TURBULENT COAGULATION OF COLLOIDAL PARTICLES

Theoretical predictions for the coagulation rate induced by turbulent shear have often been based on the hypothesis that the turbulent veloc ity gradient is persistent (Saffman & Turner 1956) and that hydrodynam ic and interparticle interactions (van der Waals attraction and electr ostatic double-layer repulsion) between colloidal particles can be neg lected. In the present work we consider the effects of interparticle f orces on the turbulent coagulation rate, and we explore the response o f the coagulation rate to changes in the Lagrangian velocity gradient correlation time (i.e. the characteristic evolution time for the veloc ity gradient in a reference frame following the fluid motion). Stokes equations of motion apply to the relative motion of the particles whos e radii are much smaller than the lengthscales of turbulence (i.e, sma ll particle Reynolds numbers). We express the fluid motion in the vici nity of a pair of particles as a locally linear flow with a temporally varying velocity gradient. The fluctuating velocity gradient is assum ed to be isotropic and Gaussian with statistics taken from published d irect numerical simulations of turbulence (DNS). Numerical calculation s of particle trajectories are used to determine the rate of turbulent coagulation in the presence and absence of particle interactions. Res ults from the numerical simulations correctly reproduce calculated coa gulation rates for the asymptotic limits of small and large total stra in where total strain is a term used to describe the product of the ch aracteristic strain rate and its correlation time. Recent DNS indicate that the correlation times for the fluctuating strain and rotation ra te are of the same order as the Kolmogorov time (Pope 1990), suggestin g theories that assume either small or large total strain may poorly a pproximate the turbulent coagulation rate. Indeed, simulations for iso tropic random hows with intermediate total strain indicate that the co agulation rate in turbulence is significantly different from the analy tical limits for large and small total strain. The turbulent coagulati on rate constant for non-interacting monodisperse particles scaled wit h the Kolmogorov time and the particle radius is 8.62 +/- 0.02, wherea s the commonly used model of Saffman & Turner (1956) predicts a value of 10.35 for non-rotational flows in the limit of persistent turbulent velocity gradients. Additional simulations incorporating hydrodynamic interactions and van der Waals attraction were used to estimate the a ctual rate of particle coagulation. For typical values of these parame ters, particle interactions reduced the coagulation rate constant by a t least 50%. In general, the collision efficiency (the ratio of coagul ation with particle interactions to that without) decreased with incre asing particle size and Kolmogorov shear rate.