Exponential Scaling in Early-stage Agglomeration of Adhesive Particles in Turbulence

TL;DR

This study uses DNS-DEM simulations to reveal an exponential size distribution in early-stage particle agglomeration within turbulence, providing a new scaling law and extending Smoluchowski's theory to adhesive particles.

Contribution

It introduces a universal exponential scaling law for agglomerate sizes and develops an agglomeration kernel incorporating structure and sticking probability, extending classical theory.

Findings

Exponential size distribution valid across various conditions

Derived a relationship between sticking probability and particle properties

Reproduced DNS-DEM results with a simplified 1D model

Abstract

We carry out direct numerical simulation together with an adhesive discrete element method calculation (DNS-DEM) to investigate agglomeration of particles in homogeneous isotropic turbulence (HIT). We report an exponential-form scaling for the size distribution of early-stage agglomerates, which is valid across a wide range of particle inertia and inter-particle adhesion values. Such scaling allows one to quantify the state of agglomeration using a single scale parameter. An agglomeration kernel is then constructed containing the information of agglomerate structures and the sticking probability. An explicit relationship between the sticking probability and microscale particle properties is also proposed based on the scaling analysis of the equation for head-on collisions. Our results extend Smoluchowski's theory to the condition of non-coalescing solid adhesive particles and can reproduce DNS-DEM results with a simple one-dimensional simulation.