Turbulent concentration diffusion in multiphase flow Phys. Fluids 24, 093301 (2012) The effects of hydrodynamic interaction and inertia in determining the high-frequency dynamic modulus of a viscoelastic fluid with two-point passive microrheology Phys. Fluids 24, 073103 (2012) The generalized Buckley-Leverett and the regularized Buckley-Leverett equations J. Math. Phys. 53, 053701 (2012) Added mass of a pair of discs Phys. Fluids 23, 103601 (2011) Effect of axial and transverse magnetic fields on the flow behavior of ferrofluids featuring different levels of interparticle interaction Phys. Fluids 23, 093102 (2011) Additional information on Phys. Fluids

The average settling velocity in homogeneous turbulence of a small rigid spherical particle, subject to a Stokes drag force, is shown to depend on the particle inertia and the free-fall terminal velocity in still fluid. With no inertia the particle settles on average at the same rate as in still fluid, assuming there is no mean flow. Particle inertia produces a bias in each trajectory towards regions of high strain rate or low vorticity, which affects the mean settling velocity. Results from a Gaussian random velocity field show that this produces an increased settling velocity.

The average settling velocity in homogeneous turbulence of a small rigid spherical particle, subject to a Stokes drag force, has been shown to differ from that in still fluid owing to a bias from the particle inertia (Maxey 1987). Previous numerical results for particles in a random flow field, where the flow dynamics were not considered, showed an increase in the average settling velocity. Direct numerical simulations of the motion of heavy particles in isotropic homogeneous turbulence have been performed where the flow dynamics are included. These show that a significant increase in the average settling velocity can occur for particles with inertial response time and still-fluid terminal velocity comparable to the Kolmogorov scales of the turbulence. This increase may be as much as 50% of the terminal velocity, which is much larger than was previously found. The concentration field of the heavy particles, obtained from direct numerical simulations, shows the importance of the inertial bias with particles tending to collect in elongated sheets on the peripheries of local vortical structures. This is coupled then to a preferential sweeping of the particles in downward moving fluid. Again the importance of Kolmogorov scaling to these processes is demonstrated. Finally, some consideration is given to larger particles that are subject to a nonlinear drag force where it is found that the nonlinearity reduces the net increase in settling velocity.