Hydrodynamic interactions between aerosol particles in the transition regime

Abstract

We present a method for calculating the hydrodynamic interactions between particles in the kinetic (or transition regime), characterized by non-negligible particle Knudsen numbers. Such particles are often present in aerosol systems. The method is based on our extended Kirkwood–Riseman theory (Corson et al., Phys. Rev. E, vol. 95 (1), 2017c, 013103), which accounts for interactions between spheres using the velocity field around a translating sphere as a function of Knudsen number. Results for the two-sphere problem at small Knudsen numbers are in good agreement with those obtained using Felderhof’s interaction actions for mixed slip-stick boundary conditions, which are accurate to order $r^{-7}$ (Felderhof, Physica A, vol. 89 (2), 1977, pp. 373–384). The strength of the interactions decreases with increasing Knudsen number. Results for two fractal aggregates demonstrate that one can apply a point force approach for interactions between particles in the transition regime; the interaction tensor is similar to the Oseen tensor for continuum flow. Using this point force approach, we present an analysis for the settling of an unbounded cloud of particles. Our analysis shows that for sufficiently high volume fractions and cloud radii, the cloud behaves as a gas droplet in continuum flow even when the individual particles are small relative to the mean free path of the gas. The method presented here can be applied in a Brownian dynamics simulation analogous to Stokesian dynamics to study the behaviour of a dense aerosol system.

The effect of electric-field-induced alignment on the electrical mobility of fractal aggregates

“…Generally speaking, the mobility ratio is constant with increasing N near the continuum regime and decreases with N in the free molecule regime. At intermediate Knudsen numbers, the aligned versus random behavior becomes more continuum-like at large N; this is analogous to the behavior we have observed for the translational friction coefficient of soot-like aggregates (Corson et al 2017b). We will explain this behavior in Section 4.…”

“…We also show that the ratio of fully aligned to random mobility is a function of the number of primary spheres and the primary sphere size. Near the continuum regime, the mobility ratio is approximately constant with N, and near the free molecule regime, the mobility ratio decreases with N. We discuss this topic in some detail in the SI, but the brief explanation is as follows: the mobility of an aggregate in the continuum and free molecule regimes is roughly inversely proportional to the radius of gyration (Meakin et al 1985;Sorensen 2011;Corson et al 2017b) and the orientation-averaged projected area (Zhang et al 2012), respectively. Similarly, the continuum and free molecule aligned mobilities are correlated to the inverses of the radius of gyration about the major axis of the polarizability tensor (i.e., the z 0 -axis), R gz 0 , and the projected area in the plane normal to the z 0 -axis, PA z 0 (see the SI)s Averaged over 20 cases, the ratio R g =R gz 0 is approximately constant (after accounting for the statistical fluctuations described above) with N, while PA=PA z 0 decreases with N, mirroring the trends in the mobility ratios in the continuum and free molecule limits.…”

“…Beyond the experimental issues mentioned above, it is also difficult to accurately calculate the mobility of a fractal aggregate in the transition regime. We have estimated that our EKR method yields orientation-averaged translational friction coefficients within 10% of the true value (Corson et al 2017b), which translates to uncertainties in any estimate of the primary sphere size or the number of primary spheres. An obvious example is our attempt to fit our results to the data of Li et al (2016), as illustrated by Figure 1: our estimated aggregate sizes (in terms of N) are likely within about 10% of the true value (though the actual error estimate depends on the relationship between N and the friction coefficient).…”

Capture rate consequences of multispherule aggregate formation in gases—combined roles of direct interception and interspherule momentum “shielding”

“…For sufficiently large N aggregates (e.g., N >> 300), we exploited effective porous medium methods (Tandon and Rosner 1995;Rosner andTandon 2017, 2018), using adjusted sphere model (ASM) to embrace the Knudsen transition regime. Efficient computational methods for smaller aggregates, of interest in many applications and to validate ASM, have been recently been developed and illustrated by Corson et al (2017).…”

A computational fluid dynamics study of flame gas sampling in horizontal dilution tubes

“…Thermophoretical effects can eventually accelerate the particle motion relative to the gas in the cooling region in front of the orifice (Saggese et al., 2016). In and behind the orifice, the nanoparticle trajectories can be expected to follow the gas flow and, particle–flow interactions are negligible due to the very small volume fraction (Corson, Mulholland, & Zachariah, 2018; Friedlander, 2000). Hence, as first approximation, two-phase flow modelling is not really mandatory to capture the important flow properties and processes in the dilution tube.…”