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

Abstract

Our recent work on the consequences of multispherule cluster aggregate (CA) formation and deposition-rates on much larger solid targets has emphasized the decisive role of "momentumshielding" in determining aggregate "mobility" compared to N isolated spherules in the same gaseous environment-an effect analogous to the drag-reduction advantages experienced by birds electing to move "in formation." The extent of "momentum shielding" is conveniently quantified via a dimensionless function: S mom (N;Kn 1 , aggregate structure), which facilitates predicting the depositionrate consequences of aggregation in aerosol flow systems when the cluster deposition mechanism is dominated by either: (i) isothermal convective-diffusion (C-D), (ii) thermophoresis (T-P) or: (iii) inertial impaction (I-I). Significantly, isothermal C-D was found to be the only transport-mechanism leading to aggregation-induced reductions in spherule deposition rates on large targets (cf. isolated spherules present at the same mainstream spherule volume fraction). However, we demonstrate here that, for aggregate deposition on sufficiently small solid targets-e.g., fibrous filter elements with diameters of O(10 mm)-even these reductions, which exceed one decade for N D O(10 3), can be overcome by the mechanism of "direct-interception" (D-I) associated with nonzero effective aggregate size, without the need to invoke either inertial impaction or thermophoresis. This is especially true for Diffusion-Limited (i.e., "open") CAs (with D f D 1.8) at gas pressures such that the constituent spherules are near the continuum (Kn 1 << 1) limit. Our present analysis and numerical illustrations exploit the fact that direct-interception is expected to play a negligible role for the capture of individual (dense) nanospherules (perhaps comparable in size to the prevailing gas molecule mean-free-path) but the underlying theory, exploited, extended, and illustrated here, was developed with the help of initial capture rate experimental data for much larger diameter (but unaggregated) aerosols on single filter fibers in low Re crossflow. With such small diameter targets, we demonstrate that this "interception" augmentation for large CAs can occur even for the limiting case of rcp D f D 3 aggregates, before the expected onset of CA-inertial effects-i.e., Stk N << Stk crit , where, for Re D O(1), Stk crit is also O(1). A simple method is also presented for predicting interception-modified spherule deposition rates in the presence of log-normal type aggregate size distributions.

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

“…By balancing the total thermal force (as recently predicted /correlated for a single isolated spherule in a local temperature gradient by Young [2011]) on an N-spherule fractal aggregate against the transition regime total orientation-averaged aggregate drag (Section 2 above), we have recently predicted (Rosner and Tandon 2017) N-dependent dimensionless aggregate TP-diffusivities.…”

“…This is a physical consequence of the growing importance of gasgas molecular encounters as one leaves the free-molecule domain (where only gas molecule/solid encounters need be accounted for). Not surprisingly, at each Kn 1 the momentum shielding increases with N-nearly as a power-law (see Section 5.7 and Rosner and Tandon 2017). When dealing with coagulation-aged populations of aggregates, the illustrative calculations below includes predictions of the size distribution of deposited aggregates (in the absence of break-up' Section 6.3).…”

“…For, say, DLCAs with D f D 1.8 and k 0 D 1.3, available numerical results for h mom have been approximated (Sorensen 2011) as: N ¡0.54 (for N 74) and 0.65¢N ¡0.44 (N > 74) and this recommendation was, in fact, used in our previous analysis of aggregate thermophoresis (Rosner and Tandon 2017). However, we have noticed that there is an appreciable spread among recent estimates, with the numerical results of Filippov (2000) (for DLCAs with N D 100) leading to h mom -values higher than this correlation by ca.…”

“…In Section 3 we review recent results for the thermophoretic (TP-) properties of large aggregates. As discussed in Rosner and Tandon (2017), these were obtained by combining the FA mobility results summarized in Section 2 with recent higher-order kinetic theory predictions (Young 2011) of the thermal force on an isolated spherule in a local temperature gradient. Because we ultimately seek deposition-rate results from "coagulation-aged" populations of aggregates or isolated, single-size spherules, in Section 4 we briefly review previous results for the "self-preserving" spreads of such aggregate size distributions, accounting for systematic effects of gas rarefaction.…”

“…While the additional mechanism of "direct interception" (normally associated with effective CA size comparable to the target size when Re << 1, as in fibrous filtration (Rosner 2000;Friedlander 2000) is beyond our present scope (Rosner and Tandon 2017b) we call attention to such extensions in Section 6.2.…”