Inertial particles

J. T. Kelly, B. Asqharian, and B. A. Wong. Inertial particle deposition in a monkey nasal mold compared with that in human nasal replicas. Inhal Toxicol 17 823-830... 

When particles change their direction of movement, as for example around bluff bodies such as cylinders or bends in tubing, inertial forces tend to modify their flow paths relative to the suspending gas. Particles may depart from the path of gas molecules (streamlines) and collide with the larger body (Fig. 2). This is the principle underlying inertial particle collectors. 

P. Fede, O. Simonin, P. Villedieu, and K. D. Squires. Stochastic modeling of the turbulent subgrid fluid velocity along inertial particle trajectories. In Proc. of the Summer Program, pages 247-258. Center for Turbulence Research, NASA Ames/Stanford Univ., 2006. 

Ammar, Y. Reeks, M. 2009 Agglomeration of inertial particles in a random rotating symmetric straining flow. International Journal of Multiphase Flow 35, 840-853. 

Zaichik, L. L, Simonin, O. Aupchenkov, V. M. 2003 Two statistical models for predicting collision rates of inertial particles in homogeneous isotropic turbulence. Physics of Fluids 15(10), 2995-3005. 

Figure 2.24 Distribution of heavy inertial particles (j3 = 0) in a stochastic model flow at two different Stokes numbers St = 10-2 (left) and St = 1 (right) (Bee, 2003).

Another interesting effect of the particle inertia is that it can transform non-attracting chaotic sets into chaotic attractors. This has been shown by Benczik et al. (2002) who studied the motion of inertial particles in the time-periodic Karman vortex flow that produces transient chaotic advection of non-inertial particles, while inertial particles are trapped indefinitely in the wake indicating the presence of an attractor. 

E. Balkovsky, G. Falkovich, and A. Fouxon. Intermittent distribution of inertial particles in turbulent flows. Phys. Rev. Lett., 86 2790-2793, 2001a. 

J. Bee. Fractal clustering of inertial particles in random flows. Phys. Fluids, 15 81, 2003. 

J. Bee. Multifractal concentrations of inertial particles in smooth random flows. J. Fluid Mech., 528 255-277, 2005. 

The data suggest that both the initial deposition rate and the asymptotic deposit mass are both dependent upon the bulk velocity u raised to the power 0.6 - 0.7. The results were also compared with the mass transfer rates of Cleaver and Yates [1975] and Metzner and Friend [1958]. Although the dimensionless particle relaxation times (see Section 7.3) were below 0.1, the inertial deposition rates calculated from the theory of Cleaver and Yates were of an order of magnitude higher than the difiusional rates calculated and indeed measured. The measured power on velocity of 0.7 compared to a theoretical value of 0.875 for difrusion and 2 for inertial particle transfer, suggest a diffiision controlled mechanism. 

Figure 3 Schematic filter characteristic of the human respiratory tract for aerosol particles. Three domains can be recognized the domain of deposition decreasing with particle size is solely due to diffusional particle transport, the domain of minimum deposition is due to simultaneous diffusional and gravitational particle transport, and the domain of deposition increasing with particle size due to gravitational and inertial particle transport.

Marple V, Olson BA, Miller NC. The role of inertial particle collectors in evaluating pharmaceutical aerosol delivery systems. J Aerosol Med 1998 11(1) S139-S153. 

In another limiting case of highly inertial particles, it is possible to assume that particles move along straight trajectories. Then the cross section of collision can be found from simple geometrical arguments ... 

Wereley ST, Lueptow RM. (1999) Inertial particle motion in a Taylor Couette rotating filter. Phys. Fluids, 11 325-333. 

Monchaux, R., Bourgoin, M., Cartellier, A. (2012). Analyzing preferential concentration and clustering of inertial particles in turbulence. International Journal of Multiphase Flow, 40, 1-18. 

Chen, L., Goto, S., Vassilicos, J. C. (2006). Turbulent clustering of stagnatimi points and inertial particles. Journal of Fluid Mechanics, 553, 143-154. 

Zhou, Y. Wexler, A.S. and Wang, L.P. Modelling turbulent collision of bidisperse inertial particles. Fluid Mech. 2001,433,77-104. 

Obviously, inertial particles are not capable of exactly following the fluid velocity fluctuations (see also Dehbi, 2008) a drift correction velocity, or a drifting velocity, and an extra time scale pertinent to the turbulence as seen viewed by the particles may be used to take this effect into account (Mudde and Simonin, 1999 VioUet and Simonin, 1994). The result of this drifting velocity is that the particles get dispersed. While usually proper attention is being paid to the Reynolds number restrictions for the use of empirical correlations, these more generic considerations with respect to the details of the fluid mechanics hardly receive attention. 

Kaufmann A, Moreau M, Simonin O, Helie J Comparison between Lagrangian and mesoscopic Eulerian modelling approaches for inertial particles suspended in decaying isotropic turbulence, J Comput Phys 227 6448-6472, 2008. http //dx.doi.org/10. 1016/j.jcp.2008.03.004. 

Pai MG, Subramaniam S Two-way coupled stochastic model for dispersion of inertial particles in turbulence, J Fluid Mech 700 29—62, 2012. http //dx.doi.org/10.1017/jfin. 2012.89. 

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