Determination of the Scalar Friction Factor for Nonspherical Particles and Aggregates Across the Entire Knudsen Number Range by Direct Simulation Monte Carlo (DSMC)

Abstract

The friction factor of an aerosol particle depends upon the Knudsen number (Kn), as gas molecule-particle momentum transfer occurs in the transition regime. For spheres, the friction factor can be calculated using the Stokes-Millikan equation (with the slip correction factor). However, a suitable friction factor relationship remains sought-after for nonspherical particles. We use direct simulation Monte Carlo (DSMC) to evaluate an algebraic expression for the transition regime friction factor that is intended for application to arbitrarily shaped particles. The tested friction factor expression is derived from dimensional analysis and is analogous to Dahneke's adjusted sphere expression. In applying this expression to nonspherical objects, we argue for the use of two previously developed drag approximations in the continuum (Kn → 0) and free molecular (Kn → ∞) regimes: the Hubbard-Douglas approximation and the projected area (PA) approximation, respectively. These approximations lead to two calculable geometric parameters for any particle: the Smoluchowski radius, R S , and the projected area, PA. Dimensional analysis reveals that Kn should be calculated with PA/π R S as the normalizing length scale, and with Kn defined in this manner, traditional relationships for the slip correction factor should apply for arbitrarily shaped particles. Furthermore, with this expression, Kn-dependent parameters, such as the dynamic shape factor, are readily calculable for nonspherical objects. DSMC calculations of the orientationally averaged drag on spheres and test aggregates (dimers, and open and dense 20-mers) in the range Kn = 0.05-10 provide strong support for the proposed method for friction factor calculation in the transition regime. Experimental measurements of the drag on aggregates composed of 2-5 primary particles further agree well with DSMC results, with differences of less than 10% typically between theoretical predictions, numerical calculations, and experimental measurements.

Morphology and mobility of synthetic colloidal aggregates

“…The expected ferences in the structural and dynamical properties of the generated clusters, even though the numerical constants in Eqs. (14,15) …”

“…clusters to obtain the mean hydrodynamic radius, R h , and an estimate of the hydrodynamic-radius variability, herein chosen to be the ratio of the hydrodynamic radius standard deviation to the mean hydrodynamic radius, Equations (14,15) suggest that neither the fractal dimension nor the fractal prefactor are separately necessary to estimate R h , as it may be fitted solely on N, R g (and, of course, R 1 ). The general dependence may, thus, be simplified via the implicit dependence on k f and d f through…”

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

“…Hogan and coworkers Zhang et al 2012) used an alternative approach to solve the diffusion equation via Brownian dynamics simulations of point mass particles to determine the friction coefficient of power-law aggregates across the entire transition regime.…”

“…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.…”

“…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.…”