Particle mass density

Secondary nucleation results from the presence of solute particles in solution. Recent reviews [16,17] have classified secondary nucleation into three categories apparent, true, euid contact. Apparent secondary nucleation refers to the small fragments washed from the surface of seeds when they are introduced into the crystallizer. True secondary nucleation occurs due simply to the presence of solute particles in solution. Contact secondary nucleation occurs when a growing particle contacts the walls of the container, the stirrer, the pump impeller, or other particles, producing new nuclei. A review of contact nucleation, frequently the most significant nucleation mechanism, is presented by Garside and Davey [18], who give empirical evidence that the rate of contact nucleation depends on stirrer rotation rate (RPM), particle mass density, Mj>, and saturation ratio. 

Deposition in the thoracic region is the sum of aerodynamic and thermodynamic deposition of particulate material. Aerodynamic deposition depends on aerodynamic particle size, total volumetric flow rate, anatomical dead space, tidal volume, functional residual capacity (FRC) (combined residual and expiratory reserve volume or the amount of air remaining in the lungs after a tidal expiration) and diameter of the airways. Thermodynamic deposition depends on anatomical and physical characteristics, such as tidal volume, anatomical dead space, functional residual capacity and the transit time of air within each region. Thermodynamic particle size, which is derived from the diffusion coefficient, particle shape factor and the particles mass density, influence thermodynamic deposition. 

Particle mass density (p) is assumed to be triangularly distributed ranging from 1 to 10g-cm with a mode of 3g-cm (ICRP, 1994). The ICRP recommends a reference value of 3g-cm, because it is a typical value for many natural materials. The assumed range includes particles such as polystyrene, Teflon, iron oxide and uranium oxide (ICRP, 1994). 

Although the estimates of deposition in the respiratory tract are generally most sensitive to the input parameters of trachea diameter (<4), particle mass density (p), and... 

Breathing rate, trachea diameter and particle mass density have the greatest infiuence on particulate deposition for 1 pm AMAD particles. 

Generally, fractional deposition in the lung, as modeled in ICRP 66 (1994), is directly proportional to particle mass density and BR, and inversely proportional to trachea diameter. Other parameters play a relatively minor role in modefing regional deposition within the respiratory tract for adults, adolescents and 10-year-old children. The parameters of anatomical dead space and windspeed are more important to deposition in infants and children. Research into these more sensitive parameters and their distributions may lead to reduction in the uncertainty of... 

Countercurrent Separation and Elutriation. The process known as elutriation in cell separation is a refined method for separation of cells having close mass densities. Cells can be separated by making use of differences in the critical velocity of cells. If the mass densities of two cells are identical, but the sizes are different, then the larger particle has a higher critical velocity than the smaller one. 

On a given metallic particle, the repulsive force, E, is dependent on particle mass, AF electrical conductivity. O density, p and shape, s. 

Panicles entrained in the airstream deposit along the airway as a function of size, density, airstream velocity, and breathing frequency. Sizes of rougjily spherical or irregularly shaped particles arc commonly characterized by relating the settling velociiy of the particle to that of an idealized spherical particle. For example, an irregular particle which settles at the same rate as a 5 pm spherical particle has a mean mass aerodynamic diameter (MMAD) of. 5 pm. Since spherical particle mass, is a function of particle diameter, J... 

Pj = solids density (kg m" ) d = particle mass median diameter (m)... 

Since cyclones rely on centrifugal force to separate particulates from the air or gas stream, particle mass is the dominant factor that controls efficiency. For particulates with high densities (e.g., ferrous oxides), cyclones can achieve 99 per cent or better removal efficiencies, regardless of particle size. Lighter particles (e.g., tow or flake) dramatically reduce cyclone efficiency. 

In order to examine the nature of the friction coefficient it is useful to consider the various time, space, and mass scales that are important for the dynamics of a B particle. Two important parameters that determine the nature of the Brownian motion are rm = (m/M) /2, that depends on the ratio of the bath and B particle masses, and rp = p/(3M/4ttct3), the ratio of the fluid mass density to the mass density of the B particle. The characteristic time scale for B particle momentum decay is xB = Af/ , from which the characteristic length lB = (kBT/M)i lxB can be defined. In derivations of Langevin descriptions, variations of length scales large compared to microscopic length but small compared to iB are considered. The simplest Markovian behavior is obtained when both rm << 1 and rp 1, while non-Markovian descriptions of the dynamics are needed when rm << 1 and rp > 1 [47]. The other important times in the problem are xv = ct2/v, the time it takes momentum to diffuse over the B particle radius ct, and Tp = cr/Df, the time it takes the B particle to diffuse over its radius. 

Figure 1. Attrition modes and their effects on the particle size distribution (q3 = mass density distribution).

Such an approach is conceptually different from the continuum description of momentum transport in a fluid in terms of the NS equations. It can be demonstrated, however, that, with a proper choice of the lattice (viz. its symmetry properties), with the collision rules, and with the proper redistribution of particle mass over the (discrete) velocity directions, the NS equations are obeyed at least in the incompressible limit. It is all about translating the above characteristic LB features into the physical concepts momentum, density, and viscosity. The collision rules can be translated into the common variable viscosity, since colliding particles lead to viscous behavior indeed. The reader interested in more details is referred to Succi (2001). 

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