Confined floating active carpets generate coherent vortical flows that enhance transport

TL;DR

This work addresses how vertical confinement in slick-like interfacial films shapes flows generated by a finite active carpet of micro-swimmers. It develops a two-fluid Stokeslet/stresslet framework with an image-system to model flow in a floating biofilm and introduces a scale-invariant criterion based on the confinement ratio $H/R$. The key result is that intermediate confinement (roughly $1 < H/R < 3$) yields coherent 3D vortex-ring-like flows that enhance advection of tracers toward the carpet edges, while strong or weak confinement suppresses or redirects transport. These findings reveal a geometry-driven mechanism by which microbial colonies can optimize nutrient uptake and spread in constrained habitats, with broader implications for active-matter transport near interfaces and potential parallels to ciliary-like surface flows.

Abstract

Slicks are thin viscous films that can be found at the air--water interface of water bodies such as lakes, rivers and oceans. These micro-layers are enriched in surfactants, organic matter, and microorganisms, and exhibit steep physical and chemical gradients across only tens to hundreds of micrometers. In such geometrically confined environments, the hydrodynamics and transport of nutrients, pollutants, and microorganisms are constrained, yet they collectively sustain key biogenic processes. It remains however largely unexplored how the hydrodynamic flows and transport are affected by the vertical extent of slicks relative to the size of microbial colonies. Here, we study this question by combining analytical and numerical approaches to model a microbial colony as an active carpet: a two-dimensional distribution of micro-swimmers exerting dipolar forces. We show that there exists a ratio between the carpet size and the confinement height that is optimal for the enhancement of particle transport toward the colony edges through advective flows that recirculate in 3D vortex-ring-like patterns with a characteristic length comparable to the confinement height. Our results demonstrate that finite, coherent vortex-ring-like structures can arise solely from the geometrical confinement ratio of slick thickness to microbial colony size. These findings shed light on the interplay between collective activity and out-of-equilibrium transport, and on how microbial communities form, spread, and persist in geometrically constrained environments such as surface slicks.

Figures (7)

• Figure 1: An active carpet of size $R$ is immersed in a viscous sea slick of thickness $\mathrm{H}$, bounded above by the air-slick interface and below by the slick-water interface. The relative viscosity $\lambda$ is the ratio between the viscosities of the underlying water and the slick. The active carpet is composed of micro-swimmers of characteristic size $\ell$, suspended at a distance $h$ from the slick-water interface. Each micro-swimmer generates an extensile flow of strength $\kappa$. Background shows an image of a sea-surface slick. Credits: NASA/JPL-Caltech NASA.
• Figure 2: Collective average velocity field within the slick. Panels from top to bottom correspond to a)$\mathrm{H}/R=2$ (thick slick), b)$\mathrm{H}/R=1$ and c) $\mathrm{H}/R=1/2$ (thin slick). The contours are the logarithm base 10 of the velocity field magnitude in the $y=0$ plane. The black arrows are the velocity vectors. The red dashed lines in a) indicate the diameter of the floating active carpet, $2R$.
• Figure 3: (a) Transversal collective velocity at the slick center for confined (blue) to non-confined cases (green). The pink dashed line is the stagnation height of the fluid velocity $(z/H)_\text{stag}$ as a reference. Inset: Analytical value of the stagnation height for a varying confinement (pink, solid line). The degree of confinement is indicated by the black arrow. (b) Normalized flow circulation over a closed curve defined as an ellipse centered at $z=H/2$ with width $(4R/3$ and height $(H-5)/2$. Inset: Average velocity over closed curve.
• Figure 4: Lagrangian trajectories of tracer particles. Top panels (a-c) show representative tracer particle trajectories for $\mathrm{H}/R=2$, $\mathrm{H}/R=1$ and $\mathrm{H}/R=1/2$ with their respective insets zooming between $[-2R,2R]$ shown in (d-f). Red circles correspond to the active carpet edge.
• Figure 5: Analysis of tracer trajectories Top panels (a-c) show the $xz-\text{plane}$ projections of the trajectories for the cases $\mathrm{H}/R=2$, $\mathrm{H}/R=1$ and $\mathrm{H}/R=1/2$ in Fig. \ref{['fig:5']}. Middle panels show the radial distribution of the final positions with histograms in blue and PDF's in red solid lines for (a-c). Bottom panels show the vertical distribution of the final positions with histograms in green and PDF's in red solid lines for (a-c).