Kolmogorovian Active Turbulence of a Sparse Assembly of Interacting Marangoni Surfers

Abstract

Active matter, composed of self-propelled entities, forms a wide class of out-of-equilibrium systems that display striking collective behaviors, among which, the so-called active turbulence where spatially and time-disordered flow patterns spontaneously arise in a variety of active systems. De facto, the active turbulence naming suggests a connection with a second seminal class of out-of-equilibrium systems, inertial turbulence, even though the latter is of very different nature with energy injected at global system scale rather than at the elementary scale of single constituents. Indeed, the existence of a possible strong tie between active and canonical turbulence remains an open question and a field of profuse research. Using an assembly of self-propelled interfacial particles, we show experimentally that the statistical properties of particles' velocities display a turbulentlike behavior, as described by the celebrated 1941 phenomenology of Kolmogorov. Moreover, the analogy between the dynamics of the self-propelled particles and inertial turbulence is observed to hold consistently both in the Eulerian and Lagrangian frameworks. Unlike the swimmers' velocities distribution, the subsurface fluid flow is found not turbulent, thus making Marangoni surfers' assemblies different from other active systems generating turbulence, such as living matter. Identifying an active system in the universality class of inertial turbulence not only benefits its future development but may also provide new insights into the long-standing description of turbulent flows, arguably one of the biggest remaining mysteries in classical physics.

Mixing and unmixing induced by active camphor particles

“…In the second case we consider a fixed number of swimmers N = 15, with increasing radius: here the rms velocity does not vary much, although the Reynolds number increases with increasing radius. Given the range of Reynolds numbers considered here, Re p ∈ [20,100], the flow of water remains perfectly laminar although the dynamics of the swimmers is fluctuating in space and time as observed in our previous study [22]. At the beginning of an experiment, a patch of passive floaters constituted of glass bubbles (see properties in [28]) is introduced in the system of interfacial swimmers near the center of the bath.…”

“…Camphor disk swimmers are made by punching an agarose sheet (0.5 mm in thickness) filled with solid camphor grains [22][23][24]. Depending on the size of the puncher, the radius R of the camphor 014501-2 disks considered hereafter ranges from 1 to 4 mm.…”

“…As soon as enough swimmers are present, the system starts to exhibit spatiotemporal fluctuations [22], so that their velocity is better characterized using the root mean square u rms = ( u 2…”

“…In this article, we propose to experimentally investigate an original configuration of interfacial mixing, where small floating particles are stirred by active interfacial particles, in the absence of any other underlying forced flow. More precisely, we consider the mixing of a patch of micrometric hollow glass spheres floating on water, stirred by millimetric interfacial active camphor disks [22]. The motivation of exploring this configuration is twofold: (i) in a recent study [22] we have shown that the dynamics of such active disks mimics very accurately the statistical multiscale properties of homogeneous isotropic turbulence (in particular, a Kolmogorov-like spectrum has been found), although the underlying flow itself remains almost at rest; it is therefore tempting to investigate the mixing induced when such active disks are used as stirrers.…”

“…More precisely, we consider the mixing of a patch of micrometric hollow glass spheres floating on water, stirred by millimetric interfacial active camphor disks [22]. The motivation of exploring this configuration is twofold: (i) in a recent study [22] we have shown that the dynamics of such active disks mimics very accurately the statistical multiscale properties of homogeneous isotropic turbulence (in particular, a Kolmogorov-like spectrum has been found), although the underlying flow itself remains almost at rest; it is therefore tempting to investigate the mixing induced when such active disks are used as stirrers. (ii) The self-motility of these camphor disks is driven by self-generated surface tension gradients (related to a symmetry breaking of the dissolution of camphor in water) [23]; one may therefore expect that the mixed microparticles experience some additional phoretic drift (due to the surface tension gradients) eventually leading to an effective compressibility behavior, as previously described.…”