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The study of Lagrangian turbulence and of turbulent transport of material particles has received growing interest in recent years. New experimental techniques based on multiple fast cameras, silicon strip detectors, or ultrasonic or laser Doppler velocimetry allows nowadays to track simultaneously thousands of particles in highly developed turbulent flows. When the particle density is different from the one of the carrying fluid and/or when the particle-size is large as compared to the dissipative turbulent-scale, interesting not yet fully explored effects emerge. While Lagrangian investigations through Direct Numerical Simu- lations of passive tracers have provided good support to the experimental measurements, the study of finite-size particles turns out to be extremely difficult. Several hydrodynamical effects - such as drag, added mass, lift, and history force - require careful modeling. In this condition, even for dilute suspensions, a Lagrangian equation of motion for a finite-size particle is presently not available. Here we propose a model equation which considers the finite- size corrections of the classical point-particle equation derived by Maxey & Riley (1983). The proposed model deals with the corrections to the pressure gradient force, the added mass force and the drag term. The original part of the model is the introduction of suitable volume and surface averages of the fluid velocity and acceleration, which are able to account for the so called first Faxen corrections and for higher order corrections terms. |
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