- Letter
Variance of the velocity in suspensions of particles does not diverge
Phys. Rev. Fluids 9, L102301 – Published 11 October, 2024Erratum Phys. Rev. Fluids 11, 069901 (2026)
DOI: https://doi.org/10.1103/PhysRevFluids.9.L102301
Abstract
In fluid dynamics, a classic calculation pertaining to suspensions of uniform spheres predicted that the variance of the velocity should diverge with system size. Experiments, on the other hand, find that while the variance grows with system size in small systems, it asymptotes to a fixed value for sufficiently large systems. Here, I show that this discrepancy between theory and experiment is resolved by accounting for the inertia of the particles. Using the unsteady Stokes‘ Green’s functions, the leading order contribution to the variance is determined to be finite for systems of infinite extent.
