A non-inertial model for particle aggregation under turbulence
arxiv(2024)
摘要
A new model for particle coalescence in a turbulent environment is presented,
aiming to prove that turbulence enhances coalescence, for small-moderate Stokes
numbers. The model is non-inertial, namely the velocity of particles is the
velocity of the fluid; and a variant of Stokes number is introduced, based on
space scales. Particles interact by coalescence and a sparse local regime is
chosen, but instead of independent Brownian motions acting on different
particles, we impose a common noise, modeling the turbulent fluid and having a
length scale. In the scaling limit it becomes delta correlated and gives rise
to a deterministic limit PDE for the density. The mean coalescence rate in this
limit equation is not the trivial one of mean field theory but, through the
solution of an auxiliary cell-equation, incorporates in the right qualitative
way the dependence on the Stokes number and the turbulent kinetic energy.
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