Colloidal Microworms Propelling via a Cooperative Hydrodynamic Conveyor Belt

Fernando Martinez-Pedrero, Antonio Ortiz-Ambriz, Ignacio Pagonabarraga, and Pietro Tierno

Phys. Rev. Lett. 115, 138301 – Published 22 September 2015

Abstract

We study propulsion arising from microscopic colloidal rotors dynamically assembled and driven in a viscous fluid upon application of an elliptically polarized rotating magnetic field. Close to a confining plate, the motion of this self-assembled microscopic worm results from the cooperative flow generated by the spinning particles which act as a hydrodynamic “conveyor belt.” Chains of rotors propel faster than individual ones, until reaching a saturation speed at distances where induced-flow additivity vanishes. By combining experiments and theoretical arguments, we elucidate the mechanism of motion and fully characterize the propulsion speed in terms of the field parameters.

Received 13 March 2015

DOI:https://doi.org/10.1103/PhysRevLett.115.138301

Authors & Affiliations

Fernando Martinez-Pedrero¹, Antonio Ortiz-Ambriz¹, Ignacio Pagonabarraga^2,3, and Pietro Tierno^1,3,*

¹Estructura i Constituents de la Matèria, Universitat de Barcelona, 08028 Barcelona, Spain
²Departament de Física Fonamental, Universitat de Barcelona, 08028 Barcelona, Spain
³Institut de Nanociència i Nanotecnologia, IN2UB, Universitat de Barcelona, 08028 Barcelona, Spain

^*ptierno@ub.edu

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Issue

Vol. 115, Iss. 13 — 25 September 2015

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Images

Figure 1

(a) Schematic of an ensemble of paramagnetic colloids rotating close to a glass plate and subjected to an elliptically polarized rotating field. (b) Microscope images showing the motion of a chain (blue line) and of an individual rotor (red line) subjected to a rotating field with $H_{0} = 1500 A m^{- 1}$ , $β = 0.49$ , and $ω = 62.8 rad s^{- 1}$ at $t = 0 s$ (top) and 8.3 s later (bottom). (c) Regions in the ( $H_{x}, H_{z}$ ) plane where colloidal “walkers” [43, 44] (empty triangles), translating worms (filled squares), or both types of dynamics (filled triangles) are observed ( $ω = 62.8 rad s^{- 1}$ ). (d) Average speed of the colloidal worms $⟨ v ⟩$ vs number of particles $N$ .
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Figure 2

(a) Sequence of images showing a worm composed by $N = 7$ free rotors (top) or rotors with pairs of particles permanently linked (orange segments, bottom). (b) Propelling chain of $N = 5$ rotors at the glass-water interface (top) and at the air-water interface (bottom). Field parameters for (a) and (b) are $H_{0} = 1500 A m^{- 1}$ , $β = 0.49$ , and $ω = 125 rad s^{- 1}$ . (c) Schematics illustrating the rotors locations with respect to the interface in (b). (d) Position ( $x - x_{0}$ ) versus time for the chains of particles. Black (blue) line refers to (a), gray (pink) to (b).
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Figure 3

Normalized average speed $⟨ v ⟩ / ⟨ v_{0} ⟩$ of colloidal worms as a function of the number of rotors $N$ for different ellipticity $β$ ( $ω = 62.8 rad s^{- 1}$ , $H_{0} = 2300 A m^{- 1}$ ). Points denote experimental data while the continuous line is a fit following Eq. (1). Inset shows the average surface distance $⟨ d ⟩$ vs $β$ .
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Figure 4

(a) Normalized average flow speed $⟨ v_{f} ⟩ / ⟨ v_{0} ⟩$ vs elevation from the surface $z / h$ and calculated following the model in Ref. [34]. (b) Colloidal worm dragging a $2 μ m$ silica particle (red trajectory), VideoS3 in Ref. [34]. (c) Plots of the distance versus time for the worm (empty circles) and silica particle (filled squares).
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