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A simple theory, based on observations of snowflake distribution in aturbulent flow, is proposed to model the growth of inertial particles as aresult of dynamic clustering at scales larger than the Kolmogorov length scale.Particles able to stick or coalesce are expected to grow in size in flowregions where preferential concentration is predicted by a critical Stokesnumber $St=\tau_p/\tau_f \simeq 1 $. We postulate that, during growth, $St$remains critical, with the particle response time $\tau_p$ evolving accordingto the specific flow time scale $\tau_f$ defined by the vortices around whichprogressively larger particles end up orbiting. This mechanism leads to theprediction of the limiting size of aggregating particles in a turbulent flow.Such limit is determined by the extent of the turbulent inertial range, whichcan be formulated as a function of accessible integral-scale quantities. Theproposed dynamically critical Stokes growth provides a framework to interpretparticle aggregation, size growth and particle cluster growth in variousgeophysical multi-phase flows.

Particle growth in turbulent flow under dynamically critical Stokes conditions