The objective of the paper is to present a statistical model for predicting pair dispersion and preferential concentration of particles suspended in an isotropic homogeneous turbulent flow field. This model is based on a kinetic equation for the probability density function of the relative velocities of two particles. The model developed is applied to predict the pair relative velocity statistics and the accumulation effect of heavy particles in a steady-state suspension. The effect of particle inertia on the predicted Eulerian two-point particle velocity correlations is demonstrated and compared with known results of numerical simulation.

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The objective of the paper is to present and compare two models for the collision rate of inertial particles immersed in homogeneous isotropic turbulence. The merits and demerits of several known collision models are discussed. One of the models proposed in the paper is based on the assumption that the velocities of the fluid and a particle obey a correlated Gaussian distribution. The other model stems from a kinetic equation for the probability density function of the relative velocity distribution of two particles. The predictions obtained by means of these two models are compared with numerical simulations published in the literature.

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This paper presents two statistical models for predicting collision rates of bidisperse heavy particles suspended in homogeneous isotropic turbulence. One of the models is based on the assumption that the joint fluid-particle velocity distribution function is Gaussian. The other model stems from a kinetic equation for the two-point probability density function of the velocity distributions of two particles. The validity of these models is tested against DNS data by Zhou, Wexler, and Wang [J. Fluid Mech. 433, 77 (2001)]. Comparisons between the model predictions and DNS results demonstrate encouraging agreement.

The purposes of the paper are threefold: (i) to refine the statistical model of preferential particle concentration in isotropic turbulence that was previously proposed by Zaichik and Alipchenkov [Phys. Fluids 15, 1776 (2003)], (ii) to investigate the effect of clustering of low-inertia particles using the refined model, and (iii) to advance a simple model for predicting the collision rate of aerosol particles. The model developed is based on a kinetic equation for the two-point probability density function of the relative velocity distribution of particle pairs. Improvements in predicting the preferential concentration of low-inertia particles are attained due to refining the description of the turbulent velocity field of the carrier fluid by including a difference between the time scales of the of strain and rotation rate correlations. The refined model results in a better agreement with direct numerical simulations for aerosol particles.

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The objective of the paper is to elucidate a connection between two approaches that have been separately proposed for modelling the statistical spatial properties of inertial particles in turbulent fluid flows. One of the approaches proposed recently by Février, Simonin, and Squires ͓J. Fluid Mech. 533, 1 ͑2005͔͒ is based on the partitioning of particle turbulent velocity field into spatially correlated ͑mesoscopic Eulerian͒ and random-uncorrelated ͑quasi-Brownian͒ components. The other approach stems from a kinetic equation for the two-point probability density function of the velocity distributions of two particles ͓Zaichik and Alipchenkov, Phys. Fluids 15, 1776 ͑2003͔͒. Comparisons between these approaches are performed for isotropic homogeneous turbulence and demonstrate encouraging agreement.