Research ArticleCONDENSED MATTER PHYSICS

Artificial rheotaxis

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Science Advances  01 May 2015:
Vol. 1, no. 4, e1400214
DOI: 10.1126/sciadv.1400214
  • Fig. 1 Artificial rheotaxis of self-propelled particles.

    (A) Spherical 3-methacryloxypropyl trimethoxysilane polymer (TPM) containing a hematite cube (left) undergo a thermal treatment, resulting in an anisotropic particle with the hematite cube protruding out (right). (B) Dependence of the propulsion velocity V0 on the concentration of hydrogen peroxide fuel (H2O2). The data are empirically fit (black dashed line) by the Michaelis-Menten kinetics, V0 = Vmax[H2O]/(B + [H2O2]). Inset: Trajectories of different particles. We observe an isotropic propulsion in the absence of any flow and once activated by light. Note that the particles do not swim in bulk and only self-propel near a substrate. (C) Experimental setup. A syringe pump is connected to the capillary and induces a flow along the x direction. The particle (red sphere) resides at an altitude y near the bottom surface. It experiences a shear flow v = γ˙ y, where γ˙ is the local shear rate, near the nonslip boundary condition. This results in a translational velocity of the particle V(y/R), which depends on the ratio of the distance of the center of the particle to the wall with the radius R of the particle. (D) Trajectories of the particles for various flows and V0 ~ 8 μm/s. The direction of the flow is indicated by the blue arrow. In the absence of any light, the particle is used as a flow tracer advected at velocity V* (dashed line). Under light activation, the particle makes a U turn, and the hematite protrusion faces the flow (solid line). The alignment together with the polarity of the self-propulsion results in the upstream migration of the particles.

  • Fig 2 Mechanism in a nutshell and modelization.

    (A) Projection of the average velocity (Vx) along the direction of the flow as a function of V*. The measurements are performed for various hydrogen peroxide concentration [H202 = 1, 3, and 10% (v/v)] (respectively red, blue, and purple symbols). The velocity V0 depends on the fuel concentration. Fit of the experimental data with the model (see main text) for V0 = 4 μm/s (red dashed line) and V0 = 8 μm/s (blue dashed line) measured in the absence of any flow. (B) Model for the artificial rheotaxis and notation. We assume that the hematite component acts as a fixed pivot, linked to the substrate. We denote by θ the angle made by the tail-head direction of the particle with the flow (see sketch). The flow exerts a viscous drag Fs on the body of the particle, leading to a torque MFs, aligning the particle with the flow. The polarity of the particle induces an upstream migration. (C) Normalized angular distributions P(θ) for increasing V* in the range 0.6 to 20 μm/s. Expected Boltzmann distribution P(θ) ∝ exp[Kcos(θ)] (dashed line) superimposed on the experimental histograms, with K as the fitting parameter. Inset: Measurements of K as a function V*[log-log scale]. The data agree with the linear scaling K = V*/exp (black dashed line) predicted by our model. We obtain 1//exp = 1.5 ± 0.5 s/μm from the fit to the experimental data.

  • Fig. 3 Self-organization in a nonuniform flow field.

    A pulled micropipette is placed above a glass substrate where artificial swimmers reside, dispersed in a fuel solution. The same fuel solution is ejected out of the nozzle of the micropipette (red arrow) inducing a diverging flow decaying from the tip. Initially, the particles are randomly distributed in the sample. Under light activation, the particles migrate toward the tip and stop at a finite distance. They form a circle around the tip. Turning off the light, the particles are flushed away by the flow. The behavior is quantified the distance ΔR(t), as a distance to the nozzle (one color for each particle). The particles move toward the tip and stay at a finite and constant distance (inset, t = 177 s). Turning off the light (black arrows), they are flushed away by the flow (inset, t = 180 s). The velocity with which the particles are ejected provides a measure of the flow velocity at the position of mechanical equilibrium. We measure U* = 7 ± 1 μm/s (black dashed line), in agreement with our expectations for the considered active particles. Turning on the light, the particles migrate against the flow and reform a circle at the same distance from the tip.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/1/4/e1400214/DC1

    Movie S1. Dynamics of the self-propelled particles in the absence of any external flow and shear.

    Movie S2. Dynamics of the self-propelled particles under shear, at slow flow (V* = 4 μm/s) and for a self-propulsion velocity of the particles (V0 = 8 μm/s).

    Movie S3. Dynamics of the self-propelled particles under shear, at fast flow (V* = 20 μm/s) and the self-propulsion velocity of the particles (V0 = 8 μm/s).

    Movie S4. Organization of the particles in a diverging flow.

  • Supplementary Materials

    This PDF file includes:

    • Legends for movies S1 to S4

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    Other Supplementary Material for this manuscript includes the following:

    • Movie S1 (.mov format). Dynamics of the self-propelled particles in the absence of any external flow and shear.
    • Movie S2 (.mov format). Dynamics of the self-propelled particles under shear, at slow flow (V* = 4 μm/s) and for a self-propulsion velocity of the particles (V0 = 8 μm/s).
    • Movie S3 (.mov format). Dynamics of the self-propelled particles under shear, at fast flow (V* = 20 μm/s) and the self-propulsion velocity of the particles (V0 = 8 μm/s).
    • Movie S4 (.mov format). Organization of the particles in a diverging flow.

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