Numerical models for turbulent fluid-particle flows are reviewed. The two approaches typically used for modeling the dispersed (particle) phase are the trajectory and two-fluid formulations, while volume-averaged models are most common for the continuous (fluid) phase. Thereview is structured according to the turbulence models used for the continuous phase: turbulence energy-dissipation models, large-eddy simulations, direct numerical simulations, and discrete vortex models. The applications of these models to simulate particle dispersion due to fluid turbulence and the adjustments to the models to account for the modulation of the carrier phase turbulence by the particles are addressed.

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Experimental and numerical results concerning solid particle motion in a plane wake are presented that demonstrate the importance of large-scale vortex structures in self-organizing dispersion processes. Previous studies have demonstrated that a time scale ratio involving the aerodynamic response time of the particles and a characteristic time of the vortex structures is an important parameter for indicating the qualitative and quantitative nature of the dispersion process. A stretching and folding mechanism associated with vortex development and merging interactions has been suggested as a description for characterizing particle dispersion in plane mixing layers at intermediate time scale ratios. For plane wakes where large-scale vortex mergers rarely occur, a highly organized particle dispersion process focuses intermediate time scale ratio particles along the boundaries of the large-scale vortices. The fractal correlation dimension associated with chaotic systems is found to be a useful parameter for quantifying the relative organization of the dispersion patterns as a function of the particle time scale ratio.

The three-dimensional mixing layer is characterized by both two-dimensional and streamwise large-scale structures. Understanding the effects of those large-scale structures on the dispersion of particles is very important. Using a pseudospectral method, the large-scale structures of a three-dimensional temporally developing mixing layer and the associated dispersion patterns of particles were simulated. The Fourier expansion was used for spatial derivatives due to the periodic boundary conditions in the streamwise and the spanwise directions and the free-slip boundary condition in the transverse direction. A second-order Adam–Bashforth scheme was used in the time integration. Both a two-dimensional perturbation, which was based on the unstable wavenumbers of the streamwise direction, and a three-dimensional perturbation, derived from an isotropic energy spectrum, were imposed initially. Particles with different Stokes numbers were traced by the Lagrangian approach based on one-way coupling between the continuous and the dispersed phases.The time scale and length scale for the pairing were found to be twice those for the rollup. The streamwise large-scale structures develop from the initial perturbation and the most unstable wavelength in the spanwise direction was found to be about two thirds of that in the streamwise direction. The pairing of the spanwise vortices was also found to have a suppressing effect on the development of the three-dimensionality. Particles with Stokes number of the order of unity were found to have the largest concentration on the circumference of the two-dimensional large-scale structures. The presence of the streamwise large-scale structures causes the variation of the particle concentrations along the spanwise and the transverse directions. The extent of variation also increases with the development of the three-dimensionality, which results in the ‘mushroom’ shape of the particle distribution.

Bevacizumab delayed corneal epithelial wound healing and inhibited integrin expression. When bevacizumab is used to reduce the development of new corneal vessels, slight delays in epithelial wound healing are possible and cellular proliferation is to be expected.