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

Figures & data

Table 1. Statistical parameters and normalized correlations chosen to characterize two important classes of fractal (-like) aggregates (FAs).

	Type of FA
Parameter	DLCA	RLCA
Df	1.8	2.1
ko	1.3	0.94
β	0.665	0.464
ηPA	0.478 + 0.5228^.N^−0.23	0.644 + (1.78/N)
ηmom	N^−0.54 (N ≤ 74)	1.33^.N^−0.572
(Sorensen 2011)	0.65^.N^−0.44 (N > 74)

Figure 1. Predicted behavior of aggregate “momentum shielding function”: S_mom(Kn₁; N); dependence on Knudsen number (based on spherule radius) and total spherule number n (>>1); unless otherwise specified results are for diffusion-limited cluster aggregates with D_f = 1.8. (See Section 2.3 for test of ASM; see the Appendix for a special case: D_f = 3 with uniform [low] solid fraction [dashed contours].)

Figure 2. Predicted behavior of aggregate “momentum shielding function”: S_mom(Kn₁; N); dependence on Knudsen number (based on spherule radius) and total spherule number N (>>1) for reaction-limited cluster aggregates with D_f = 2.1; comparison between results of permeable sphere model (Section 2.1 and the Appendix) and correlation (Table 1 and Sorensen 2011).

Figure 3. Predicted deposition rate ratios resulting from mainstream aggregation (at const total spherule volume fraction). Sensitivity to particle deposition mechanism and Knudsen number, (mfp)/R₁, for monodisperse mainstream aggregate population (all particle with N = 1000 and σ_g = 1) and coagulation-aged, “self-preserving” populations of DLCAs, = O(10³) with D_f = 1.8.

Figure 4. Predicted deposition rate ratios resulting from mainstream aggregation (at const total spherule volume fraction). Sensitivity to particle deposition mechanism and Knudsen number, (mfp)/R₁, for monodisperse mainstream aggregate population (all particle with N = 1000 and σ_g = 1) and coagulation-aged, “self-preserving” populations of RLCAs, = O(10³) with D_f = 2.1.

Figure 5. Predicted mainstream and wall fractal-like aggregate distributions due to expected N-dependent convective diffusion, thermophoretic diffusivities and eddy impaction deposition rates. Comparison between mainstream- and predicted wall-log-normal distributions mainstream aggregate population characterized by N_g,∞ = 1000, D_f = 1.8 and Kn_R1 = 1.32.

Figure 6. Predicted mainstream and wall fractal-like aggregate distributions due to expected N-dependent convective diffusion, thermophoretic diffusivities, and eddy impaction deposition rates. Comparison between mainstream- and predicted wall-log-normal distributions mainstream aggregate population characterized by N_g,∞ = 1000, D_f = 2.1, and Kn_R1 = 1.32.

Figure A1. Behavior of the Brinkman function, f_B(κ), describing the drag on a sphere of uniform permeability in Re << 1 Flow when Kn_N << 1; log-log representation of Equation (A1[A1] ) showing asymptotic behavior at small and large dimensionless radius, ≡ R_max/χ^1/2.

Sorensen, C. M. (2011). The Mobility of Fractal Aggregates: A Review. Aerosol Sci. Technol., 45:765–779.

 Web of Science ®Google Scholar