Second-order stochastic modeling of particle resuspension: macroscopic degeneracy and anomalous pre-detachment transport

Abstract

Particle resuspension models are commonly evaluated using the macroscopic resuspended fraction, although this integrated observable may conceal the temporal dynamics leading to detachment. Here, a second-order Markovian Lagrangian stochastic model is developed by augmenting the angular-velocity state with a finite-correlated tangential acceleration. The model is examined over turbulent channel flows with ($Re_τ\in [60, 430]$) and compared with an established first-order formulation. The two models produce nearly overlapping resuspended fractions, revealing a macroscopic degeneracy between distinct stochastic descriptions. Multiscale trajectory statistics break this degeneracy. The acceleration-augmented formulation changes the short-time regularity from $S_2(τ) \propto τ$ to $S_2(τ) \propto τ^2$, sustains angular-velocity correlation, and produces stronger directional asymmetry and heavier increment tails. The survivor-conditioned mean square displacement exposes a Reynolds-number-dependent anomalous-transport window, in which the attached-particle ensemble grows more rapidly than the diffusive reference and locally approaches ballistic and super-ballistic scaling before crossing toward diffusion-like transport. This finite-time pathway records how particles approach detachment and is compressed out of the macroscopic resuspended fraction. At $Re_τ\approx 60$, the trajectories enter a distinct low-Reynolds-number statistical state characterized by converging velocity and acceleration decorrelation and near-Gaussian increments. These results establish multiscale trajectory statistics as essential discriminants between stochastic resuspension models and identify finite acceleration correlation as a source of dynamical information beyond macroscopic detachment kinetics.