Average Particle Number Density Research Articles

Explanation of differences in experimental and computational results for the preferential concentration of inertial particles

Using one-way coupled direct numerical simulations of inertial particles in homogeneous isotropic turbulence we investigate the non-linear dependence of local particle concentrations in particle clusters on the number density of particles used in the simulation per volume. We show that the Reynolds-number dependence of local concentrations in clusters can be predicted for sufficiently high Reynolds numbers by a scaling relation that depends on the average particle number density and the Kolmogorov length. Depending on the average particle number density and gravity, a maximum of preferential concentration does not necessarily occur at Stokes numbers around unity. This explains the differences observed between recent experimental and computational results.

Peri-Implant Distribution of Polyethylene Debris in Postmortem-Retrieved Knee Arthroplasties: Can Polyethylene Debris Explain Loss of Cement-Bone Interlock in Successful Total Knee Arthroplasties?

BackgroundLoss of mechanical interlock between cement and bone with in vivo service has been recently quantified for functioning, nonrevised, cemented total knee arthroplasties (TKAs). The cause of interlocking trabecular resorption is not known. The goal of this study is to quantify the distribution of PE debris at the cement-bone interface and determine if polyethylene (PE) debris is locally associated with loss of interlock. MethodsFresh, nonrevised, postmortem-retrieved TKAs (n = 8) were obtained en bloc. Laboratory-prepared constructs (n = 2) served as negative controls. The intact cement-bone interface of each proximal tibia was embedded in Spurr’s resin, sectioned, and imaged under polarized light to identify birefringent PE particles. PE wear particle number density was quantified at the cement-bone interface and distal to the interface, and then compared with local loss of cement-bone interlock. ResultsThe average PE particle number density for postmortem-retrieved TKAs ranged from 8.6 (1.3) to 24.9 (3.1) particles/mm2 (standard error) but was weakly correlated with years in service. The average particle number density was twice as high as distal (>5mm) to the interface compared to at the interface. The local loss of interlock at the interface was not related to the presence, absence, or particle density of PE. ConclusionPE debris can migrate extensively along the cement-bone interface of well-fixed tibial components. However, the amount of local bone loss at the cement-bone interface was not correlated with the amount of PE debris at the interface, suggesting that the observed loss of trabecular interlock in these well-fixed TKAs may be due to alternative factors.

Spatial and temporal distribution of atmospheric aerosols in the lowermost troposphere over the Amazonian tropical rainforest

Abstract. We present measurements of aerosol physico-chemical properties below 5 km altitude over the tropical rain forest and the marine boundary layer (MBL) obtained during the LBA-CLAIRE 1998 project. The MBL aerosol size distribution some 50-100km of the coast of French Guyana and Suriname showed a bi-modal shape typical of aged and cloud processed aerosol. The average particle number density in the MBL was 383cm-3. The daytime mixed layer height over the rain forest for undisturbed conditions was estimated to be between 1200-1500m. During the morning hours the height of the mixed layer increased by 144-180mh-1. The median daytime aerosol number density in the mixed layer increased from 450cm-3 in the morning to almost 800cm-3 in the late afternoon. The evolution of the aerosol size distribution in the daytime mixed layer over the rain forest showed two distinct patterns. Between dawn and midday, the Aitken mode particle concentrations increased, whereas later during the day, a sharp increase of the accumulation mode aerosol number densities was observed, resulting in a doubling of the morning accumulation mode concentrations from 150cm-3 to 300cm-3. Potential sources of the Aitken mode particles are discussed here including the rapid growth of ultrafine aerosol particles formed aloft and subsequently entrained into the mixed layer, as well as the contribution of emissions from the tropical vegetation to Aitken mode number densities. The observed increase of the accumulation mode aerosol number densities is attributed to the combined effect of: the direct emissions of primary biogenic particles from the rain forest and aerosol in-cloud processing by shallow convective clouds. Based on the similarities among the number densities, the size distributions and the composition of the aerosol in the MBL and the nocturnal residual layer we propose that the air originating in the MBL is transported above the nocturnal mixed layer up to 300-400km inland over the rain forest by night without significant processing.

A model for soot formation in a laminar diffusion flame

A simple model has been developed for the prediction of soot volume fractions in a laminar diffusion flame. Measurements and computations of a counterflow flame have been used to evaluate the correlation between soot surface growth rates and the mixture fraction or fuel atom mass fraction. An average particle number density was used to permit the determination of the aerosol surface area. Equations for the momentum, mixture fraction, and soot volume fraction were solved numerically for an axisymmetric laminar diffusion flame. Good agreement was obtained with the measurements for two different experimental conditions.

Entry of solar wind particles into Earth's magnetosphere

Entry of solar wind particles into Earth's magnetosphere is studied. Particles can move directly across an “open” magnetopause layer, where the magnetic field has a nonzero normal component (Bn ≠ 0). Under the assumption that the Walén relation holds near the open magnetopause, the solar wind particle influx can be expressed as , where is the average particle number density, ψB is the open magnetic flux at the magnetopause, μ0 is the permeability of free space, and mi is the ion mass. The total particle flux from the solar wind to the entire magnetosphere for a moderate negative value of IMF Bz is estimated to be ∼7.0×1028 s−1, although most of the particles leave from the antisolar end of the tail without being trapped. The peak flux through the dayside magnetopause is ∼1.1×1027 s−1, while the peak flux through the near‐Earth tail magnetopause (|x| ≤ 30RE) is ∼3.0×1027 s−1. The average particle flux through the dayside and tail magnetopause in the region with |x| ≤ 200RE is found to be ∼7.9×1027 s−1, which is comparable to the tailward particle flux (∼7.1×1027 s−1) observed at |x| ≃ 200 − 220RE in the distant tail. On the other hand, the total flux through the closed magnetopause (Bn = 0) into the boundary layer in the region with |x| ≤ 200RE is estimated to be ∼7×1027 s−1, which is also comparable to the observed flux. For comparison, the ionospheric source contributes a particle flux of only 3 − 5 × 1026 s−1. Thus, the ionosphere can be an important particle source for the inner magnetosphere (|x| ≤ 30RE), but not for the entire tail or entire magnetosphere.

Consistent Fourth Virial Coefficient for a Square-Well Potential Gas

The fourth virial coefficient D is derived for a classical gas composed of particles interacting according to the square-well potential having the form ψ(r) = ∞ for r<1, ψ(r)=—ε for 1<r<2, and ψ(r)=0 for r>2, where ε is the magnitude of the attractive well depth and the hard-core diameter is the unit of distance. The calculations are based on the Born—Green—Yvon equation and the density modified form of the original Kirkwood superposition approximation expression, viz., g(3)(r, s, t) = g(2)(r)g(2)(s)g(2)(t)[1+X1n], where g(2) and g(3) are, respectively, the pair and triplet distributions, n is the average particle number density, and (r, s, t) are the triplet particle-separation distances. The approximation is invoked that X1 is a function of the gas temperature T and of ψ, but is independent of (r, s, t). X1 is chosen in order to ensure consistency between the values of D calculated independently from fluctuation theory and from the virial theorem. The expression derived for X1 in this way is Eq. (21) of the text. Consistent values of D are then to be determined from Eq. (22). Data for D are calculated as function of T according to the present arguments and a comparison is made in the form of a graph with alternative calculated data.