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

摘要

Aggregated particles nucleated and grown by Brownian encounters in atmospheric pressure gaseous flames, usually have primary particles (of radius R-1) smaller than the prevailing gas molecule mean-free-path, l(g). This simplifies their drift behavior in a strong temperature gradient, i.e., thermophoresis (TP), as has been exploited in the popular technique of TP/TEM soot sampling. Indeed, thermophoretic sampling has become the effective "calibration standard" because it also provides unambiguous aggregate morphology information and is independent of optical properties needed to interpret alternate "non-invasive" methods. However, we show here that at pressures of current engineering interest (e.g., 30-50 bar) the Knudsen number (Kn(1) = l(g)/R-1) is O(1) and the sensitivity of aggregate TP-behavior to pressure, morphology and, especially, aggregate size is altered considerably. While the recent gas kinetic theory results of Young reveal that the thermal force on each spherule should diminish as one leaves the free-molecule limit, large fractal-like aggregates receive the benefit of inter-particle "momentum shielding," and we predict that larger aggregates drift faster than smaller ones in the same temperature gradient. We show that aggregate TP-diffusivity approximately scales with a Kn(1)-dependent power, k, of the spherule number N, where the exponent k is as large as 0.44 for aggregates characterized by "dimension" D-f = 1.8, k(p)/k(g) = 1000 and Kn(1) below O(1). However, if the particle thermal conductivity far exceeds that of the carrier gas, the reduction in thermal force overwhelms the inter-particle momentum shielding below about Kn1 = 0.7, with the aggregate TP-diffusivity becoming inadequate for TP-sampling near Kn(1) = 0.2. Based on these results we conclude that to infer accurate high-pressure mainstream aggregate size distributions and volume fractions via TP-sampling, it is necessary to correct observed TEM-information for the expected "over-representation" of large aggregates. These appreciable corrections (up to 40 for the number-mean aggregate size and approximately one-decade for the associated spherule volume fraction, phi(infinity), at pressure near 50 bar), are shown to be straightforward to implement for sufficiently large mainstream (N) over bar and approximately log-normal aggregate populations.