. Process.96(4), 869–872 (2009).
[CrossRef]

Huang, Q.-A.

. Liu, J. Shang, J. Tang, and Q.-A. Huang, “Micromachining of Pyrex 7740 glass by silicon molding and vacuum anodic bonding,” J. Microelectromech. Syst.20(4), 909–915 (2011).
[CrossRef]

Itoh, S.

Kerker, M.

M. Sitarski and M. Kerker, “Monte Carlo simulation of photophoresis of submicron aerosol particles,” J. Atmos. Sci.41(14), 2250–2262 (1984).
[CrossRef]

Kotz, K. T.

K. T. Kotz, K. A. Noble, and G. W. Faris, “Optical microfluidics,” Appl. Phys. Lett.85(13), 2658–2660 (2004).
[CrossRef]

Liu, .

. Liu, J. Shang, J. Tang, and Q.-A. Huang, “Micromachining of Pyrex 7740 glass by silicon molding and vacuum anodic bonding,” J. Microelectromech. Syst.20(4), 909–915 (2011).
[CrossRef]

Lyon, K. C.

C. W. Parmelee, K. C. Lyon, and C. G. Harman, “The surface tensions of molten glass,” Univ. Illinois Eng. Exp. Station Bull.36, 5–50 (1939).

Maeda, S.

S. Maeda, “Kihou no seisei to undou” Chem. Eng. J.31, 438–443 (1967) (in Japanese).

Noble, K. A.

K. T. Kotz, K. A. Noble, and G. W. Faris, “Optical microfluidics,” Appl. Phys. Lett.85(13), 2658–2660 (2004).
[CrossRef]

Parmelee, C. W.

C. W. Parmelee, K. C. Lyon, and C. G. Harman, “The surface tensions of molten glass,” Univ. Illinois Eng. Exp. Station Bull.36, 5–50 (1939).

Shang, J.

. Liu, J. Shang, J. Tang, and Q.-A. Huang, “Micromachining of Pyrex 7740 glass by silicon molding and vacuum anodic bonding,” J. Microelectromech. Syst.20(4), 909–915 (2011).
[CrossRef]

Sitarski, M.

M. Sitarski and M. Kerker, “Monte Carlo simulation of photophoresis of submicron aerosol particles,” J. Atmos. Sci.41(14), 2250–2262 (1984).
[CrossRef]

Tang, J.

. Liu, J. Shang, J. Tang, and Q.-A. Huang, “Micromachining of Pyrex 7740 glass by silicon molding and vacuum anodic bonding,” J. Microelectromech. Syst.20(4), 909–915 (2011).
[CrossRef]

Tokura, H.

H. Hidai, M. Yoshioka, K. Hiromatsu, and H. Tokura, “Structural changes in silica glass by continuous-wave laser backside irradiation,” J. Am. Ceram. Soc.93, 1597–1601 (2010).

H. Hidai, T. Yamazaki, S. Itoh, K. Hiromatsu, and H. Tokura, “Metal particle manipulation by laser irradiation in borosilicate glass,” Opt. Express18(19), 20313–20320 (2010).
[CrossRef] [PubMed]

H. Hidai, M. Yoshioka, K. Hiromatsu, and H. Tokura, “Glass modification by continuous-wave laser backside irradiation (CW-LBI),” Appl. Phys., A Mater. Sci. Process.96(4), 869–872 (2009).
[CrossRef]

Weinert, F. M.

F. M. Weinert and D. Braun, “Optically driven fluid flow along arbitrary microscale patterns using thermoviscous expansion,” J. Appl. Phys.104(10), 104701 (2008).
[CrossRef]

Yamazaki, T.

Yoshioka, M.

H. Hidai, M. Yoshioka, K. Hiromatsu, and H. Tokura, “Structural changes in silica glass by continuous-wave laser backside irradiation,” J. Am. Ceram. Soc.93, 1597–1601 (2010).

H. Hidai, M. Yoshioka, K. Hiromatsu, and H. Tokura, “Glass modification by continuous-wave laser backside irradiation (CW-LBI),” Appl. Phys., A Mater. Sci. Process.96(4), 869–872 (2009).
[CrossRef]

Young, N. O.

N. O. Young, J. S. Goldstein, and M. J. Block, “The motion of bubbles in a vertical temperature gradient,” J. Fluid Mech.6(03), 350–356 (1959).
[CrossRef]

Appl. Phys. Lett.

K. T. Kotz, K. A. Noble, and G. W. Faris, “Optical microfluidics,” Appl. Phys. Lett.85(13), 2658–2660 (2004).
[CrossRef]

Appl. Phys., A Mater. Sci. Process.

H. Hidai, M. Yoshioka, K. Hiromatsu, and H. Tokura, “Glass modification by continuous-wave laser backside irradiation (CW-LBI),” Appl. Phys., A Mater. Sci. Process.96(4), 869–872 (2009).
[CrossRef]

Chem. Eng. J.

S. Maeda, “Kihou no seisei to undou” Chem. Eng. J.31, 438–443 (1967) (in Japanese).

J. Am. Ceram. Soc.

H. Hidai, M. Yoshioka, K. Hiromatsu, and H. Tokura, “Structural changes in silica glass by continuous-wave laser backside irradiation,” J. Am. Ceram. Soc.93, 1597–1601 (2010).

J. Appl. Phys.

F. M. Weinert and D. Braun, “Optically driven fluid flow along arbitrary microscale patterns using thermoviscous expansion,” J. Appl. Phys.104(10), 104701 (2008).
[CrossRef]

J. Atmos. Sci.

M. Sitarski and M. Kerker, “Monte Carlo simulation of photophoresis of submicron aerosol particles,” J. Atmos. Sci.41(14), 2250–2262 (1984).
[CrossRef]

J. Fluid Mech.

N. O. Young, J. S. Goldstein, and M. J. Block, “The motion of bubbles in a vertical temperature gradient,” J. Fluid Mech.6(03), 350–356 (1959).
[CrossRef]

J. Microelectromech. Syst.

. Liu, J. Shang, J. Tang, and Q.-A. Huang, “Micromachining of Pyrex 7740 glass by silicon molding and vacuum anodic bonding,” J. Microelectromech. Syst.20(4), 909–915 (2011).
[CrossRef]

Opt. Express

Phys. Rev. Lett.

A. Ashkin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett.24(4), 156–159 (1970).
[CrossRef]

Univ. Illinois Eng. Exp. Station Bull.

C. W. Parmelee, K. C. Lyon, and C. G. Harman, “The surface tensions of molten glass,” Univ. Illinois Eng. Exp. Station Bull.36, 5–50 (1939).

Supplementary Material (1)

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Figures (6)

Fig. 1
Fig. 1

Schematic drawing of the simulation model.

Fig. 2
Fig. 2

Time-lapse photographs taken during particle migration (Media 1). The image in (b) was taken 5 s after the image in (a). The laser power was 21.3 W.

Fig. 3
Fig. 3

Temporal behavior of temperature at r = 40 μm, θ = 0°. The laser power was 21.3 W.

Fig. 4
Fig. 4

Temperature distributions (a) in stainless-steel particle and glass and (b) on the surface of the particle. The laser power was 21.3 W. Arrows show the flow within and around the particle. The broken line shows the interface of the particle and glass.

Fig. 5
Fig. 5

Speeds of stainless-steel particle migration under laser illumination at various powers.

Fig. 6
Fig. 6

Speed of stainless-steel particle migration under laser illumination. The laser power was 21.3 W.

Equations (16)

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v r = v 0 { 1 2 2( 3μ'+2μ 4μ'+4μ ) r 0 r +2( μ' 4μ'+4μ ) ( r 0 r ) 3 }cosθ
v θ = v 0 { 1( 3μ'+2μ 4μ'+4μ ) r 0 r ( μ' 4μ'+4μ ) ( r 0 r ) 3 }sinθ
v r '=2 v 0 { ( r 0 r ) 2 1 }( μ 4μ'+4μ )cosθ
v θ '=2 v 0 { 2 ( r 0 r ) 2 1 }( μ 4μ'+4μ )sinθ
cρ t T(t,r,θ)= k r 2 { r ( r 2 r T(t,r,θ) )+ 1 sinθ θ ( sinθ θ T(t,r,θ) ) } + Q las (t,r,θ) Q rad (t,r,θ),
Q las ( t,r,θ )={ r ( 1R )I( r,θ )cosθ( r= r 0 ,0θπ/2 ) 0( otherwise ) ,
I( r,θ )= 2P π w 2 exp{ 2 (rsinθ) 2 w 2 },
Q rad ( t,r,θ )={ r εβ( T 4 ( t,r,θ ) T 0 4 )( r= r 0 ) 0( r r 0 ) ,
T( t,r,θ ) | t=0 = T 0
T( t,r,θ ) | r= r ib = T 0 ,
p( T )=2 σ( T ) r 0 .
F sur = 0 π 2π r 0 2 sinθcosθp( T )dθ =4π r 0 0 π sinθcosθσ( T( t c , r 0 ,θ ) )dθ .
F res =6π r 0 μV
σ(T)=5.38× 10 5 T+0.333
10logμ(T)=120740 (T273) 1.441
F sur F res =m dV dt ,

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