Slip correction factors for nonspherical bodies—III the form of the general law

A semi-analytical model describing the motion of fibrous particles ranging from nano-to micro scale was developed, and some important differences in respiratory tract transport and deposition between fibrous particles of various sizes and shapes were elucidated. The aim of this work was to gain information regarding health risks associated with inhalation exposure to small fibers such as carbon nanotubes. The model, however, is general in the sense that it can be applied to arbitrary flows and geometries at small fiber Stokes and Reynolds numbers. Deposition due to gravitational settling, Brownian motion and interception was considered, and results were presented for steady, laminar, fully developed parabolic flow in straight airways. Regarding particle size, our model shows that decrease in particle size leads to reduced efficiency of sedimentation but increased intensity of Brownian diffusion, as expected. We studied the effects due to particle shape alone by varying the aspect ratios and diameters of the microfibers simultaneously, such that the effect of particle mass does not come into play. Our model suggests that deposition both due to gravitational settling and Brownian diffusion decreases with increased fiber aspect ratio. Regarding the combined effect of fiber size and shape, our results suggest that for particles with elongated shape the probability of reaching the vulnerable gas-exchange region in the deep lung is highest for particles with diameters in the size range 10-100 nm and lengths of several micrometers. Note that the popular multi-walled carbon nanotubes fall into this size-range.

Section: Hydrodynamic Force and Torquementioning

confidence: 99%

Section: Hydrodynamic Force and Torquementioning

confidence: 99%

Respiratory Deposition of Fibers in the Non-Inertial Regime—Development and Application of a Semi-Analytical Model

Högberg

Åkerstedt

Lundström

et al. 2010

“…Preining (1967) presented a method of calculating the slip correction for ellipsoids at intermediate Kn from the formula of Fuchs and Stechkina, by using a single size parameter related to D A p The method is confined to low axis ratios. Dahneke (1973) proposed an adjusted sphere method to approximate the slip correction factor of nonspherical particles based on the knowledge of a particle's drag force in the continuum and free molecule limits F $ and F,*. Interpolation of intermediate values is conveniently based on the Knudsen-Weber formula…”

Section: Determination Of the Slip Coefficientmentioning

confidence: 99%

Dynamics and Measurement of Smokes. II The Aerodynamic Diameter of Chain Aggregates in the Transition Regime

Kasper

1982

Aerodynamic diameters of linear Fez O3 chain aggregates with up to 160 primary particles ranging in mean diameter from 0.035 to 0.12 pm were measured with a cylindrical aerosol centrifuge. Aerodynamic diameters closely follow the semiempirical expression DAE,,, = k (~l~~)~l~B~ exp(l.5 InZ og)ii'16, were pIpo is the ratio of particle density to unit density; Dl and og are the mean diameter and geometric standard deviation of the primary particles, respectively; and n is the average number of primary particles in a chain found at the location corresponding to DAE . The coefficient kis a function of 4 only. In the continuum limit (a 5 0.02 pm) k appears to reach a constant value that is consistent with earlier measurements by Stoher et al. (1970). The results suggest a predominant settling orientation normal to the chain axis for centrifuge measurements. terminal settling velocity of a particle (cm/sec) q dynamic gas viscosity (g/cm sec)i, mean free path of gas p bulk particle densitygeometric standard deviation of primary particle size distribution

“…To our knowledge, the only theory applicable over the entire transition regime is the Adjusted-Sphere Method (ASM) introduced by Dahneke (1973) and more recently used by Hogan and co-workers Zhang et al 2012). Accordingly, a virtual adjusted sphere is posited to exist, whose radius R adj is constant and independent of flow conditions.…”

Section: Introductionmentioning

confidence: 99%

“…It has been applied to geometric objects (Dahneke 1973), straight chains (Dahneke 1982), and fractal-like aggregates (Zhang et al 2012), while different authors have used it to analyze experimental results (Rogak and Flagan 1992;Shapiro et al 2012). The proper hydrodynamic radius of an aggregate is the equivalent mobility radius.…”

Section: Introductionmentioning

confidence: 99%

Friction Coefficient and Mobility Radius of Fractal-Like Aggregates in the Transition Regime

Melas

Isella

Konstandopoulos

et al. 2014

The influence of geometric properties and particle size on mobility properties of fractal-like aggregates was studied in the mass and momentum-transfer transition regimes. Two methodologies were investigated. The Collision Rate Method (CRM) that determines the slip correction factor through the ratio of two fictitious Brownian particle-aggregate effective collision rates, and the Adjusted Sphere Method (ASM) that assumes the existence of a virtual, flowindependent adjusted sphere with the same slip correction factor as the aggregate over the entire transition regime. The simulated fractal-like aggregates were synthetic as they were generated via a cluster-cluster agglomeration algorithm. The CRM was used to calculate the adjusted-sphere radius of various aggregates: we found it to be weakly dependent on the monomer Knudsen number for Kn greater than 0.5. Numerical expressions for the aggregate orientationally-averaged projected area and the adjusted-sphere radius are proposed. Both expressions depend on geometric, nonensemble averaged quantities: the radius of gyration and the number of monomers. The slip correction factor and the mobility radius of DLCA and RLCA aggregates were calculated using the ASM: for a given number of monomers, fractal dimension and prefactor, and Knudsen number their values were approximately constant (averaged over aggregate realizations). A fractal-like scaling law based on the mobility radius was found to hold. The mobility fractal dimension and prefactor were determined for different aggregates. The hydrodynamic radius, proportional to the friction coefficient, © 2014 European Union Received 4 July 2014; accepted 8 October 2014. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons. org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium provide the original work is properly cited. The moral rights of the named author(s) have been asserted.Address correspondence to Yannis Drossinos, European Commission, Joint Research Centre, Ispra, VA I-21027, Italy. E-mail: ioannis. drossinos@jrc.ec.europa.eu Color versions of one or more of the figures in the article can be found online at www.tandfonline.com/uast. and the dynamic shape factor of DLCA and RLCA aggregates were also calculated.