Calculating the rotational friction coefficient of fractal aerosol particles in the transition regime using extended Kirkwood-Riseman theory

Abstract

We apply our extended Kirkwood-Riseman theory to compute the translation, rotation, and coupling friction tensors and the scalar rotational friction coefficient for an aerosol fractal aggregate in the transition flow regime. The method can be used for particles consisting of spheres in contact. Our approach considers only the linear velocity of the primary spheres in a rotating aggregate and ignores rotational and coupling interactions between spheres. We show that this simplified approach is within approximately 40% of the true value for any particle for Knudsen numbers between 0.01 and 100. The method is especially accurate (i.e., within about 5%) near the free-molecule regime, where there is little interaction between the particle and the flow field, and for particles with low fractal dimension (≲2) consisting of many spheres, where the average distance between spheres is large and translational interaction effects dominate. Our results suggest that there is a universal relationship between the rotational friction coefficient and an aggregate Knudsen number, defined as the ratio of continuum to free-molecule rotational friction coefficients.

Characterisation of a charged particle levitated nano-oscillator

“…Furthermore, it only works for spheres and it can therefore be challenging to differentiate a single sphere from a cluster. Indeed, in the case of two particles joined together such as a nanodumbbell, the expected linewidth should be smaller by 8 % compared to a sphere (independently from the size of the spheres and assuming a stochastic rotational motion of the dumbbell) [41], which is comparable to the statistical uncertainty of the measurement shown here. In comparison, a change in mass by a factor 2 for a spherical object corresponds to a reduction in linewidth by 21 %, easier to measure.…”

Analytical expression for the rotational friction coefficient of DLCA aggregates over the entire Knudsen regime

“…Unfortunately, in many practical situations aerosol particles are fractal-like aggregates in the transition flow regime, so a different approach is needed to analyze their rotational behavior. Recently, we (Corson et al 2017c) demonstrated that our extended Kirkwood-Riseman (EKR) method (Corson et al 2017a,b) can be applied to the rotational problem.…”

“…In addition, one would now need to invert a 6N-by-6N matrix (instead of a 3Nby-3N matrix, as in our current method) to obtain the translational, rotational, and coupling friction tensors. .See Corson et al [2017c] for further discussion./ Rotational and coupling hydrodynamic interactions are weaker (i.e., lower order in r ij ) than the translational hydrodynamic interactions described by T $ ij , so we ignore these effects in our EKR method. The resulting error is appreciable (around 30-40%) for very small, dense (i.e., high fractal dimension) aggregates but decreases as the aggregate size (and thus the average distance between spheres) increases (Corson et al 2017c).…”

“…For particles formed by diffusion-limited cluster aggregation (DLCA), which is the focus of this work, k 0 % 1:3 and d f % 1:78. In this article, we build on our prior work on the rotational friction coefficient of aggregates (Corson et al 2017c). Here, we apply our extended Kirkwood-Riseman (EKR) theory to determine the rotational friction coefficient of DLCA aggregates over a parameter range of interest to aerosol scientists.…”

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We apply a self-consistent field method (Corson et al 2017c) to calculate the rotational friction coefficient for fractal aerosol particles in the transition flow regime. Our method considers hydrodynamic interactions between spheres in a rotating aggregate due to the linear velocities of the spheres.

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