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

There are ubiquitous situations in relation to the agglomeration of solid non-Brownian adhesive particles, ranging from electrostatic agglomerators, flocculation during water treatment, the assemblage of preplanetary grains to the growth of dendrites during aerosol filtration. We carry out direct numerical simulation together with an adhesive discrete element method calculation (DNS-DEM) to investigate agglomeration of non-Brownian adhesive particles in homogeneous isotropic turbulence (HIT). We focus on the effect of van der Waals adhesion and track the dynamics of individual particles both while they are traveling alone through the fluid and while they are colliding with other particles. 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 proposed containing the information of agglomerate structures and adhesion-controlled sticking probability. The kernel function extends Smoluchowski’s theory to the condition of non-coalescing particles and can reproduce DNS-DEM results with simple one-dimensional population balance equation.