Abstract

We discuss a scheme that incorporates restricted spatial input location, orthogonal sort, and movement direction features, with particle sorting achieved by using an asymmetric potential cycled on and off, while movement is accomplished by photophoresis. Careful investigation has uncovered the odds of sorting between certain pairs of particle sizes to be solely dependent on radii in each phase of the process. This means that the most effective overall sorting can be achieved by maximizing the number of phases. This optimized approach is demonstrated using numerical simulation to permit grading of a range of nanometer-scale particle sizes.

© 2009 Optical Society of America

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References

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  1. M. P. MacDonald, G. C. Spalding, and K. Dholakia, “Microfluidic sorting in an optical lattice,” Nature 426, 421-424 (2003).
    [CrossRef] [PubMed]
  2. T. Imasaka, Y. Kawabata, T. Kaneta, and I. Ishidzu, “Optical chromatography,” Anal. Chem. 67, 1763-1765 (1995).
    [CrossRef]
  3. T. Cižmár, M. Siler, M. Sery, P. Zemanek, V. Garcés-Chávez, and K. Dholakia, “Optical sorting and detection of sub-micron objects in a motional standing wave,” Phys. Rev. B 74, 035105 (2006).
    [CrossRef]
  4. J. Baumgartl, G. M. Hannappel, D. J. Stevenson, D. Day, M. Gu, and K. Dholakia, “Optical redistribution of microparticles and cells between microwells,” Lab Chip 9, 1334-1336 (2009).
    [CrossRef] [PubMed]
  5. Y. Hayashi, S. Ashihara, T. Shimura, and K. Kuroda, “Simultaneous separation of polydisperse particles using an asymmetric nonperiodic optical stripe pattern,” Appl. Opt. 48, 1543-1552 (2009).
    [CrossRef] [PubMed]
  6. A. Neild, T. W. Ng, and W. M. S. Yii, “Optical sorting of dielectric Rayleigh spherical particles with scattering and standing waves,” Opt. Express 17, 5321-5329 (2009).
    [CrossRef] [PubMed]
  7. L. Gorre-Talini, S. Jeanjean, and P. Silberzan, “Sorting of brownian particles by the pulsed application of an asymmetric potential,” Phys. Rev. E 56, 2025-2034 (1997).
    [CrossRef]
  8. B. Yan, R. M. Miura, and Y.-D. Chen, “Direction reversal of fluctuation-induced biased Brownian motion on distorted ratchets,” J. Theor. Biol. 210, 141-150 (2001).
    [CrossRef] [PubMed]
  9. C. R. Doering, W. Horsthemke, and J. Riordan, “Non-equilibrium fluctuation induced transport,” Phys. Rev. Lett. 72, 2984-2987 (1994).
    [CrossRef] [PubMed]
  10. A. Haljas, R. Mankin, A. Sauga, and E. Reiter, “Anomalous mobility of Brownian particles in a tilted symmetric sawtooth potential,” Phys. Rev. E 70, 041107 (2004).
    [CrossRef]
  11. J. Rousselet, L. Salome, A. Ajdari, and J. Prost, “Directional motion of Brownian particles induced by a periodic asymmetric potential,” Nature 370, 446-447 (1994).
    [CrossRef] [PubMed]
  12. T. W. Ng, A. Neild, and P. Heeraman, “Continuous and fast sorting of Brownian particles,” Opt. Lett. 33, 584-586 (2008).
    [CrossRef] [PubMed]
  13. R. Di Leonardo, J. Leach, H. Mushfique, J. M. Cooper, G. Ruocco, and M. J. Padgett, “Multipoint holographic optical velocimetry in microfluidic systems,” Phys. Rev. Lett. 96, 134502 (2006).
    [CrossRef] [PubMed]
  14. P. Zemánek, A. Jonáš, L. Sramek, and M. Liška, “Optical trapping of Rayleigh particles using a Gaussian standing wave,” Opt. Commun. 151, 273-285 (1998).
    [CrossRef]
  15. P. Zemánek, A. Jonáš, P. Jákl, J. Ježek, M. Šery, and M. Liška, “Theoretical comparison of optical traps created by standing wave and single beam,” Opt. Commun. 220, 401-412 (2003).
    [CrossRef]
  16. A. Neild, S. Oberti, F. Beyeler, J. Dual, and B. J. Nelson, “A micro-particle positioning technique combining an ultrasonic manipulator and a microgripper,” J. Micromech. Microeng. 16, 1562-1570 (2006).
    [CrossRef]
  17. A. Neild, S. Oberti, and J. Dual, “Design, modeling and characterization of microfluidic devices for ultrasonic manipulation,” Sens. Actuators B 121, 452-461 (2007).
    [CrossRef]

2009 (3)

2008 (1)

2007 (1)

A. Neild, S. Oberti, and J. Dual, “Design, modeling and characterization of microfluidic devices for ultrasonic manipulation,” Sens. Actuators B 121, 452-461 (2007).
[CrossRef]

2006 (3)

A. Neild, S. Oberti, F. Beyeler, J. Dual, and B. J. Nelson, “A micro-particle positioning technique combining an ultrasonic manipulator and a microgripper,” J. Micromech. Microeng. 16, 1562-1570 (2006).
[CrossRef]

R. Di Leonardo, J. Leach, H. Mushfique, J. M. Cooper, G. Ruocco, and M. J. Padgett, “Multipoint holographic optical velocimetry in microfluidic systems,” Phys. Rev. Lett. 96, 134502 (2006).
[CrossRef] [PubMed]

T. Cižmár, M. Siler, M. Sery, P. Zemanek, V. Garcés-Chávez, and K. Dholakia, “Optical sorting and detection of sub-micron objects in a motional standing wave,” Phys. Rev. B 74, 035105 (2006).
[CrossRef]

2004 (1)

A. Haljas, R. Mankin, A. Sauga, and E. Reiter, “Anomalous mobility of Brownian particles in a tilted symmetric sawtooth potential,” Phys. Rev. E 70, 041107 (2004).
[CrossRef]

2003 (2)

M. P. MacDonald, G. C. Spalding, and K. Dholakia, “Microfluidic sorting in an optical lattice,” Nature 426, 421-424 (2003).
[CrossRef] [PubMed]

P. Zemánek, A. Jonáš, P. Jákl, J. Ježek, M. Šery, and M. Liška, “Theoretical comparison of optical traps created by standing wave and single beam,” Opt. Commun. 220, 401-412 (2003).
[CrossRef]

2001 (1)

B. Yan, R. M. Miura, and Y.-D. Chen, “Direction reversal of fluctuation-induced biased Brownian motion on distorted ratchets,” J. Theor. Biol. 210, 141-150 (2001).
[CrossRef] [PubMed]

1998 (1)

P. Zemánek, A. Jonáš, L. Sramek, and M. Liška, “Optical trapping of Rayleigh particles using a Gaussian standing wave,” Opt. Commun. 151, 273-285 (1998).
[CrossRef]

1997 (1)

L. Gorre-Talini, S. Jeanjean, and P. Silberzan, “Sorting of brownian particles by the pulsed application of an asymmetric potential,” Phys. Rev. E 56, 2025-2034 (1997).
[CrossRef]

1995 (1)

T. Imasaka, Y. Kawabata, T. Kaneta, and I. Ishidzu, “Optical chromatography,” Anal. Chem. 67, 1763-1765 (1995).
[CrossRef]

1994 (2)

C. R. Doering, W. Horsthemke, and J. Riordan, “Non-equilibrium fluctuation induced transport,” Phys. Rev. Lett. 72, 2984-2987 (1994).
[CrossRef] [PubMed]

J. Rousselet, L. Salome, A. Ajdari, and J. Prost, “Directional motion of Brownian particles induced by a periodic asymmetric potential,” Nature 370, 446-447 (1994).
[CrossRef] [PubMed]

Ajdari, A.

J. Rousselet, L. Salome, A. Ajdari, and J. Prost, “Directional motion of Brownian particles induced by a periodic asymmetric potential,” Nature 370, 446-447 (1994).
[CrossRef] [PubMed]

Ashihara, S.

Baumgartl, J.

J. Baumgartl, G. M. Hannappel, D. J. Stevenson, D. Day, M. Gu, and K. Dholakia, “Optical redistribution of microparticles and cells between microwells,” Lab Chip 9, 1334-1336 (2009).
[CrossRef] [PubMed]

Beyeler, F.

A. Neild, S. Oberti, F. Beyeler, J. Dual, and B. J. Nelson, “A micro-particle positioning technique combining an ultrasonic manipulator and a microgripper,” J. Micromech. Microeng. 16, 1562-1570 (2006).
[CrossRef]

Chen, Y.-D.

B. Yan, R. M. Miura, and Y.-D. Chen, “Direction reversal of fluctuation-induced biased Brownian motion on distorted ratchets,” J. Theor. Biol. 210, 141-150 (2001).
[CrossRef] [PubMed]

Cižmár, T.

T. Cižmár, M. Siler, M. Sery, P. Zemanek, V. Garcés-Chávez, and K. Dholakia, “Optical sorting and detection of sub-micron objects in a motional standing wave,” Phys. Rev. B 74, 035105 (2006).
[CrossRef]

Cooper, J. M.

R. Di Leonardo, J. Leach, H. Mushfique, J. M. Cooper, G. Ruocco, and M. J. Padgett, “Multipoint holographic optical velocimetry in microfluidic systems,” Phys. Rev. Lett. 96, 134502 (2006).
[CrossRef] [PubMed]

Day, D.

J. Baumgartl, G. M. Hannappel, D. J. Stevenson, D. Day, M. Gu, and K. Dholakia, “Optical redistribution of microparticles and cells between microwells,” Lab Chip 9, 1334-1336 (2009).
[CrossRef] [PubMed]

Dholakia, K.

J. Baumgartl, G. M. Hannappel, D. J. Stevenson, D. Day, M. Gu, and K. Dholakia, “Optical redistribution of microparticles and cells between microwells,” Lab Chip 9, 1334-1336 (2009).
[CrossRef] [PubMed]

T. Cižmár, M. Siler, M. Sery, P. Zemanek, V. Garcés-Chávez, and K. Dholakia, “Optical sorting and detection of sub-micron objects in a motional standing wave,” Phys. Rev. B 74, 035105 (2006).
[CrossRef]

M. P. MacDonald, G. C. Spalding, and K. Dholakia, “Microfluidic sorting in an optical lattice,” Nature 426, 421-424 (2003).
[CrossRef] [PubMed]

Di Leonardo, R.

R. Di Leonardo, J. Leach, H. Mushfique, J. M. Cooper, G. Ruocco, and M. J. Padgett, “Multipoint holographic optical velocimetry in microfluidic systems,” Phys. Rev. Lett. 96, 134502 (2006).
[CrossRef] [PubMed]

Doering, C. R.

C. R. Doering, W. Horsthemke, and J. Riordan, “Non-equilibrium fluctuation induced transport,” Phys. Rev. Lett. 72, 2984-2987 (1994).
[CrossRef] [PubMed]

Dual, J.

A. Neild, S. Oberti, and J. Dual, “Design, modeling and characterization of microfluidic devices for ultrasonic manipulation,” Sens. Actuators B 121, 452-461 (2007).
[CrossRef]

A. Neild, S. Oberti, F. Beyeler, J. Dual, and B. J. Nelson, “A micro-particle positioning technique combining an ultrasonic manipulator and a microgripper,” J. Micromech. Microeng. 16, 1562-1570 (2006).
[CrossRef]

Garcés-Chávez, V.

T. Cižmár, M. Siler, M. Sery, P. Zemanek, V. Garcés-Chávez, and K. Dholakia, “Optical sorting and detection of sub-micron objects in a motional standing wave,” Phys. Rev. B 74, 035105 (2006).
[CrossRef]

Gorre-Talini, L.

L. Gorre-Talini, S. Jeanjean, and P. Silberzan, “Sorting of brownian particles by the pulsed application of an asymmetric potential,” Phys. Rev. E 56, 2025-2034 (1997).
[CrossRef]

Gu, M.

J. Baumgartl, G. M. Hannappel, D. J. Stevenson, D. Day, M. Gu, and K. Dholakia, “Optical redistribution of microparticles and cells between microwells,” Lab Chip 9, 1334-1336 (2009).
[CrossRef] [PubMed]

Haljas, A.

A. Haljas, R. Mankin, A. Sauga, and E. Reiter, “Anomalous mobility of Brownian particles in a tilted symmetric sawtooth potential,” Phys. Rev. E 70, 041107 (2004).
[CrossRef]

Hannappel, G. M.

J. Baumgartl, G. M. Hannappel, D. J. Stevenson, D. Day, M. Gu, and K. Dholakia, “Optical redistribution of microparticles and cells between microwells,” Lab Chip 9, 1334-1336 (2009).
[CrossRef] [PubMed]

Hayashi, Y.

Heeraman, P.

Horsthemke, W.

C. R. Doering, W. Horsthemke, and J. Riordan, “Non-equilibrium fluctuation induced transport,” Phys. Rev. Lett. 72, 2984-2987 (1994).
[CrossRef] [PubMed]

Imasaka, T.

T. Imasaka, Y. Kawabata, T. Kaneta, and I. Ishidzu, “Optical chromatography,” Anal. Chem. 67, 1763-1765 (1995).
[CrossRef]

Ishidzu, I.

T. Imasaka, Y. Kawabata, T. Kaneta, and I. Ishidzu, “Optical chromatography,” Anal. Chem. 67, 1763-1765 (1995).
[CrossRef]

Jákl, P.

P. Zemánek, A. Jonáš, P. Jákl, J. Ježek, M. Šery, and M. Liška, “Theoretical comparison of optical traps created by standing wave and single beam,” Opt. Commun. 220, 401-412 (2003).
[CrossRef]

Jeanjean, S.

L. Gorre-Talini, S. Jeanjean, and P. Silberzan, “Sorting of brownian particles by the pulsed application of an asymmetric potential,” Phys. Rev. E 56, 2025-2034 (1997).
[CrossRef]

Ježek, J.

P. Zemánek, A. Jonáš, P. Jákl, J. Ježek, M. Šery, and M. Liška, “Theoretical comparison of optical traps created by standing wave and single beam,” Opt. Commun. 220, 401-412 (2003).
[CrossRef]

Jonáš, A.

P. Zemánek, A. Jonáš, P. Jákl, J. Ježek, M. Šery, and M. Liška, “Theoretical comparison of optical traps created by standing wave and single beam,” Opt. Commun. 220, 401-412 (2003).
[CrossRef]

P. Zemánek, A. Jonáš, L. Sramek, and M. Liška, “Optical trapping of Rayleigh particles using a Gaussian standing wave,” Opt. Commun. 151, 273-285 (1998).
[CrossRef]

Kaneta, T.

T. Imasaka, Y. Kawabata, T. Kaneta, and I. Ishidzu, “Optical chromatography,” Anal. Chem. 67, 1763-1765 (1995).
[CrossRef]

Kawabata, Y.

T. Imasaka, Y. Kawabata, T. Kaneta, and I. Ishidzu, “Optical chromatography,” Anal. Chem. 67, 1763-1765 (1995).
[CrossRef]

Kuroda, K.

Leach, J.

R. Di Leonardo, J. Leach, H. Mushfique, J. M. Cooper, G. Ruocco, and M. J. Padgett, “Multipoint holographic optical velocimetry in microfluidic systems,” Phys. Rev. Lett. 96, 134502 (2006).
[CrossRef] [PubMed]

Liška, M.

P. Zemánek, A. Jonáš, P. Jákl, J. Ježek, M. Šery, and M. Liška, “Theoretical comparison of optical traps created by standing wave and single beam,” Opt. Commun. 220, 401-412 (2003).
[CrossRef]

P. Zemánek, A. Jonáš, L. Sramek, and M. Liška, “Optical trapping of Rayleigh particles using a Gaussian standing wave,” Opt. Commun. 151, 273-285 (1998).
[CrossRef]

MacDonald, M. P.

M. P. MacDonald, G. C. Spalding, and K. Dholakia, “Microfluidic sorting in an optical lattice,” Nature 426, 421-424 (2003).
[CrossRef] [PubMed]

Mankin, R.

A. Haljas, R. Mankin, A. Sauga, and E. Reiter, “Anomalous mobility of Brownian particles in a tilted symmetric sawtooth potential,” Phys. Rev. E 70, 041107 (2004).
[CrossRef]

Miura, R. M.

B. Yan, R. M. Miura, and Y.-D. Chen, “Direction reversal of fluctuation-induced biased Brownian motion on distorted ratchets,” J. Theor. Biol. 210, 141-150 (2001).
[CrossRef] [PubMed]

Mushfique, H.

R. Di Leonardo, J. Leach, H. Mushfique, J. M. Cooper, G. Ruocco, and M. J. Padgett, “Multipoint holographic optical velocimetry in microfluidic systems,” Phys. Rev. Lett. 96, 134502 (2006).
[CrossRef] [PubMed]

Neild, A.

A. Neild, T. W. Ng, and W. M. S. Yii, “Optical sorting of dielectric Rayleigh spherical particles with scattering and standing waves,” Opt. Express 17, 5321-5329 (2009).
[CrossRef] [PubMed]

T. W. Ng, A. Neild, and P. Heeraman, “Continuous and fast sorting of Brownian particles,” Opt. Lett. 33, 584-586 (2008).
[CrossRef] [PubMed]

A. Neild, S. Oberti, and J. Dual, “Design, modeling and characterization of microfluidic devices for ultrasonic manipulation,” Sens. Actuators B 121, 452-461 (2007).
[CrossRef]

A. Neild, S. Oberti, F. Beyeler, J. Dual, and B. J. Nelson, “A micro-particle positioning technique combining an ultrasonic manipulator and a microgripper,” J. Micromech. Microeng. 16, 1562-1570 (2006).
[CrossRef]

Nelson, B. J.

A. Neild, S. Oberti, F. Beyeler, J. Dual, and B. J. Nelson, “A micro-particle positioning technique combining an ultrasonic manipulator and a microgripper,” J. Micromech. Microeng. 16, 1562-1570 (2006).
[CrossRef]

Ng, T. W.

Oberti, S.

A. Neild, S. Oberti, and J. Dual, “Design, modeling and characterization of microfluidic devices for ultrasonic manipulation,” Sens. Actuators B 121, 452-461 (2007).
[CrossRef]

A. Neild, S. Oberti, F. Beyeler, J. Dual, and B. J. Nelson, “A micro-particle positioning technique combining an ultrasonic manipulator and a microgripper,” J. Micromech. Microeng. 16, 1562-1570 (2006).
[CrossRef]

Padgett, M. J.

R. Di Leonardo, J. Leach, H. Mushfique, J. M. Cooper, G. Ruocco, and M. J. Padgett, “Multipoint holographic optical velocimetry in microfluidic systems,” Phys. Rev. Lett. 96, 134502 (2006).
[CrossRef] [PubMed]

Prost, J.

J. Rousselet, L. Salome, A. Ajdari, and J. Prost, “Directional motion of Brownian particles induced by a periodic asymmetric potential,” Nature 370, 446-447 (1994).
[CrossRef] [PubMed]

Reiter, E.

A. Haljas, R. Mankin, A. Sauga, and E. Reiter, “Anomalous mobility of Brownian particles in a tilted symmetric sawtooth potential,” Phys. Rev. E 70, 041107 (2004).
[CrossRef]

Riordan, J.

C. R. Doering, W. Horsthemke, and J. Riordan, “Non-equilibrium fluctuation induced transport,” Phys. Rev. Lett. 72, 2984-2987 (1994).
[CrossRef] [PubMed]

Rousselet, J.

J. Rousselet, L. Salome, A. Ajdari, and J. Prost, “Directional motion of Brownian particles induced by a periodic asymmetric potential,” Nature 370, 446-447 (1994).
[CrossRef] [PubMed]

Ruocco, G.

R. Di Leonardo, J. Leach, H. Mushfique, J. M. Cooper, G. Ruocco, and M. J. Padgett, “Multipoint holographic optical velocimetry in microfluidic systems,” Phys. Rev. Lett. 96, 134502 (2006).
[CrossRef] [PubMed]

Salome, L.

J. Rousselet, L. Salome, A. Ajdari, and J. Prost, “Directional motion of Brownian particles induced by a periodic asymmetric potential,” Nature 370, 446-447 (1994).
[CrossRef] [PubMed]

Sauga, A.

A. Haljas, R. Mankin, A. Sauga, and E. Reiter, “Anomalous mobility of Brownian particles in a tilted symmetric sawtooth potential,” Phys. Rev. E 70, 041107 (2004).
[CrossRef]

Sery, M.

T. Cižmár, M. Siler, M. Sery, P. Zemanek, V. Garcés-Chávez, and K. Dholakia, “Optical sorting and detection of sub-micron objects in a motional standing wave,” Phys. Rev. B 74, 035105 (2006).
[CrossRef]

Šery, M.

P. Zemánek, A. Jonáš, P. Jákl, J. Ježek, M. Šery, and M. Liška, “Theoretical comparison of optical traps created by standing wave and single beam,” Opt. Commun. 220, 401-412 (2003).
[CrossRef]

Shimura, T.

Silberzan, P.

L. Gorre-Talini, S. Jeanjean, and P. Silberzan, “Sorting of brownian particles by the pulsed application of an asymmetric potential,” Phys. Rev. E 56, 2025-2034 (1997).
[CrossRef]

Siler, M.

T. Cižmár, M. Siler, M. Sery, P. Zemanek, V. Garcés-Chávez, and K. Dholakia, “Optical sorting and detection of sub-micron objects in a motional standing wave,” Phys. Rev. B 74, 035105 (2006).
[CrossRef]

Spalding, G. C.

M. P. MacDonald, G. C. Spalding, and K. Dholakia, “Microfluidic sorting in an optical lattice,” Nature 426, 421-424 (2003).
[CrossRef] [PubMed]

Sramek, L.

P. Zemánek, A. Jonáš, L. Sramek, and M. Liška, “Optical trapping of Rayleigh particles using a Gaussian standing wave,” Opt. Commun. 151, 273-285 (1998).
[CrossRef]

Stevenson, D. J.

J. Baumgartl, G. M. Hannappel, D. J. Stevenson, D. Day, M. Gu, and K. Dholakia, “Optical redistribution of microparticles and cells between microwells,” Lab Chip 9, 1334-1336 (2009).
[CrossRef] [PubMed]

Yan, B.

B. Yan, R. M. Miura, and Y.-D. Chen, “Direction reversal of fluctuation-induced biased Brownian motion on distorted ratchets,” J. Theor. Biol. 210, 141-150 (2001).
[CrossRef] [PubMed]

Yii, W. M. S.

Zemanek, P.

T. Cižmár, M. Siler, M. Sery, P. Zemanek, V. Garcés-Chávez, and K. Dholakia, “Optical sorting and detection of sub-micron objects in a motional standing wave,” Phys. Rev. B 74, 035105 (2006).
[CrossRef]

Zemánek, P.

P. Zemánek, A. Jonáš, P. Jákl, J. Ježek, M. Šery, and M. Liška, “Theoretical comparison of optical traps created by standing wave and single beam,” Opt. Commun. 220, 401-412 (2003).
[CrossRef]

P. Zemánek, A. Jonáš, L. Sramek, and M. Liška, “Optical trapping of Rayleigh particles using a Gaussian standing wave,” Opt. Commun. 151, 273-285 (1998).
[CrossRef]

Anal. Chem. (1)

T. Imasaka, Y. Kawabata, T. Kaneta, and I. Ishidzu, “Optical chromatography,” Anal. Chem. 67, 1763-1765 (1995).
[CrossRef]

Appl. Opt. (1)

J. Micromech. Microeng. (1)

A. Neild, S. Oberti, F. Beyeler, J. Dual, and B. J. Nelson, “A micro-particle positioning technique combining an ultrasonic manipulator and a microgripper,” J. Micromech. Microeng. 16, 1562-1570 (2006).
[CrossRef]

J. Theor. Biol. (1)

B. Yan, R. M. Miura, and Y.-D. Chen, “Direction reversal of fluctuation-induced biased Brownian motion on distorted ratchets,” J. Theor. Biol. 210, 141-150 (2001).
[CrossRef] [PubMed]

Lab Chip (1)

J. Baumgartl, G. M. Hannappel, D. J. Stevenson, D. Day, M. Gu, and K. Dholakia, “Optical redistribution of microparticles and cells between microwells,” Lab Chip 9, 1334-1336 (2009).
[CrossRef] [PubMed]

Nature (2)

M. P. MacDonald, G. C. Spalding, and K. Dholakia, “Microfluidic sorting in an optical lattice,” Nature 426, 421-424 (2003).
[CrossRef] [PubMed]

J. Rousselet, L. Salome, A. Ajdari, and J. Prost, “Directional motion of Brownian particles induced by a periodic asymmetric potential,” Nature 370, 446-447 (1994).
[CrossRef] [PubMed]

Opt. Commun. (2)

P. Zemánek, A. Jonáš, L. Sramek, and M. Liška, “Optical trapping of Rayleigh particles using a Gaussian standing wave,” Opt. Commun. 151, 273-285 (1998).
[CrossRef]

P. Zemánek, A. Jonáš, P. Jákl, J. Ježek, M. Šery, and M. Liška, “Theoretical comparison of optical traps created by standing wave and single beam,” Opt. Commun. 220, 401-412 (2003).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. B (1)

T. Cižmár, M. Siler, M. Sery, P. Zemanek, V. Garcés-Chávez, and K. Dholakia, “Optical sorting and detection of sub-micron objects in a motional standing wave,” Phys. Rev. B 74, 035105 (2006).
[CrossRef]

Phys. Rev. E (2)

L. Gorre-Talini, S. Jeanjean, and P. Silberzan, “Sorting of brownian particles by the pulsed application of an asymmetric potential,” Phys. Rev. E 56, 2025-2034 (1997).
[CrossRef]

A. Haljas, R. Mankin, A. Sauga, and E. Reiter, “Anomalous mobility of Brownian particles in a tilted symmetric sawtooth potential,” Phys. Rev. E 70, 041107 (2004).
[CrossRef]

Phys. Rev. Lett. (2)

C. R. Doering, W. Horsthemke, and J. Riordan, “Non-equilibrium fluctuation induced transport,” Phys. Rev. Lett. 72, 2984-2987 (1994).
[CrossRef] [PubMed]

R. Di Leonardo, J. Leach, H. Mushfique, J. M. Cooper, G. Ruocco, and M. J. Padgett, “Multipoint holographic optical velocimetry in microfluidic systems,” Phys. Rev. Lett. 96, 134502 (2006).
[CrossRef] [PubMed]

Sens. Actuators B (1)

A. Neild, S. Oberti, and J. Dual, “Design, modeling and characterization of microfluidic devices for ultrasonic manipulation,” Sens. Actuators B 121, 452-461 (2007).
[CrossRef]

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Figures (7)

Fig. 1
Fig. 1

Schematic description of the particle-sorting technique. A mixture of various sized particles is delivered through a small aperture. This is passed through a planar periodic but asymmetrical spatial potential in the x direction that is cycled on and off in time and is oriented orthogonal to the input delivery of the particles. A photophoretic force that does not interact with the asymmetric potential is applied downward in the y direction. The various-sized sorted particles are harvested from apertures at the output.

Fig. 2
Fig. 2

Gaussian probability density functions of small and large particles with the potential landscape applied included. Setting the barrier length to correspond with b results in optimal sorting.

Fig. 3
Fig. 3

Probability density functions (right-hand side) of four particle sizes after 0.1 s . It can be seen that the intersection points of each pair of curves across are different.

Fig. 4
Fig. 4

(a) and (c) Histograms of each particle population after 600 s . (b) and (d) Sorting maps over the full simulated period for a potential off-time of 0.4 s . Barrier grading was applied with (a) and (b) but not with (c) and (d).

Fig. 5
Fig. 5

Sorting maps over the full simulated period for a minimum barrier length of (a) 700 and (b)  400 nm .

Fig. 6
Fig. 6

Separation performance of different pairs of particle sizes.

Fig. 7
Fig. 7

Sorting map for full system with, in the x direction, a minimum barrier length of 700 nm and, in the y direction, photophoretic forces. The x axis is plotted as the distance traversed in the y direction over the length of the chamber in this direction.

Tables (4)

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Table 1 Optimized Sorting Percentages with Different Pairs of Particle Sizes

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Table 2 Optimized Barrier Length with Different Pairs of Particle Sizes

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Table 3 Simulation Statistics of Separation Time and Location with Different Particle Populations a

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Table 4 Separation Times (in Seconds) for Sorting with Different Pairs of Particle Sizes a

Equations (9)

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m d 2 x d t 2 + d v ( x ) d x + β d x d t 2 β k T ξ ( x ) = 0 ,
m d 2 y d t 2 + d v ( y ) d y + β d y d t 2 β k T ξ ( y ) = 0 ,
d x d t = 2 k T β ξ ( x ) 1 β d v ( x ) d x ,
d y d t = 1 β d v ( y ) d y = 2 P n R 2 β c w 2 Q ,
p d f ( R i ) = 1 4 π D i t e x 2 4 D i t ,
X 1 2 = k T t ln R 1 R 2 3 π μ ( R 1 R 2 ) ,
z 1 = R 1 R 2 ln R 1 R 2 ( R 1 R 2 1 ) ,
z 2 = ln R 1 R 2 ( R 1 R 2 1 ) .
max ( % ) = Gaussian c d f ( z 1 ) Gaussian c d f ( z 2 ) .

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