The inertial It\^o drift and its applications to particle collision

Abstract

The small mass $\mu$ limit of an inertial system driven by an Ornstein Uhlenbeck fluid force, with correlation time $\epsilon$ going to zero, leads to a first order system with an additional drift, which we call inertial-It\^{o}-drift, depending on the limit $\alpha$ of the ratio $\mu/\epsilon$; the drift being zero when $\alpha=0$, corresponding to the Stratonovich integral in the limit equation, as in the Wong-Zakai theory, when applied directly to the first-order system with Ornstein-Uhlenbeck driver. We discuss the application of this result to particles driven by Stokes force;\ we identify inertial centrifugal effects and the so-called turbophoretic effect, as examples of the inertial-It\^{o}-drift. We also analyze concentration effects and their link with the theory of particle collision in turbulent fluids.