Confinement Enhances the Diversity of Microbial Flow Fields

Despite their importance in many biological, ecological, and physical processes, microorganismal fluid flows under tight confinement have not been investigated experimentally. Strong screening of Stokelets in this geometry suggests that the flow fields of different microorganisms should be universally dominated by the 2D source dipole from the swimmer’s finite-size body. Confinement therefore is poised to collapse differences across microorganisms, which are instead well established in bulk. We combine experiments and theoretical modeling to show that, in general, this is not correct. Our results demonstrate that potentially minute details like microswimmer spinning and the physical arrangement of the propulsion appendages have in fact a leading role in setting qualitative topological properties of the hydrodynamic flow fields of microswimmers under confinement. This is well captured by an effective 2D model, even under relatively weak confinement. These results imply that active confined hydrodynamics is much richer than in bulk and depends in a subtle manner on the size, shape, and propulsion mechanisms of the active components.

Figure 1

The far-field signature of a force-free system depends on the relative $z$ position of the forces. Illustrated with a three-forces system. (a),(d) The three forces are in a plane $\parallel$ to the plates. The resulting flow field is quadrupolar with a $r^{-3}$ velocity decay. (b),(e) The forces are in a plane $\perp$ to the plates. The resulting flow field is dipolar with a $r^{-2}$ velocity decay. (c),(f) Effect of spinning the plane of forces. The central quadrupolar region depends on both the radius of the orbit described by the forces and the on-axis separation between thrust and drag (red and green arrows, respectively, in the first row). Gray scale shows $\cos (\alpha )$, where $\alpha$ is the angle between the local velocity and the swimming axis $x$.

Figure 2

CR flow fields. (a)–(e) Experimental flow fields for CR for (a) $H=60\mu \mathrm{m}$, (b) $H=43\mu \mathrm{m}$, (c) $H=29\mu \mathrm{m}$, (d) $H=21.5\mu \mathrm{m}$, (e) $H=14\mu \mathrm{m}$. (f)–(j) Corresponding flow fields obtained from best fits to the effective 2D model. Blue dots, Stokeslet location; black dot, source-dipole location. Gray scale follows the convention in Fig. 1. All panels show streamlines (solid lines) and local velocity vector fields (red arrows). (k)–(o) Magnitudes of the difference between experimental and fitted flows, normalized by the experimental magnitude. Dashed circles in (o) indicate the region of the experimental flows used to determine the best fits.

Figure 3

OM flow fields. Experimental flow fields for OM for (a) $H=21.5\mu \mathrm{m}$, (b) $H=29\mu \mathrm{m}$. (c),(d) Corresponding flow fields obtained from best fits to the effective 2D model. Blue dots, Stokeslet location; black dot, source-dipole location. Gray scale follows the convention in Fig. 1. All panels show streamlines (solid lines) and local velocity vector fields (red arrows). (e),(f) Magnitudes of the difference between experimental and fitted flows, normalized by the experimental magnitude.

Figure 4

Dependence of (a) the dipole strength $I_d$, (b) on-axis force separation $|x_0-x_1|$, (c) 2D Stokeslet strength $F_S$ as a function of normalized sample thickness $H/d$ for all of the microorganisms studied. OM, ⋆; CR, ∘. (d) $F_S$ normalized by the bulk drag $F_{S_{\mathrm{bulk}}}$ on CM and OM cell bodies modeled as prolate ellipsoids moving at the measured $H$-dependent speeds. The solid line is the prediction for a sphere of diameter $d$ moving at the center of the Hele-Shaw cell [40]; the dashed line is the solid line diminished by 40%. Error bars throughout represent fit uncertainties to average experimental flow fields.