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Rapid expulsion of microswimmers by a vortical flow

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ABSTRACT

Interactions of microswimmers with their fluid environment are exceptionally complex. Macroscopic shear flow alters swimming trajectories in a highly nontrivial way and results in dramatic reduction of viscosity and heterogeneous bacterial distributions. Here we report on experimental and theoretical studies of rapid expulsion of microswimmers, such as motile bacteria, by a vortical flow created by a rotating microparticle. We observe a formation of a macroscopic depletion area in a high-shear region, in the vicinity of a microparticle. The rapid migration of bacteria from the shear-rich area is caused by a vortical structure of the flow rather than intrinsic random fluctuations of bacteria orientations, in stark contrast to planar shear flow. Our mathematical model reveals that expulsion is a combined effect of motility and alignment by a vortical flow. Our findings offer a novel approach for manipulation of motile microorganisms and shed light on bacteria–flow interactions.

No MeSH data available.


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Formation of a depletion zone.Distribution of bacteria in the vicinity of the rotating particle. Bacteria imaged approximately 0–5 μm above the surface of the sessile drop. Scale bar, 100 μm. Rotation frequency is 20 Hz. (a) Illustration of bacterial orientation one second after the start of rotation and the chosen coordinate system. (b) A stationary distribution of bacteria and a depletion zone: concentration of swimming bacteria around the rotating particle is reduced. (c) A depletion zone fades away after cessation of rotation. Bacteria trapped by the rotating particle are released. (d) Radius of the depletion zone Rd normalized by the particle radius R=30 μm versus frequency. The value of Rd is determined from the condition that at r=Rd the concentration of bacteria is one half of the equilibrium concentration. Error bars (s.d.) are calculated over a sequence of 10 non-consecutive frames. Solid red line is the fit to equation (7), Rd∝ω1/3.
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f1: Formation of a depletion zone.Distribution of bacteria in the vicinity of the rotating particle. Bacteria imaged approximately 0–5 μm above the surface of the sessile drop. Scale bar, 100 μm. Rotation frequency is 20 Hz. (a) Illustration of bacterial orientation one second after the start of rotation and the chosen coordinate system. (b) A stationary distribution of bacteria and a depletion zone: concentration of swimming bacteria around the rotating particle is reduced. (c) A depletion zone fades away after cessation of rotation. Bacteria trapped by the rotating particle are released. (d) Radius of the depletion zone Rd normalized by the particle radius R=30 μm versus frequency. The value of Rd is determined from the condition that at r=Rd the concentration of bacteria is one half of the equilibrium concentration. Error bars (s.d.) are calculated over a sequence of 10 non-consecutive frames. Solid red line is the fit to equation (7), Rd∝ω1/3.

Mentions: In our experiment, a pendent drop of bacterial suspension (10 μl) is attached to a microscope glass slide, see Methods. A nickel particle of radius R≈30 μm is placed in the center of the drop, and the gravity force keeps the particle around the nadir. Two pairs of orthogonal Helmholtz coils create a uniform rotating magnetic field forcing the particle to spin with the field frequency. If the magnetic field is turned off, then bacteria are swimming randomly in the vicinity of the particle and their spatial and angular distributions are homogeneous. When a rotating magnetic field with frequency 2–40 Hz is applied, the spinning particle creates a macroscopic vortex with a diameter of a few hundred microns. This vortex advects bacteria along streamlines and aligns their bodies parallel to the local flow direction (Fig. 1a). Rarely bacteria flip their orientations. While the spatial distribution (during first few seconds) is almost uniform, the orientational distribution acquires two sharp peaks near relative angle and , see Fig. 1a for the definition of relative angle . Within a few seconds the concentration of motile bacteria in the vicinity of the particle starts to decrease resulting in a formation of a macroscopic depletion zone. The depletion zone expands over a few minutes (Fig. 1b). The trajectories of bacteria are represented by unwinding spirals with a slowly changing curvature. Since the shear flow created by a spherical particle is decaying roughly as 1/r2 with the distance r from the origin, see Supplementary Fig. 1, at a certain distance the rotational diffusion of bacteria overcomes the shear-induced alignment. That limits the depletion zone diameter. For not too high concentrations, most of the bacteria are confined to a thin layer near the surface of the drop due to hydrodynamic attraction/steric collision272829. This confinement allows an effective two-dimensional approximation for the interaction between bacteria and flow created by the rotating particle.


Rapid expulsion of microswimmers by a vortical flow
Formation of a depletion zone.Distribution of bacteria in the vicinity of the rotating particle. Bacteria imaged approximately 0–5 μm above the surface of the sessile drop. Scale bar, 100 μm. Rotation frequency is 20 Hz. (a) Illustration of bacterial orientation one second after the start of rotation and the chosen coordinate system. (b) A stationary distribution of bacteria and a depletion zone: concentration of swimming bacteria around the rotating particle is reduced. (c) A depletion zone fades away after cessation of rotation. Bacteria trapped by the rotating particle are released. (d) Radius of the depletion zone Rd normalized by the particle radius R=30 μm versus frequency. The value of Rd is determined from the condition that at r=Rd the concentration of bacteria is one half of the equilibrium concentration. Error bars (s.d.) are calculated over a sequence of 10 non-consecutive frames. Solid red line is the fit to equation (7), Rd∝ω1/3.
© Copyright Policy - open-access
Related In: Results  -  Collection

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Show All Figures
getmorefigures.php?uid=PMC4814579&req=5

f1: Formation of a depletion zone.Distribution of bacteria in the vicinity of the rotating particle. Bacteria imaged approximately 0–5 μm above the surface of the sessile drop. Scale bar, 100 μm. Rotation frequency is 20 Hz. (a) Illustration of bacterial orientation one second after the start of rotation and the chosen coordinate system. (b) A stationary distribution of bacteria and a depletion zone: concentration of swimming bacteria around the rotating particle is reduced. (c) A depletion zone fades away after cessation of rotation. Bacteria trapped by the rotating particle are released. (d) Radius of the depletion zone Rd normalized by the particle radius R=30 μm versus frequency. The value of Rd is determined from the condition that at r=Rd the concentration of bacteria is one half of the equilibrium concentration. Error bars (s.d.) are calculated over a sequence of 10 non-consecutive frames. Solid red line is the fit to equation (7), Rd∝ω1/3.
Mentions: In our experiment, a pendent drop of bacterial suspension (10 μl) is attached to a microscope glass slide, see Methods. A nickel particle of radius R≈30 μm is placed in the center of the drop, and the gravity force keeps the particle around the nadir. Two pairs of orthogonal Helmholtz coils create a uniform rotating magnetic field forcing the particle to spin with the field frequency. If the magnetic field is turned off, then bacteria are swimming randomly in the vicinity of the particle and their spatial and angular distributions are homogeneous. When a rotating magnetic field with frequency 2–40 Hz is applied, the spinning particle creates a macroscopic vortex with a diameter of a few hundred microns. This vortex advects bacteria along streamlines and aligns their bodies parallel to the local flow direction (Fig. 1a). Rarely bacteria flip their orientations. While the spatial distribution (during first few seconds) is almost uniform, the orientational distribution acquires two sharp peaks near relative angle and , see Fig. 1a for the definition of relative angle . Within a few seconds the concentration of motile bacteria in the vicinity of the particle starts to decrease resulting in a formation of a macroscopic depletion zone. The depletion zone expands over a few minutes (Fig. 1b). The trajectories of bacteria are represented by unwinding spirals with a slowly changing curvature. Since the shear flow created by a spherical particle is decaying roughly as 1/r2 with the distance r from the origin, see Supplementary Fig. 1, at a certain distance the rotational diffusion of bacteria overcomes the shear-induced alignment. That limits the depletion zone diameter. For not too high concentrations, most of the bacteria are confined to a thin layer near the surface of the drop due to hydrodynamic attraction/steric collision272829. This confinement allows an effective two-dimensional approximation for the interaction between bacteria and flow created by the rotating particle.

View Article: PubMed Central - PubMed

ABSTRACT

Interactions of microswimmers with their fluid environment are exceptionally complex. Macroscopic shear flow alters swimming trajectories in a highly nontrivial way and results in dramatic reduction of viscosity and heterogeneous bacterial distributions. Here we report on experimental and theoretical studies of rapid expulsion of microswimmers, such as motile bacteria, by a vortical flow created by a rotating microparticle. We observe a formation of a macroscopic depletion area in a high-shear region, in the vicinity of a microparticle. The rapid migration of bacteria from the shear-rich area is caused by a vortical structure of the flow rather than intrinsic random fluctuations of bacteria orientations, in stark contrast to planar shear flow. Our mathematical model reveals that expulsion is a combined effect of motility and alignment by a vortical flow. Our findings offer a novel approach for manipulation of motile microorganisms and shed light on bacteria–flow interactions.

No MeSH data available.


Related in: MedlinePlus