  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.
