Abstract

We propose a theoretical framework to predict the three-dimensional shapes of optically deformed micron-sized emulsion droplets with ultra-low interfacial tension. The resulting shape and size of the droplet arises out of a balance between the interfacial tension and optical forces. Using an approximation of the laser field as a Gaussian beam, working within the Rayleigh-Gans regime and assuming isotropic surface energy at the oil-water interface, we numerically solve the resulting shape equations to elucidate the three-dimensional droplet geometry. We obtain a plethora of shapes as a function of the number of optical tweezers, their laser powers and positions, surface tension, initial droplet size and geometry. Experimentally, two-dimensional droplet silhouettes have been imaged from above, but their full side-on view has not been observed and reported for current optical configurations. This experimental limitation points to ambiguity in differentiating between droplets having the same two-dimensional projection but with disparate three-dimensional shapes. Our model elucidates and quantifies this difference for the first time. We also provide a dimensionless number that indicates the shape transformation (ellipsoidal to dumbbell) at a value ≈ 1.0, obtained by balancing interfacial tension and laser forces, substantiated using a data collapse.

© 2014 Optical Society of America

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2013 (1)

2011 (2)

D. A. Woods, C. D. Mellor, J. M. Taylor, C. D. Bain, A. D. Ward, “Nanofluidic networks created and controlled by light,” Soft Matter 7, 2517–2520 (2011).
[CrossRef]

G. Hirasaki, C. Miller, M. Puerto, “Recent advances in surfactant EOR,” SPE J. 16, 889–907 (2011)
[CrossRef]

2009 (3)

P. C. F. Møller, L. B. Oddershede, “Quantification of droplet deformation by electromagnetic trapping,” Europhys. Lett. 88, 48005 (2009).
[CrossRef]

M. I. Mishchenko, “Electromagnetic scattering by nonspherical particles: a tutorial review,” J. Quantum Spectrosc. Radiat. Transfer 110, 808–832 (2009).
[CrossRef]

F. Xu, J. Lock, G. Gouesbet, C. Tropea, “Optical stress on the surface of a particle: homogeneous sphere,” Phys. Rev. A 79, 053808 (2009).
[CrossRef]

2008 (2)

G. M. Gibson, J. Leach, S. Keen, A. J. Wright, M. J. Padgett, “Measuring the accuracy of particle position and force in optical tweezers using high-speed video microscopy,” Opt. Express 16, 14561–14570 (2008).
[CrossRef] [PubMed]

H. Chrabi, D. Lasseux, E. Arquis, R. Wunenburger, J.-P. Delville, “Stretching and squeezing of sessile dielectric drops by the optical radiation pressure,” Phys. Rev. E 77, 066706 (2008).
[CrossRef]

2006 (3)

D. McGloin, “Optical tweezers: 20 years on,” Philos. Trans. R. Soc. A 364, 3521–3537 (2006).
[CrossRef]

R. Karlsson, A. Karlsson, A. Ewing, P. Dommersnes, J.-F. Joanny, A. Jesorka, O. Orwar, “Chemical analysis in nanoscale surfactant networks,” Anal. Chem. 78, 5961–5968 (2006).
[CrossRef] [PubMed]

A. D. Ward, M. G. Berry, C. D. Mellor, C. D. Bain, “Optical sculpture: controlled deformation of emulsion droplets with ultralow interfacial tensions using optical tweezers,” Chem. Commun. 2006, 4515–4517 (2006).
[CrossRef]

2005 (1)

P. M. Hansen, V. K. Bhatia, N. Harrit, L. Oddershede, “Expanding the optical trapping range of Gold nanoparticles,” Nano Lett. 5, 1937–1942 (2005).
[CrossRef] [PubMed]

2004 (2)

2001 (2)

J. Guck, R. Ananthakrishnan, H. Mahmood, T. J. Moon, C. C. Cunningham, J. Käs, “The optical stretcher: a novel laser tool to micromanipulate cells,” Biophys. J. 81, 767–784 (2001).
[CrossRef] [PubMed]

A. Casner, J.-P. Delville, “Giant deformations of a liquid-liquid interface induced by the optical radiation pressure,” Phys. Rev. Lett. 87, 054503 (2001).
[CrossRef] [PubMed]

2000 (2)

R. J. Davenport, G. J. Wuite, R. Landick, C. Bustamante, “Single-molecule study of transcriptional pausing and arrest by E. coli RNA polymerase,” Science 287, 2497–2500 (2000).
[CrossRef] [PubMed]

J. Guck, R. Ananthakrishnan, T. J. Moon, C. C. Cunningham, J. Käs, “Optical deformability of soft biological dielectrics,” Phys. Lett. 84, 5451–5454 (2000).
[CrossRef]

1999 (2)

I. Brevik, R. Kluge, “Oscillations of a water droplet illuminated by a linearly polarized laser pulse,” J. Opt. Soc. Am. B 16, 976–985 (1999).
[CrossRef]

H. A. Stone, J. R. Lister, M. P. Brenner, “Drops with conical ends in electric and magnetic fields,” Proc. R. Soc. London A 455, 329–347 (1999).
[CrossRef]

1995 (1)

P. J. H. Bronkhorst, G. J. Streekstra, J. Grinbergen, E. J. Nijhof, J. J. Sixma, G. J. Brakenhoff, “A new method to study shape recovery of red blood cells using multiple optical trapping,” Biophys. J. 69, 1666–1673 (1995).
[CrossRef] [PubMed]

1993 (1)

M. Goffredi, V. T. Liveri, G. J. Vassallo, “Refractive index of water-AOT-n-heptane microemulsions,” J. Solut. Chem. 22, 941–949 (1993).
[CrossRef]

1990 (1)

S. Block, L. Goldstein, B. Schnapp, “Bead movement by single kinesin molecules studied with optical tweezers,” Nature 348, 348–352 (1990).
[CrossRef] [PubMed]

1989 (3)

E. Evans, A. Yeung, “Apparent viscosity and cortical tension of blood granulocytes determined by micropipet aspiration,” Biophys. J. 56, 151–160 (1989).
[CrossRef] [PubMed]

H. M. Lai, P. T. Leung, K. L. Poon, K. Young, “Electrostrictive distortion of a micrometer-sized droplet by a laser pulse,” J. Opt. Soc. Am. B 6, 2430–2437 (1989).
[CrossRef]

J. P. Barton, D. R. Alexander, “Fifthorder corrected electromagnetic field components for a fundamental Gaussian beam,” Appl. Phys. 66, 2800–2802 (1989).
[CrossRef]

1988 (1)

1986 (1)

1985 (1)

D. Blackmore, L. Ting, “Surface integral of its mean curvature vector,” SIAM Rev. 27, 569–572 (1985)
[CrossRef]

1973 (1)

A. Ashkin, J. M. Dziedzic, “Radiation pressure on a free liquid surface,” Phys. Rev. Lett. 30, 139–142 (1973).
[CrossRef]

1964 (1)

G. Taylor, “Disintegration of water drops in an electric field,” Proc. R. Soc. London A 280, 383–397 (1964).
[CrossRef]

Alexander, D. R.

J. P. Barton, D. R. Alexander, “Fifthorder corrected electromagnetic field components for a fundamental Gaussian beam,” Appl. Phys. 66, 2800–2802 (1989).
[CrossRef]

Ananthakrishnan, R.

J. Guck, R. Ananthakrishnan, H. Mahmood, T. J. Moon, C. C. Cunningham, J. Käs, “The optical stretcher: a novel laser tool to micromanipulate cells,” Biophys. J. 81, 767–784 (2001).
[CrossRef] [PubMed]

J. Guck, R. Ananthakrishnan, T. J. Moon, C. C. Cunningham, J. Käs, “Optical deformability of soft biological dielectrics,” Phys. Lett. 84, 5451–5454 (2000).
[CrossRef]

Arquis, E.

H. Chrabi, D. Lasseux, E. Arquis, R. Wunenburger, J.-P. Delville, “Stretching and squeezing of sessile dielectric drops by the optical radiation pressure,” Phys. Rev. E 77, 066706 (2008).
[CrossRef]

Ashkin, A.

Bain, C. D.

D. A. Woods, C. D. Mellor, J. M. Taylor, C. D. Bain, A. D. Ward, “Nanofluidic networks created and controlled by light,” Soft Matter 7, 2517–2520 (2011).
[CrossRef]

A. D. Ward, M. G. Berry, C. D. Mellor, C. D. Bain, “Optical sculpture: controlled deformation of emulsion droplets with ultralow interfacial tensions using optical tweezers,” Chem. Commun. 2006, 4515–4517 (2006).
[CrossRef]

Barton, J. P.

J. P. Barton, D. R. Alexander, “Fifthorder corrected electromagnetic field components for a fundamental Gaussian beam,” Appl. Phys. 66, 2800–2802 (1989).
[CrossRef]

Berry, M. G.

A. D. Ward, M. G. Berry, C. D. Mellor, C. D. Bain, “Optical sculpture: controlled deformation of emulsion droplets with ultralow interfacial tensions using optical tweezers,” Chem. Commun. 2006, 4515–4517 (2006).
[CrossRef]

Bhatia, V. K.

P. M. Hansen, V. K. Bhatia, N. Harrit, L. Oddershede, “Expanding the optical trapping range of Gold nanoparticles,” Nano Lett. 5, 1937–1942 (2005).
[CrossRef] [PubMed]

Bjorkholm, J. E.

Blackmore, D.

D. Blackmore, L. Ting, “Surface integral of its mean curvature vector,” SIAM Rev. 27, 569–572 (1985)
[CrossRef]

Block, S.

S. Block, L. Goldstein, B. Schnapp, “Bead movement by single kinesin molecules studied with optical tweezers,” Nature 348, 348–352 (1990).
[CrossRef] [PubMed]

Block, S. M.

K. C. Neuman, S. M. Block, “Optical trapping,” Rev. Sci. Instrum. 75, 2787–2809 (2004).
[CrossRef]

Brakenhoff, G. J.

P. J. H. Bronkhorst, G. J. Streekstra, J. Grinbergen, E. J. Nijhof, J. J. Sixma, G. J. Brakenhoff, “A new method to study shape recovery of red blood cells using multiple optical trapping,” Biophys. J. 69, 1666–1673 (1995).
[CrossRef] [PubMed]

Brenner, M. P.

H. A. Stone, J. R. Lister, M. P. Brenner, “Drops with conical ends in electric and magnetic fields,” Proc. R. Soc. London A 455, 329–347 (1999).
[CrossRef]

Brevik, I.

Bronkhorst, P. J. H.

P. J. H. Bronkhorst, G. J. Streekstra, J. Grinbergen, E. J. Nijhof, J. J. Sixma, G. J. Brakenhoff, “A new method to study shape recovery of red blood cells using multiple optical trapping,” Biophys. J. 69, 1666–1673 (1995).
[CrossRef] [PubMed]

Bustamante, C.

R. J. Davenport, G. J. Wuite, R. Landick, C. Bustamante, “Single-molecule study of transcriptional pausing and arrest by E. coli RNA polymerase,” Science 287, 2497–2500 (2000).
[CrossRef] [PubMed]

Casner, A.

A. Casner, J.-P. Delville, “Giant deformations of a liquid-liquid interface induced by the optical radiation pressure,” Phys. Rev. Lett. 87, 054503 (2001).
[CrossRef] [PubMed]

Chang, R. K.

Chrabi, H.

H. Chrabi, D. Lasseux, E. Arquis, R. Wunenburger, J.-P. Delville, “Stretching and squeezing of sessile dielectric drops by the optical radiation pressure,” Phys. Rev. E 77, 066706 (2008).
[CrossRef]

Chu, S.

Cunningham, C. C.

J. Guck, R. Ananthakrishnan, H. Mahmood, T. J. Moon, C. C. Cunningham, J. Käs, “The optical stretcher: a novel laser tool to micromanipulate cells,” Biophys. J. 81, 767–784 (2001).
[CrossRef] [PubMed]

J. Guck, R. Ananthakrishnan, T. J. Moon, C. C. Cunningham, J. Käs, “Optical deformability of soft biological dielectrics,” Phys. Lett. 84, 5451–5454 (2000).
[CrossRef]

Davenport, R. J.

R. J. Davenport, G. J. Wuite, R. Landick, C. Bustamante, “Single-molecule study of transcriptional pausing and arrest by E. coli RNA polymerase,” Science 287, 2497–2500 (2000).
[CrossRef] [PubMed]

Delville, J.-P.

H. Chrabi, D. Lasseux, E. Arquis, R. Wunenburger, J.-P. Delville, “Stretching and squeezing of sessile dielectric drops by the optical radiation pressure,” Phys. Rev. E 77, 066706 (2008).
[CrossRef]

A. Casner, J.-P. Delville, “Giant deformations of a liquid-liquid interface induced by the optical radiation pressure,” Phys. Rev. Lett. 87, 054503 (2001).
[CrossRef] [PubMed]

Dharmadhikari, A.

Dharmadhikari, J.

Dommersnes, P.

R. Karlsson, A. Karlsson, A. Ewing, P. Dommersnes, J.-F. Joanny, A. Jesorka, O. Orwar, “Chemical analysis in nanoscale surfactant networks,” Anal. Chem. 78, 5961–5968 (2006).
[CrossRef] [PubMed]

Dziedzic, J. M.

Ellingsen, S. Å.

Evans, E.

E. Evans, A. Yeung, “Apparent viscosity and cortical tension of blood granulocytes determined by micropipet aspiration,” Biophys. J. 56, 151–160 (1989).
[CrossRef] [PubMed]

Ewing, A.

R. Karlsson, A. Karlsson, A. Ewing, P. Dommersnes, J.-F. Joanny, A. Jesorka, O. Orwar, “Chemical analysis in nanoscale surfactant networks,” Anal. Chem. 78, 5961–5968 (2006).
[CrossRef] [PubMed]

Gibson, G. M.

Goffredi, M.

M. Goffredi, V. T. Liveri, G. J. Vassallo, “Refractive index of water-AOT-n-heptane microemulsions,” J. Solut. Chem. 22, 941–949 (1993).
[CrossRef]

Goldstein, L.

S. Block, L. Goldstein, B. Schnapp, “Bead movement by single kinesin molecules studied with optical tweezers,” Nature 348, 348–352 (1990).
[CrossRef] [PubMed]

Gouesbet, G.

F. Xu, J. Lock, G. Gouesbet, C. Tropea, “Optical stress on the surface of a particle: homogeneous sphere,” Phys. Rev. A 79, 053808 (2009).
[CrossRef]

Grinbergen, J.

P. J. H. Bronkhorst, G. J. Streekstra, J. Grinbergen, E. J. Nijhof, J. J. Sixma, G. J. Brakenhoff, “A new method to study shape recovery of red blood cells using multiple optical trapping,” Biophys. J. 69, 1666–1673 (1995).
[CrossRef] [PubMed]

Guck, J.

J. Guck, R. Ananthakrishnan, H. Mahmood, T. J. Moon, C. C. Cunningham, J. Käs, “The optical stretcher: a novel laser tool to micromanipulate cells,” Biophys. J. 81, 767–784 (2001).
[CrossRef] [PubMed]

J. Guck, R. Ananthakrishnan, T. J. Moon, C. C. Cunningham, J. Käs, “Optical deformability of soft biological dielectrics,” Phys. Lett. 84, 5451–5454 (2000).
[CrossRef]

Hansen, P. M.

P. M. Hansen, V. K. Bhatia, N. Harrit, L. Oddershede, “Expanding the optical trapping range of Gold nanoparticles,” Nano Lett. 5, 1937–1942 (2005).
[CrossRef] [PubMed]

Harrit, N.

P. M. Hansen, V. K. Bhatia, N. Harrit, L. Oddershede, “Expanding the optical trapping range of Gold nanoparticles,” Nano Lett. 5, 1937–1942 (2005).
[CrossRef] [PubMed]

Herzberger, M.

M. Herzberger, Modern Geometrical Optics (Interscience, 1958).

Hirasaki, G.

G. Hirasaki, C. Miller, M. Puerto, “Recent advances in surfactant EOR,” SPE J. 16, 889–907 (2011)
[CrossRef]

Jesorka, A.

R. Karlsson, A. Karlsson, A. Ewing, P. Dommersnes, J.-F. Joanny, A. Jesorka, O. Orwar, “Chemical analysis in nanoscale surfactant networks,” Anal. Chem. 78, 5961–5968 (2006).
[CrossRef] [PubMed]

Joanny, J.-F.

R. Karlsson, A. Karlsson, A. Ewing, P. Dommersnes, J.-F. Joanny, A. Jesorka, O. Orwar, “Chemical analysis in nanoscale surfactant networks,” Anal. Chem. 78, 5961–5968 (2006).
[CrossRef] [PubMed]

Karlsson, A.

R. Karlsson, A. Karlsson, A. Ewing, P. Dommersnes, J.-F. Joanny, A. Jesorka, O. Orwar, “Chemical analysis in nanoscale surfactant networks,” Anal. Chem. 78, 5961–5968 (2006).
[CrossRef] [PubMed]

Karlsson, R.

R. Karlsson, A. Karlsson, A. Ewing, P. Dommersnes, J.-F. Joanny, A. Jesorka, O. Orwar, “Chemical analysis in nanoscale surfactant networks,” Anal. Chem. 78, 5961–5968 (2006).
[CrossRef] [PubMed]

Käs, J.

J. Guck, R. Ananthakrishnan, H. Mahmood, T. J. Moon, C. C. Cunningham, J. Käs, “The optical stretcher: a novel laser tool to micromanipulate cells,” Biophys. J. 81, 767–784 (2001).
[CrossRef] [PubMed]

J. Guck, R. Ananthakrishnan, T. J. Moon, C. C. Cunningham, J. Käs, “Optical deformability of soft biological dielectrics,” Phys. Lett. 84, 5451–5454 (2000).
[CrossRef]

Keen, S.

Kluge, R.

Lai, H. M.

Landick, R.

R. J. Davenport, G. J. Wuite, R. Landick, C. Bustamante, “Single-molecule study of transcriptional pausing and arrest by E. coli RNA polymerase,” Science 287, 2497–2500 (2000).
[CrossRef] [PubMed]

Lasseux, D.

H. Chrabi, D. Lasseux, E. Arquis, R. Wunenburger, J.-P. Delville, “Stretching and squeezing of sessile dielectric drops by the optical radiation pressure,” Phys. Rev. E 77, 066706 (2008).
[CrossRef]

Leach, J.

Leung, P. T.

Lister, J. R.

H. A. Stone, J. R. Lister, M. P. Brenner, “Drops with conical ends in electric and magnetic fields,” Proc. R. Soc. London A 455, 329–347 (1999).
[CrossRef]

Liveri, V. T.

M. Goffredi, V. T. Liveri, G. J. Vassallo, “Refractive index of water-AOT-n-heptane microemulsions,” J. Solut. Chem. 22, 941–949 (1993).
[CrossRef]

Lock, J.

F. Xu, J. Lock, G. Gouesbet, C. Tropea, “Optical stress on the surface of a particle: homogeneous sphere,” Phys. Rev. A 79, 053808 (2009).
[CrossRef]

Mahmood, H.

J. Guck, R. Ananthakrishnan, H. Mahmood, T. J. Moon, C. C. Cunningham, J. Käs, “The optical stretcher: a novel laser tool to micromanipulate cells,” Biophys. J. 81, 767–784 (2001).
[CrossRef] [PubMed]

Mathur, D.

McGloin, D.

D. McGloin, “Optical tweezers: 20 years on,” Philos. Trans. R. Soc. A 364, 3521–3537 (2006).
[CrossRef]

Mellor, C. D.

D. A. Woods, C. D. Mellor, J. M. Taylor, C. D. Bain, A. D. Ward, “Nanofluidic networks created and controlled by light,” Soft Matter 7, 2517–2520 (2011).
[CrossRef]

A. D. Ward, M. G. Berry, C. D. Mellor, C. D. Bain, “Optical sculpture: controlled deformation of emulsion droplets with ultralow interfacial tensions using optical tweezers,” Chem. Commun. 2006, 4515–4517 (2006).
[CrossRef]

Miller, C.

G. Hirasaki, C. Miller, M. Puerto, “Recent advances in surfactant EOR,” SPE J. 16, 889–907 (2011)
[CrossRef]

Mishchenko, M. I.

M. I. Mishchenko, “Electromagnetic scattering by nonspherical particles: a tutorial review,” J. Quantum Spectrosc. Radiat. Transfer 110, 808–832 (2009).
[CrossRef]

Møller, P. C. F.

P. C. F. Møller, L. B. Oddershede, “Quantification of droplet deformation by electromagnetic trapping,” Europhys. Lett. 88, 48005 (2009).
[CrossRef]

Moon, T. J.

J. Guck, R. Ananthakrishnan, H. Mahmood, T. J. Moon, C. C. Cunningham, J. Käs, “The optical stretcher: a novel laser tool to micromanipulate cells,” Biophys. J. 81, 767–784 (2001).
[CrossRef] [PubMed]

J. Guck, R. Ananthakrishnan, T. J. Moon, C. C. Cunningham, J. Käs, “Optical deformability of soft biological dielectrics,” Phys. Lett. 84, 5451–5454 (2000).
[CrossRef]

Neuman, K. C.

K. C. Neuman, S. M. Block, “Optical trapping,” Rev. Sci. Instrum. 75, 2787–2809 (2004).
[CrossRef]

Nijhof, E. J.

P. J. H. Bronkhorst, G. J. Streekstra, J. Grinbergen, E. J. Nijhof, J. J. Sixma, G. J. Brakenhoff, “A new method to study shape recovery of red blood cells using multiple optical trapping,” Biophys. J. 69, 1666–1673 (1995).
[CrossRef] [PubMed]

Oddershede, L.

P. M. Hansen, V. K. Bhatia, N. Harrit, L. Oddershede, “Expanding the optical trapping range of Gold nanoparticles,” Nano Lett. 5, 1937–1942 (2005).
[CrossRef] [PubMed]

Oddershede, L. B.

P. C. F. Møller, L. B. Oddershede, “Quantification of droplet deformation by electromagnetic trapping,” Europhys. Lett. 88, 48005 (2009).
[CrossRef]

Orwar, O.

R. Karlsson, A. Karlsson, A. Ewing, P. Dommersnes, J.-F. Joanny, A. Jesorka, O. Orwar, “Chemical analysis in nanoscale surfactant networks,” Anal. Chem. 78, 5961–5968 (2006).
[CrossRef] [PubMed]

Padgett, M. J.

Poon, K. L.

Puerto, M.

G. Hirasaki, C. Miller, M. Puerto, “Recent advances in surfactant EOR,” SPE J. 16, 889–907 (2011)
[CrossRef]

Roy, S.

Schnapp, B.

S. Block, L. Goldstein, B. Schnapp, “Bead movement by single kinesin molecules studied with optical tweezers,” Nature 348, 348–352 (1990).
[CrossRef] [PubMed]

Sharma, S.

Siegman, A. E.

A. E. Siegman, Lasers (University Science, 1986).

Sixma, J. J.

P. J. H. Bronkhorst, G. J. Streekstra, J. Grinbergen, E. J. Nijhof, J. J. Sixma, G. J. Brakenhoff, “A new method to study shape recovery of red blood cells using multiple optical trapping,” Biophys. J. 69, 1666–1673 (1995).
[CrossRef] [PubMed]

Spivak, M.

M. Spivak, A Comprehensive Introduction to Differential Geometry (Publish or Perish, 1975), Vol. III.

Stone, H. A.

H. A. Stone, J. R. Lister, M. P. Brenner, “Drops with conical ends in electric and magnetic fields,” Proc. R. Soc. London A 455, 329–347 (1999).
[CrossRef]

Streekstra, G. J.

P. J. H. Bronkhorst, G. J. Streekstra, J. Grinbergen, E. J. Nijhof, J. J. Sixma, G. J. Brakenhoff, “A new method to study shape recovery of red blood cells using multiple optical trapping,” Biophys. J. 69, 1666–1673 (1995).
[CrossRef] [PubMed]

Taylor, G.

G. Taylor, “Disintegration of water drops in an electric field,” Proc. R. Soc. London A 280, 383–397 (1964).
[CrossRef]

Taylor, J. M.

D. A. Woods, C. D. Mellor, J. M. Taylor, C. D. Bain, A. D. Ward, “Nanofluidic networks created and controlled by light,” Soft Matter 7, 2517–2520 (2011).
[CrossRef]

Ting, L.

D. Blackmore, L. Ting, “Surface integral of its mean curvature vector,” SIAM Rev. 27, 569–572 (1985)
[CrossRef]

Tropea, C.

F. Xu, J. Lock, G. Gouesbet, C. Tropea, “Optical stress on the surface of a particle: homogeneous sphere,” Phys. Rev. A 79, 053808 (2009).
[CrossRef]

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Dover, 1981).

Vassallo, G. J.

M. Goffredi, V. T. Liveri, G. J. Vassallo, “Refractive index of water-AOT-n-heptane microemulsions,” J. Solut. Chem. 22, 941–949 (1993).
[CrossRef]

Ward, A. D.

D. A. Woods, C. D. Mellor, J. M. Taylor, C. D. Bain, A. D. Ward, “Nanofluidic networks created and controlled by light,” Soft Matter 7, 2517–2520 (2011).
[CrossRef]

A. D. Ward, M. G. Berry, C. D. Mellor, C. D. Bain, “Optical sculpture: controlled deformation of emulsion droplets with ultralow interfacial tensions using optical tweezers,” Chem. Commun. 2006, 4515–4517 (2006).
[CrossRef]

Woods, D. A.

D. A. Woods, C. D. Mellor, J. M. Taylor, C. D. Bain, A. D. Ward, “Nanofluidic networks created and controlled by light,” Soft Matter 7, 2517–2520 (2011).
[CrossRef]

Wright, A. J.

Wuite, G. J.

R. J. Davenport, G. J. Wuite, R. Landick, C. Bustamante, “Single-molecule study of transcriptional pausing and arrest by E. coli RNA polymerase,” Science 287, 2497–2500 (2000).
[CrossRef] [PubMed]

Wunenburger, R.

H. Chrabi, D. Lasseux, E. Arquis, R. Wunenburger, J.-P. Delville, “Stretching and squeezing of sessile dielectric drops by the optical radiation pressure,” Phys. Rev. E 77, 066706 (2008).
[CrossRef]

Xu, F.

F. Xu, J. Lock, G. Gouesbet, C. Tropea, “Optical stress on the surface of a particle: homogeneous sphere,” Phys. Rev. A 79, 053808 (2009).
[CrossRef]

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E. Evans, A. Yeung, “Apparent viscosity and cortical tension of blood granulocytes determined by micropipet aspiration,” Biophys. J. 56, 151–160 (1989).
[CrossRef] [PubMed]

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Zhang, J.-Z.

Anal. Chem. (1)

R. Karlsson, A. Karlsson, A. Ewing, P. Dommersnes, J.-F. Joanny, A. Jesorka, O. Orwar, “Chemical analysis in nanoscale surfactant networks,” Anal. Chem. 78, 5961–5968 (2006).
[CrossRef] [PubMed]

Appl. Phys. (1)

J. P. Barton, D. R. Alexander, “Fifthorder corrected electromagnetic field components for a fundamental Gaussian beam,” Appl. Phys. 66, 2800–2802 (1989).
[CrossRef]

Biophys. J. (3)

E. Evans, A. Yeung, “Apparent viscosity and cortical tension of blood granulocytes determined by micropipet aspiration,” Biophys. J. 56, 151–160 (1989).
[CrossRef] [PubMed]

J. Guck, R. Ananthakrishnan, H. Mahmood, T. J. Moon, C. C. Cunningham, J. Käs, “The optical stretcher: a novel laser tool to micromanipulate cells,” Biophys. J. 81, 767–784 (2001).
[CrossRef] [PubMed]

P. J. H. Bronkhorst, G. J. Streekstra, J. Grinbergen, E. J. Nijhof, J. J. Sixma, G. J. Brakenhoff, “A new method to study shape recovery of red blood cells using multiple optical trapping,” Biophys. J. 69, 1666–1673 (1995).
[CrossRef] [PubMed]

Chem. Commun. (1)

A. D. Ward, M. G. Berry, C. D. Mellor, C. D. Bain, “Optical sculpture: controlled deformation of emulsion droplets with ultralow interfacial tensions using optical tweezers,” Chem. Commun. 2006, 4515–4517 (2006).
[CrossRef]

Europhys. Lett. (1)

P. C. F. Møller, L. B. Oddershede, “Quantification of droplet deformation by electromagnetic trapping,” Europhys. Lett. 88, 48005 (2009).
[CrossRef]

J. Opt. Soc. Am. B (3)

J. Quantum Spectrosc. Radiat. Transfer (1)

M. I. Mishchenko, “Electromagnetic scattering by nonspherical particles: a tutorial review,” J. Quantum Spectrosc. Radiat. Transfer 110, 808–832 (2009).
[CrossRef]

J. Solut. Chem. (1)

M. Goffredi, V. T. Liveri, G. J. Vassallo, “Refractive index of water-AOT-n-heptane microemulsions,” J. Solut. Chem. 22, 941–949 (1993).
[CrossRef]

Nano Lett. (1)

P. M. Hansen, V. K. Bhatia, N. Harrit, L. Oddershede, “Expanding the optical trapping range of Gold nanoparticles,” Nano Lett. 5, 1937–1942 (2005).
[CrossRef] [PubMed]

Nature (1)

S. Block, L. Goldstein, B. Schnapp, “Bead movement by single kinesin molecules studied with optical tweezers,” Nature 348, 348–352 (1990).
[CrossRef] [PubMed]

Opt. Express (2)

Opt. Lett. (2)

Philos. Trans. R. Soc. A (1)

D. McGloin, “Optical tweezers: 20 years on,” Philos. Trans. R. Soc. A 364, 3521–3537 (2006).
[CrossRef]

Phys. Lett. (1)

J. Guck, R. Ananthakrishnan, T. J. Moon, C. C. Cunningham, J. Käs, “Optical deformability of soft biological dielectrics,” Phys. Lett. 84, 5451–5454 (2000).
[CrossRef]

Phys. Rev. A (1)

F. Xu, J. Lock, G. Gouesbet, C. Tropea, “Optical stress on the surface of a particle: homogeneous sphere,” Phys. Rev. A 79, 053808 (2009).
[CrossRef]

Phys. Rev. E (1)

H. Chrabi, D. Lasseux, E. Arquis, R. Wunenburger, J.-P. Delville, “Stretching and squeezing of sessile dielectric drops by the optical radiation pressure,” Phys. Rev. E 77, 066706 (2008).
[CrossRef]

Phys. Rev. Lett. (2)

A. Ashkin, J. M. Dziedzic, “Radiation pressure on a free liquid surface,” Phys. Rev. Lett. 30, 139–142 (1973).
[CrossRef]

A. Casner, J.-P. Delville, “Giant deformations of a liquid-liquid interface induced by the optical radiation pressure,” Phys. Rev. Lett. 87, 054503 (2001).
[CrossRef] [PubMed]

Proc. R. Soc. London A (2)

H. A. Stone, J. R. Lister, M. P. Brenner, “Drops with conical ends in electric and magnetic fields,” Proc. R. Soc. London A 455, 329–347 (1999).
[CrossRef]

G. Taylor, “Disintegration of water drops in an electric field,” Proc. R. Soc. London A 280, 383–397 (1964).
[CrossRef]

Rev. Sci. Instrum. (1)

K. C. Neuman, S. M. Block, “Optical trapping,” Rev. Sci. Instrum. 75, 2787–2809 (2004).
[CrossRef]

Science (1)

R. J. Davenport, G. J. Wuite, R. Landick, C. Bustamante, “Single-molecule study of transcriptional pausing and arrest by E. coli RNA polymerase,” Science 287, 2497–2500 (2000).
[CrossRef] [PubMed]

SIAM Rev. (1)

D. Blackmore, L. Ting, “Surface integral of its mean curvature vector,” SIAM Rev. 27, 569–572 (1985)
[CrossRef]

Soft Matter (1)

D. A. Woods, C. D. Mellor, J. M. Taylor, C. D. Bain, A. D. Ward, “Nanofluidic networks created and controlled by light,” Soft Matter 7, 2517–2520 (2011).
[CrossRef]

SPE J. (1)

G. Hirasaki, C. Miller, M. Puerto, “Recent advances in surfactant EOR,” SPE J. 16, 889–907 (2011)
[CrossRef]

Other (4)

A. E. Siegman, Lasers (University Science, 1986).

M. Spivak, A Comprehensive Introduction to Differential Geometry (Publish or Perish, 1975), Vol. III.

H. C. van de Hulst, Light Scattering by Small Particles (Dover, 1981).

M. Herzberger, Modern Geometrical Optics (Interscience, 1958).

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Figures (9)

Fig. 1
Fig. 1

Droplet configurations corresponding to the “spoke” model for (a) an undeformed droplet of Rd = 5.0μm with γ = 10−6 Nm−1 and (b) the corresponding converged shape in an optical trap with P0 = 0.20W and numerical aperture NA = 1.20. The Gaussian beam is represented by the black lines, and part of the intensity distribution is also shown. The radial direction () of a “spoke” is also shown, along with the corresponding interface normal ().

Fig. 2
Fig. 2

Comparison between a very coarse mesh of Nθ = 13 & Nϕ = 12 points (green), a coarse mesh of Nθ = 25 & Nϕ = 24 points (blue) and a refined mesh of Nθ = 51 & Nϕ = 48 (red), for a Rd = 5.0μm droplet deformed in (a) two optical traps, (b) three optical traps and (c) four optical traps.

Fig. 3
Fig. 3

Deformed conformations of an initial spherical droplet with radius Rd = 2.0μm and interfacial tension γ = 10−6 Nm−1 in a single optical trap as a function of increasing laser power P0. The colour scheme represents the variation in mean curvature, in units of μm−1.

Fig. 4
Fig. 4

Variation of the maximum projected radius of a droplet as a function of (a) NA for Rd = 5.0μm and γ = 10−6 Nm−1, (b) initial droplet radius Rd with NA = 1.10 and γ = 10−6 Nm−1, (c) interfacial tension γ for Rd = 5.0μm with NA = 1.10 and (d) refractive index n1 of the droplet with Rd = 5.0μm and γ = 10−6 Nm−1 and an optical trap with NA = 1.20.

Fig. 5
Fig. 5

Relationship between the deformation of a droplet and Nd with varying (a) NA for Rd = 5.0μm and γ = 10−6 Nm−1, (b) Rd with NA = 1.10 and γ = 10−6 Nm−1 and (c) n1 for a droplet with Rd = 5.0μm and γ = 10−6 Nm−1, and an optical trap with NA = 1.20.

Fig. 6
Fig. 6

Deformation of a Rd = 2.0μm droplet using two optical traps each with P0 = 0.06W and NA = 1.20. The top images show the two-dimensional xy projections and the bottom images show the corresponding three-dimensional geometries. Both lasers are positioned at the origin for (a). The positions of the lasers are then (1.0, [0, π], 0) μm & (2.0, [0, π], 0) μm in polar coordinates for (b) and (c) respectively. The colour scheme represents the variation in mean curvature, in units of μm−1.

Fig. 7
Fig. 7

Deformation of a Rd = 2.0μm droplet using three optical traps each with P0 = 0.04W and NA = 1.20. The top images represent the two-dimensional xy projections and the bottom images show the corresponding three-dimensional geometries. All lasers are positioned at the origin for (a). The positions of the lasers are then (1.0, [ π 3, π, 5 π 3], 0) μm & (2.0, [ π 3, π, 5 π 3], 0) μm in polar coordinates for (b) and (c) respectively. The colour scheme represents the variation in mean curvature, in units of μm−1.

Fig. 8
Fig. 8

Deformation of a Rd = 2.0μm droplet using four optical traps each with P0 = 0.03W and NA = 1.20. The top images represent the two-dimensional xy projections and the bottom images show the corresponding three-dimensional geometries. All lasers are positioned at the origin for (a). The positions of the lasers are then (1.0, [ π 4, 3 π 4, 5 π 4, 7 π 4], 0) μm & (2.0, [ π 4, 3 π 4, 5 π 4, 7 π 4], 0) μm in polar coordinates for (b) and (c) respectively. The colour scheme represents the variation in mean curvature, in units of μm−1.

Fig. 9
Fig. 9

Deformation of a Rd = 2.5μm droplet with γ = 10−6 Nm−1 using two, three and four optical traps in (a)–(c) respectively. The total combined optical power is Ptotal = 24 mW with a numerical aperture of NA = 1.20 for each laser. The focus of each laser is a lateral distance 3μm from the centre of symmetry of the experiment. The top row represents the two-dimensional xy projections observed experimentally (Ref. [1] – Reproduced by permission of The Royal Society of Chemistry http://pubs.rsc.org/en/Content/ArticleLanding/2006/CC/b610060k), the middle row are our predicted shapes and the bottom row shows the corresponding three-dimensional geometries. The colour scheme for our calculated structures represents the variation in mean curvature, in units of μm−1.

Equations (16)

Equations on this page are rendered with MathJax. Learn more.

E = A γ d S V P int d V
P ( r ) = P opt ( r ) P lap ( r ) + P int
P lap ( r ) = γ n ^ ( r )
p 0 n 1 s ^ p 0 F t n 2 s ^ t p 0 F r n 1 s ^ r ,
P opt ( r ) = p 0 n 1 ( ( 2 F r + F t ) μ F t sgn ( μ ) ( n 2 / n 1 ) 2 1 + μ 2 )
d [ R ( θ , ϕ ) r ^ ] d t n ^ = β ( P opt ( θ , ϕ ) P lap ( θ , ϕ ) + P int )
d R ( θ , ϕ ) d t = β ( P opt ( θ , ϕ ) P lap ( θ , ϕ ) + P int ) / ( n ^ r ^ )
V = 1 3 S R ( θ , ϕ ) 3 sin θ d θ d ϕ
d V d t = 0 = S R ( θ , ϕ ) 2 d R ( θ , ϕ ) d t sin θ d θ d ϕ
P int = ( S R ( θ , ϕ ) 2 ( P lap + P opt ) n ^ r ^ sin θ d θ d ϕ ) / ( S R ( θ , ϕ ) 2 n ^ r ^ sin θ d θ d ϕ )
n ^ = ( r R ( θ , ϕ ) ) | ( r R ( θ , ϕ ) ) |
P lap ( R , θ , ϕ ) = γ [ 2 u R u R 2 ( cot θ R θ + 2 R θ 2 + csc 2 θ 2 R ϕ 2 ) + u 3 R 3 ( ( 1 + 1 R 2 R θ 2 ) ( R θ ) 2 + ( csc 2 θ cos θ R sin 3 R θ ) ( R ϕ ) 2 + 2 R sin 2 θ R θ R ϕ 2 R θ ϕ + 1 R sin 4 θ ( R ϕ ) 2 2 R ϕ 2 ) ] ,
u = ( 1 + 1 R 2 ( R θ ) 2 + 1 R 2 sin 2 θ ( R ϕ ) 2 ) 1 2 .
S H n ^ d A = 0
N d = P 0 n ˜ γ R d c exp ( N A )
R scale = R d R x y R d

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