Research ArticleBIOENGINEERING

Active micromachines: Microfluidics powered by mesoscale turbulence

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Science Advances  08 Jul 2016:
Vol. 2, no. 7, e1501854
DOI: 10.1126/sciadv.1501854
  • Fig. 1 Emergence of antiferromagnetic spin state in an array of rotating discs.

    (A) An array of counter-rotating discs in mesoscale turbulence generated by active matter. Rotors have a radius R = 5 and are fixed on a square lattice with cell edge of 100. The director field is shown by solid green lines and is overlaid by streamlines (black lines with arrows). Discs are colored according to their angular velocity as shown in the colorbar (red, anticlockwise; blue, clockwise). A 3 × 3 portion of an 8 × 8 lattice of rotors is shown (movies S1 and S2). (B) Cross-correlations, 〈ωi(tj(t)〉, between neighboring rotors (i, j) as a function of the minimum gap size d between rotors for (i) homeotropic anchoring, (ii) no anchoring, and (iii) planar anchoring of the director at the rotor surface. The root mean square (rms) angular velocity, Embedded Image, is shown in the inset. (C) Time correlations of rotor angular velocity 〈ω(t)ω(0)〉, normalized by its mean value 〈ω(0)2〉 for different lattice sizes as a function of scaled time T = t/(2π/ωrms) for the case with homeotropic boundary conditions on the rotor surface. Inset: The decorrelation time τ is shown as a function of gap size for d > 10.

  • Fig. 2 Rotation of a single rotor immersed in a turbulent flow of active matter with homeotropic anchoring.

    (A) Color maps show the vorticity contours, and solid lines represent streamlines. Vorticity is normalized to its maximum value, and blue and red represent clockwise and anticlockwise rotation, respectively. An animated version is available (movie S3). (B) Director field around the rotating disc. Red dots and yellow triangles denote +1/2 and −1/2 topological defects, respectively. Inset: Schematic of the wall in the director field that encircles each rotor and the resulting active flow of fluid along the wall.

  • Fig. 3 Rotational dynamics of a single rotor in mesoscale turbulence.

    (A) Mean-squared angular displacement of rotors versus time for different rotor radii R. Director boundary conditions on the rotor surface are homeotropic. (B) Persistence time as a function of R comparing homeotropic and no anchoring director boundary conditions on the rotor surface.

  • Fig. 4 Characterization of a single rotor in mesoscale turbulence.

    (A) Increasing activity results in an enhanced angular velocity. (B) Increasing activity shortens the rotational persistence time.

  • Fig. 5 Confinement-induced rotation of a disc immersed in a bath of active matter showing the transition from unidirectional to turbulent flow.

    (A) The main panel shows the variation of the angular velocity of the rotor with increasing gap size. The vertical dashed line corresponds to the characteristic length scale of bulk mesoscale turbulence measured from the vorticity-vorticity correlation function in bulk. The insets show the transition from unidirectional flow to active turbulence with increasing gap size D: (i) D = 8; (ii) D = 30; (iii) D = 70. Shown is the director field (dashed green lines), superposed by streamlines (solid black lines with arrows) and topological defects (red and blue dots denoting +1/2, and −1/2 defects, respectively). (B) Mean square angular displacement of the rotor as a function of simulation time, where the transition from propulsive to diffusive behavior is seen when gap size is > 70.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/2/7/e1501854/DC1

    movie S1. Antiferromagnetic spin state in an array of rotating discs.

    movie S2. Antiferromagnetic spin state in an array of rotating discs.

    movie S3. Rotation of a single rotor immersed in active turbulence.

    movie S4. Rotation of a single rotor immersed in active turbulence.

    movie S5. Confinement-induced rotation of a disc immersed in an active nematic bath.

  • Supplementary Materials

    This PDF file includes:

    • Legends for movies S1 to S5

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    Other Supplementary Material for this manuscript includes the following:

    • movie S1 (.mpeg format). Antiferromagnetic spin state in an array of rotating discs.
    • movie S2 (.mpeg format). Antiferromagnetic spin state in an array of rotating discs.
    • movie S3 (.mpeg format). Rotation of a single rotor immersed in active turbulence.
    • movie S4 (.mpeg format). Rotation of a single rotor immersed in active turbulence.
    • movie S5 (.mpeg format). Confinement-induced rotation of a disc immersed in an active nematic bath.

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