Technical note: Frozen moment ratio and persistent memory in shear-induced coagulation within a decaying vortex

Abstract

We report the discovery of a frozen state in shear-induced coagulation of particles within a decaying Taylor-Green vortex, using high-resolution numerical simulation based on the average kernel method. Contrary to the well-established self-similar theory predicting a moment ratio $M_C=2$ for homogeneous systems, the spatially averaged value $⟨M_C⟩$ stabilizes at approximately $4.5$ under the condition $Re=10,Sc=1,Da=1$. This frozen state arises because the statistical properties of the moment fields, established during the early vigorous flow stage, become locked in as the flow decays. The coagulation rate diminishes to negligible levels $⟨T_{coag}⟩\sim {10}^{-9}$ while convective and diffusive transport vanish, preventing the system from reaching the classical homogeneous equilibrium. Our findings reveal a strong history dependence in coagulation dynamics, demonstrating that spatially averaged moment statistics can become path-dependent and remain far from homogeneous equilibrium, even after flow motion ceases. This challenges the common reduction of spatially extended systems to zero-dimensional models and has significant implications for predicting aerosol evolution in decaying turbulence environments.