Aggregation- and rarefaction-effects on particle mass deposition rates by convective-diffusion, thermophoresis or inertial impaction: Consequences of multi-spherule ‘momentum shielding’

Abstract

At the same total spherule volume fraction in a gaseous mainstream, we predict the significant alteration of mass deposition rate attending extensive aggregation—illustrating our methods and results here not only for a mainstream of single-sized cluster aggregates, but also for coagulation-aged (near log-normal) distributions of large fractal-like aggregates (Ng = O(103), Df = 1.8 (DLCAs) or Df = 2.1 (RLCAs)) compared to isolated spherule deposition in the same environment. Because of their drastically different sensitivities to aggregation, we consider, sequentially, the particle transport mechanisms of either: ordinary isothermal convective-diffusion, thermophoresis (to a cooled solid target) or inertial impaction (without rebound). Using a rather general formulation (which incorporates Knudsen transition effects expected at elevated pressures) but neglecting direct “interception” effects, we find that for, say, Df = 2.1, N = O(103), Kn1: = mfp/R1 = 1, if convective-diffusion (with Sc >> 1) were the dominant mechanism then mainstream aggregation would decrease expected mass deposition rates to much larger targets by somewhat more than one decade. However, for thermophoresis aggregation would increase deposition rates by approximately somewhat more than one decade, and, for, say, “eddy impaction” (in a fully turbulent duct flow) aggregation would increase deposition rates by as much as nearly 1.5 decades. Physically, these large aggregation enhancement-ratios for deposition by thermophoresis or particle Inertial Impaction are attributed to drag reduction (per spherule) associated with “momentum shielding”—analogous to the aerodynamic advantages that birds, fish, bicyclists, runners,… experience when “in formation”. Using this approach, other impaction geometries and Knudsen number situations are also readily treated, as well as more “compact” even porous (Df = 3) aggregate populations. These predictive methods, illustrative results, and conclusions are expected to be useful to investigators seeking to maximize (or minimize) particle deposition rates on solid targets by exploiting control over the spherule aggregation process in the mainstream. As an important corollary, our methods also enable the quantitative deconvolution of aggregated aerosol sampling data, i.e., correcting for the systematic distortion (falsification) of sampled aggregate size distributions, pdfw(N), brought about by the size-dependent capture coefficients associated with momentum-shielding (nearly power-law: Smom ∼ Nk) for each of the mechanisms considered here (C-D, T-P, or E-I; Section 5)). As demonstrated in Section 6.3, while we expect Log-Normal-type distributions to retain their shape, we predict the systematic correction factors needed to obtain the mean and median aggregate sizes ((Formula presented.) and Ng) that must have existed in the mainstream (see Equation (30)). These correction factors become quite significant for each of the mechanisms (especially thermophoresis and impaction) when the mainstream aggregate size-spread is large (e.g., σg > ca. 2) and the pressure is high enough to cause Kn1 to drop to O(1). For completeness, the systematic consequences of the appreciable effective size of N >> 1 cluster aggregates, briefly discussed in Section 6.2, will need to be included, especially for the deposition of Df < 2 fractal-like aggregates on targets not much larger than the aggregates themselves (e.g., depth filter fibers,…). However, for capture by sufficiently large targets a noteworthy conclusion is that, of the distinct aerosol transport mechanisms considered here, isothermal convective-diffusion stands out as the only mechanism for which isolated spherules will deposit more efficiently than large-N cluster aggregates (when compared in the same flow environment at the same mainstream spherule volume fraction). Copyright © 2018 American Association for Aerosol Research.