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 (N g D O(10 3), D f D 1.8 (DLCAs) or D f D 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 convectivediffusion, 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, D f D 2.1, N D O(10 3), Kn 1 : D mfp/R 1 D 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 (D f D 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, pdf w (N), brought about by the size-dependent capture coefficients associated with momentum-shielding (nearly power-law: S mom » N k) 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 (N and N g) 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 ...

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

“…ception ("point-mass" particles) is itself O(1) (Rosner 2000). It follows from A1 and A4 that in effect we are assuming: Stk 1 << Stk N << Stk crit (Rosner and Tandon 2018).…”

“…ception ("point-mass" particles) is itself O(1) (Rosner 2000). It follows from A1 and A4 that in effect we are assuming: Stk 1 << Stk N << Stk crit (Rosner and Tandon 2018). These simultaneous conditions will be seen to be satisfied in our illustrative calculations for the "initial" spherule capture rate of, say, N D 1000 DLCAs by a repre-sentative 10 micron diameter fiber filter with a solid fraction of 0.05 ( Figure 1, Section 4).…”

“…These simultaneous conditions will be seen to be satisfied in our illustrative calculations for the "initial" spherule capture rate of, say, N D 1000 DLCAs by a repre-sentative 10 micron diameter fiber filter with a solid fraction of 0.05 ( Figure 1, Section 4). For cluster aggregates comprised of N-spherules, the corresponding result is simply: Stk N D S mom (Kn 1 ,N; CA-structure) Ã Stk 1 , where S mom is the dimensionless momentum shielding function introduced in Rosner andTandon (2017, 2018) and shown plotted (for DLCAs) in Figure 2. Thus, we consider a "clean" (initially unloaded) filament.…”

“…Using what is now known about the mobility of large multispherule cluster-aggregates (CAs), we recently showed (Rosner and Tandon 2018) that, for uncharged aerosol deposition on much "larger" stationary targets, isothermal convective-diffusion (C-D) is the only transport mechanism (compared to thermophoresis (T-P) or inertial impaction (I-I)) for which aggregation in the mainstream (at constant spherule volume fraction, f s,1 << 1) that will cause a reduction in total spherule deposition rate across the entire Knudsen number range-(including the continuum limit [Kn 1 << 1-which requires elevated pressures for sub-100 nm diameter spherules]). Moreover, this reduced deposition rate (cf.…”

Knudsen transition effects on the thermophoretic properties of fractal-like aggregates: Implications for thermophoretic sampling of high-pressure flames

“…On this basis we conclude that apparent soot volume fractions calculated from total spherule counts on TEM grids at flame pressures near 50 bar using previously available methods would be systematically high by as much as one decade. This is but one dramatic consequence of the fact that such aggregates will no longer find themselves in the more familiar "free-molecule" regime, i.e., their spherules can take advantage of increased "momentum shielding" (Rosner and Tandon 2017).…”