Asymptotic Solution of Moment Approximation of the Particle Population Balance Equation for Brownian Agglomeration

Figures & data

TABLE 1 The asymptotic solution of dimensionless particle moment (M_C), the prefactor of agglomerate growth rate and exponent of particle primary size as function of D_f

Df	MC	|(4Df − 12)/(4 − 3Df)|	|2Df /(4 − 3Df)|
2.0	3.07	2.00	2.00
2.1	2.94	1.57	1.83
2.2	2.81	1.23	1.69
2.3	2.70	0.97	1.59
2.4	2.60	0.75	1.50
2.5	2.51	0.57	1.43
2.6	2.43	0.42	1.37
2.7	2.36	0.29	1.32
2.8	2.30	0.18	1.27
2.9	2.25	0.09	1.23
3.0	2.20	0.00	1.20

FIG. 1. The decay of particle number density with time in a logarithmic plot. (a) In the free molecule regime, the asymptotic slope are −2 and −6/5 for D_f = 2 and 3, respectively, and the dimensionless time is τ = g₁(D_f)M₀^(1−λ)t. (b) In the continuum regime, the asymptotic slope remains a constant −1 for different D_f, and the dimensionless time is τ = B₂t.