From vortex ratchets to rectification of self-propelled swimmers - - PowerPoint PPT Presentation

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From vortex ratchets to rectification of self-propelled swimmers - - PowerPoint PPT Presentation

Oct 30, 2022 280 likes •568 views

From vortex ratchets to rectification of self-propelled swimmers Alejandro V. Silhanek Experimental physics of nanostructured materials Physics Department, University of Lige BELGIUM 1 Advances in nanostructured superconductors, Madrid, May

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From vortex ratchets to rectification

  • f self-propelled swimmers

Advances in nanostructured superconductors, Madrid, May 2014

Alejandro V. Silhanek

Experimental physics of nanostructured materials Physics Department, University of Liège BELGIUM

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MICROFLUIDIC CHIPS

  • Y. Jeyaram
  • V. V. Moshchalkov

KULeuven Belgium MD SIMULATIONS

  • V. Marconi
  • I. Berdakin
  • C. Condat

University of Cordoba Argentina MICROSWIMMERS

  • A. Guidobaldi

L . Giojalas University of Cordoba Argentina

The 3M collaboration

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Brownian Ratchets

Directed transport in spatially periodic systems far from equilibrium under alternating excitation, without the need of a non-zero applied force and/or temperature gradients.

1900 Lippmann, 1912 Smoluckowski, Feynman

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  • breaking the inversion symmetry of the underlying periodic

potential

  • the system has to be driven out of equilibrium

' ( ) ( )

p ext

mx U x x F t      

Fext = A sin wt

Rocking ratchets

  • P. Reimann, Phys. Rep. 361, 57 (2002); P. Hanggi and F. Marchesoni, Rev. Mod. Phys. 81, 387 (2009)
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Realization in Type-II superconductors

  • J. Van de Vondel et al.,
  • Phys. Rev. Lett. 94,

057003 (2005)

  • J. E. Villegas et al.,

Science 302 1188 (2003)

  • Y. Togawa et al.,
  • Phys. Rev. Lett.

95, 087002(2005)

  • K. Yu et al.,
  • Phys. Rev. B 76

220507(R) (2007)

  • simi-rigid objects
  • size of ~ 0.1 to 1 mm
  • no-inertia
  • guided by physical boundaries
  • Repulsive interactions
  • very homogeneous population
  • externally excited

Deterministic ratchet

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From fluxon ratchets to rectification of self- propelled objects

  • semi-rigid objects
  • size of ~ 1 mm
  • no-inertia ?
  • Repulsive interactions ?
  • guided by physical boundaries ?
  • heterogeneous population
  • driven by internal motor

BACTERIA

Brownian ratchet

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Life without inertia

E.M. Purcell, Am. J. Phys. 45, 3 (1977)

HOW FAR AN E-COLI WILL COAST IF SUDDENLY STOPS SWIMMING ?

~ 0.1 Å IN ABOUT 1 ms

 Lv term viscous term inertial   Re

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Local force on the fluid TWO SIDE BY SIDE (q=p/2) E-COLI ATTRACT EACH OTHER TWO SWIMMERS ALIGNED (q=0) REPEL EACH OTHER

  • E. Lauga and T.R. Powers, Rep. Prog. Phys. 72, 096601 (2009)

swimmer-swimmer interaction

f0 F f0

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Swimmer-wall interactions

f0 f0

  • L. Rothschild, Nature 198, 1221 (1963); Berke et al., Phys.Rev.Lett. 101, 038102 (2008)
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FLUX LENSES

Ratchet of self-propelled swimmers

Zhu, Marchesoni, Nori, Phys. Rev. Lett. 92, 180602 (2004) Hulme et al., Lab on a chip (2008) Mahmud et al., Nature Physics 5, 606 (2009) Lambert et al., Phys. Rev. Lett. 104, 168102 (2010) Galajda et al., J. Bacteriol. 189, 8704 (2007)

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  • Does the swimming strategy play a role in the

rectification efficiency ?

  • Assuming heterogeneity in a swimmer population,

say different “smartness”, can we separate them?

Now we know that ratchets work for self- propelled microorganisms, what next?

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Life without inertia

AT LOW Re THE RESPONSE IS DETERMINED BY THE FORCES EXERTED AT THAT MOMENT AND BY NOTHING IN THE PAST LINEAR AND TIME INDEPENDENT !

E.M. Purcell, Am. J. Phys. 45, 3 (1977)

THE SCALOP CANNOT SWIM AT LOW Re

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WE NEED NON RECIPROCAL BODY KINEMATICS

E.M. Purcell, Am. J. Phys. 45, 3 (1977)

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Avoiding the scalop theorem

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little tumbling long run

Berdakin et al., Phys. Rev. E 87, 052702 (2013)

Optimization of the ratchet geometry

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little tumbling long run large tumbling short run

Berdakin et al., Phys. Rev. E 87, 052702 (2013)

Little tumbling improves the rectification

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Berdakin et al., Cent. Eur. J. Phys. 11, 1653 (2013)

Quantification of the sorting efficiency

3,5 mm

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Berdakin et al., Cent. Eur. J. Phys. 11, 1653 (2013)

Ratchet enhanced diffusion

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Berdakin et al., Phys. Rev. E 87, 052702 (2013)

No tumbling at all improves the rectification

Solution  SPERM CELLS

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Wall accumulation

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No separation but trapping

Guidobaldi et al., Phys. Rev. E 89, 032720 (2014)

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The steady-state distribution of particles at the boundary is proportional to the local curvature

Di Leonardo et al., PNAS. 107, 9541 (2010)

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U-shape instead of V-shape

Guidobaldi et al., Phys. Rev. E 89, 032720 (2014)

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Guidobaldi et al., Phys. Rev. E 89, 032720 (2014)

U-shape instead of V-shape

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Guidobaldi et al., Phys. Rev. E 89, 032720 (2014)

Sperm concentrator

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Where are we heading to ?

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What for ?

Odds of winning the lottery are about 18 million to 1 The likelihood you’ll be killed by lightning is roughly 2,650,000 to 1 Odds of becoming a saint: 1 in 20 million

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Conclusion

  • Mapping of dissimilar problems: control of micro-objects via surface

patterning

  • Reversal due to swimmers interactions?
  • Ratchets in type I superconductors?
  • Geometrical ratchet may help to eliminate cellular stress and

damage assocoated with centrifugation

  • A sizable fraction of swimmers can be 100% purified even if the
  • riginal mixture are dynamically sligthly different
  • Hyperactivation may prevet sperm from becoming trapped with the

convoluted ephitelial folds of the fallopian tubes

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Thank you