Role of molecular diffusion on pair dispersion in isotropic turbulent flows

Turbulent pair dispersion is a central problem in turbulent transport and mixing. In the present work, we explore the effect of molecular diffusion, characterized by the Schmidt number Sc≡ν/D that is the ratio of the fluid viscosity to the molecular diffusivity, on pair dispersion by theoretical analysis and direct numerical simulation (DNS). The Schmidt number investigated in DNS covers the range of 10−2≤Sc≤103. Overall, the relative motion caused by molecular diffusion is more important at scales below characteristic length and time scales that are Schmidt number-dependent. Depending on whether Sc is smaller or larger than a transition value ScT≈0.14, the relative motion between particle pairs would experience different regimes of dynamics. Moreover, for mean squared separation ⟨r2⟩, there exists an optimal Schmidt number Scop≈1 that results in a growth of ⟨r2⟩ closest to the Richardson's t3 law. On the probability distribution of particle pair distance (or the distance neighbor function, DNF), molecular diffusion decreases DNF and, equivalently, overcompensates the corresponding effective diffusivity K(r,t) in the Richardson's diffusion equation, for pair distance r in the small-scale range.