On phoretic clustering of particles in turbulence

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.

References in corpus (10)

• Heavy particle concentration in turbulence at dissipative and inertial scales
• Caustic activation of rain showers
• Sling effect in collisions of water droplets in turbulent clouds
• Quantifying turbulence induced segregation of inertial particles
• Localization-delocalization transitions in turbophoresis of inertial particles
• Thermophoresis of Brownian particles driven by coloured noise
• Chaotic mixing in effective compressible flows
• Inhomogeneous distribution of droplets in cloud turbulence
• Multiple time-scale approach for a system of Brownian particles in a non-uniform temperature field
• Convective stability of turbulent Boussinesq flow in the dissipative range and flow around small particles

Cited by in corpus (9)

• Gyrotactic phytoplankton in laminar and turbulent flows: a dynamical systems approach
• Diffusiophoresis, Batchelor scale and effective Péclet numbers
• Solute-mediated colloidal vortex in a microfluidic T-junction
• Inertial particles distribute in turbulence as Poissonian points with random intensity inducing clustering and supervoiding
• Phoresis in turbulent flows
• Diffusiophoretic transport of colloids in porous media
• Lyapunov exponents and Lagrangian chaos suppression in compressible homogeneous isotropic turbulence
• Inhomogeneous preferential concentration of inertial particles in turbulent channel flow
• Fluctuations of separation of trajectories in chaos and correlation dimension