Ballistic deposition model

Void [52] developed a variety of ballistic deposition models to simulate sedimentation processes. Void used ballistic models to determine deposition densities for spherical particles which traveled via vertical paths and were deposited on horizontal surfaces. Recently, Schmitz et al. [53] used a ballistic aggregation model to describe particle aggregation at the surface of a crossflow microfiltration membrane. Schmitz and co-workers were able to account for interfacial forces empirically, and demonstrated the influence of physical and chemical variables on the resulting morphology of the fouling deposits (such as aggregate density variation with depth, and influence of shear flow and re-entrainment properties on fouling deposit density and porosity). 

Family, F. and Vicsek, T., Scaling of the active zone in the Eden process on percolation networks and the ballistic deposition model, J. Phys. A, 18, E75, 1985. 

Schlichting H. Boundary-layer theory. New York McGraw-Hill Book Company 1979. Tennekes H, Lumley JL. A first course in turbulence. Cambridge, MA MIT Press 1972. Dasgupta R, Roy S, Tarafdar S. Correlation between porosity, conductivity and permeability of sedimentary rocks—a ballistic deposition model. Physica A Stat Mech Appl 2000 275 22-32. Bejan A, Nield DA. Convection in porous media. New York Springer 2006. 

Surface scaling parameters for a number of nonequilibrium atomistic models have also been established [6, 10]. Continuum equations for the surface motion have to be used to find a solution for discrete models. Thus, for ballistic deposition [14] and the Eden model [15] the inter ce saturates, resulting in a = 1/2 and P = 1/3 for Z>pop = 2, and a 0.35 and 0.21 for Z>top = 3. Conversely, from the random deposition model P - 1/2 and, since the correlation length is always zero, fire interface does not saturate and, therefore, a is not defined. Depending on the rules used in the simulations, for the atomistic model including surfece difrusion a = 3/2 and p = 3/7 [6], a = 3/2 and p =... 

These data are confined to particles fully entrained in the inspired air. When particles are, however, inspired from propellant-based metered-dose or dry-powder inhalers, their velocity is much greater than that of the inspired air, and only a small mass fraction (nonballistic fraction) escapes inertial deposition in the oropharynx and enters the trachea. The mass fraction of particles deposited in the oropharynx (ballistic fraction) can be determined experimentally. It comprises more than 50% of the mass released from inhaler devices and therefore is much larger than that deposited in the larynx. It is usually assumed that the ballistic fraction is equal to the mass fraction collected in an induction port placed in front of a cascade impactor. Collection of particles in the impactor allows the estimation of the mass distribution of particles entering the respiratory tract. Finally, these distributions can be used to calculate regional mass depositions with a deposition model. 

Using the ICRP deposition model, Pritchard et al. (6) were able to demonstrate that this approach is suitable to predict extrathoracic (oropharyngeal) and thoracic mass deposition of particles released from a dry powder inhaler obtained by the radiotracer technique (Fig. 14). The ballistic fraction comprised 50-70% of the particle mass but only about 12% were deposited in thoracic airways and airspaces of 19 patients. 

Clark et al. (40) developed what is a mathematically similar approach to Theil s, which was applied to both DPIs and pMDIs plus spacer and chambers. (Clark et al. deliberately avoided using data from pMDIs alone because of the difficulties associated with the ballistic nature of the plume.) The basis of the technique is the assumption that lung deposition is simply the inhaled dose minus that deposited in mouth and oropharynx. This approach does not require the application of a lung deposition model and is justified for most DPIs and pMDI since the fractions exhaled after a typical 5- to 10-s breath-hold are always close to zero. As an oral deposition function, Clark et al. chose to use the function proposed by Stahlhofen et al. and Rudolf et al., which is then numerically integrated with the size distribution derived from cascade impactor data to calculate oral deposition. Subtracting oral deposition from the inhaled dose allows calculation of the lung dose. Clark used gamma camera data from seven clinical studies, four DPI and three pMDI, to evaluate the approach. On analysis, it was seen that... 

The value of a for Lg > dg agrees with those values obtained from large scale computer simulations of 3D deposits generated by Eden [42] or ballistic models... 

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