On phoretic clustering of particles in turbulence

TL;DR

This paper presents a unified framework for understanding particle clustering in turbulence due to diffusiophoretic, thermophoretic, and chemotactic effects, supported by experiments demonstrating the theory's applicability.

Contribution

The authors develop a single theoretical framework describing multi-fractal clustering of small particles in turbulence, validated by experiments with salinity-gradient-induced clustering.

Findings

Clustering occurs on multi-fractal sets described by the theory.

Pair correlations decay stretched exponentially beyond the smallest turbulence scale.

Experimental results align with theoretical predictions despite size limitations.

Abstract

We demonstrate that diffusiophoretic, thermophoretic and chemotactic phenomena in turbulence lead to clustering of particles on multi-fractal sets that can be described using one single framework, valid when the particle size is much smaller than the smallest length scale of turbulence $l_0$. To quantify the clustering, we derive positive pair correlations and fractal dimensions that hold for scales smaller than $l_0$. Statistics of the number of particles in a small volume are non-Poissonian manifesting deviations from the case of uncorrelated particles. For scales larger than $l_0$ we predict a stretched exponential decay to 1 of the pair correlation function. For the case of inhomogeneous turbulence we find that the fractal dimension depends on the inhomogeneous direction. By performing experiments of clustering of diffusiophoretic particles induced by salinity gradients in a turbulent gravity current we demonstrate clustering in conformity to the theory. The particle size in the experiment is comparable to $l_0$, outside the strict validity region of the theory, suggesting that the theoretical predictions transfer to this practically relevant regime. This clustering mechanism can provide the key to the understanding of a multitude of processes such as formation of marine snow in the ocean and population dynamics of chemotactic bacteria.