The Suitability of Particle Models in Capturing Aggregate Structure and Polydispersity

Figures & data

Table 1 TABLE 1 Comparison of the derived properties of the particle models

Property	Spherical	Surf–vol	Binary tree
type-space	Pq(p^(q))	Pq(p^(q), S^(q))
Vq
dsph,q
Ssph,q	πd^2sph,q	πd^2sph,q	πd^2sph,q
Sq	Ssph,q	S^(q)
	dsph,q		–
	–	–
nq	1		nq
dcol,q	dsph,q

Figure 1 FIG. 1 An illustration of different particle models’ description of coagulation events.

Figure 2 FIG. 2 Comparison of the normalized geometric mean collision diameter as a function of dimensionless coagulation and sintering time for each of the three particle models. The thick line depicts the intersection of the binary tree and surface-volume model predictions. (Color figure available online.)

Figure 3 FIG. 3 A contour plot depicting where the binary tree model is equivalent to the surface-volume model. The shading corresponds to within 5% deviation (with respect to collision diameter) of the surface-volume model from the binary tree model. (Color figure available online.)

Figure 4 FIG. 4 Effect of initial polydispersity,

, on morphology of particles. Shown are the normalized geometric mean

and standard deviation

of the collision and primary diameter. These were generated for

, τ/τ_C,i=5.0, on the “intersection” line of Figure 3. (Color figure available online.)

Figure 5 FIG. 5 Comparison of computational time (

) required per run for τ/τ_C,i=10 to calculate τ=0.5 s of process time. (Color figure available online.)

Figure 6 FIG. 6 Comparison of model predictions for the silica system of Shekar et al. (2012a). Depicted are the zeroth moment (M₀), volume fraction (

), arithmetic mean (

), and geometric standard deviation (

) of the collision and primary diameters. (Color figure available online.)

Figure 7 FIG. 7 Trajectory of the case of Shekar et al. (2012b) through the

,

space. The shading depicts the 5% error margins as described in Figure 3. Specific process times for the binary-tree and surface-volume models from Figure 6 are labeled. (Color figure available online.)

Figure 8 FIG. 8 Comparison of model predictions for the case of Wu et al. (1987) using a multivariate silicon model (Menz and Kraft 2013). Depicted are the zeroth moment (M₀), volume fraction (

), arithmetic mean (

), and geometric standard deviation (

) of the collision and primary diameters. (Color figure available online.)

Figure 9 FIG. 9 Trajectory of the case of Wu et al. (1987) using a multivariate silicon model (Menz and Kraft 2013) through the

,

space. The shading depicts the 5% error margins as described in Figure 3. Specific process times for the binary-tree and surface-volume models from Figure 8 are labeled, t<0.2 s omitted for clarity. (Color figure available online.)

ShekarS.MenzW.SmithA.KraftM.WagnerW.2012a43130147

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ShekarS.SmithA.MenzW.SanderM.KraftM.2012b448398

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WuJ.NguyenH.FlaganR.198732266271

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MenzW.KraftM.2013160947958

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