Influence of hydrodynamic interactions between particles on the turbulent flow in a suspensio

A model based on the theory of Felderhof and Ooms [Phys. Fluids A 1 (1989) 1091] is used to evaluate the effect of hydrodynamic interactions between particles in turbulent two-phase flows. The particles are assumed to be point-particles, obeying Stokesʹ drag law. The flow of the suspending fluid phase is assumed to be (stochastic) stationary, homogeneous, isotropic turbulence. To simplify the calculations, only two-particle hydrodynamic interactions are taken into account. The value of the reduction function J, which is a measure of the hydrodynamic interactions, is evaluated as a function of the dimensionless wave number and frequency for a range of values of the density ratio between fluid and particles. Only for relatively heavy particles, hydrodynamic interactions affect the reduction function J and the corresponding spectral transfer functions. However, it was found that the effect of the interactions between point-particles could be neglected in turbulent flows, since very little energy is present at the frequencies where the interactions took place.