Agglomerates growth in turbulent flow is theoretically investigated. Coalescence probability in the process of agglomerates growth is formulated on the basis of Kolmogoroffs theory under the assumption that agitation field is in an isotropic turbulent flow, and also on the basis of physical properties of agglomerates. And characteristic diameter (
CD) of agglomerate is defined as a diameter at which coalescence probability of two agglomerates in the same diameter is zero, and
CD is generally expressed by Eqs.(34) and (35). A population balance equation is constructed using the collision frequency function based on the Kolmogoroff s theory and the coalescence probability.
Simulation results are as follows:(1) Regardless of variation of
cw/w1, cumulative size distributions normalized by each weight mean diameter approach a specified distribution curve with lapse of agglomeration time, within a limitted time in the R>λν.
(2)
CS is proportional to
CD.
(3) Accordance with the results of (1) and (2), it was proved that it is capable to predict the cumulative size distribution at steady state.
(4) When CD suddenly increases in agglomeration process, growth pattern of agglomerates changes from slow growth to rapid growth.
(5) lf σst is equal to Qt arid the saturation degree is relatively high, CD is expressed by Eqs.(50) and (51). And also, CD is given by Eqs.(52) and (53), when each of
B1 and
B2 in Eqs (50) and (51) is kept constant and ε is proportional to
N3. The following characteristics in the agglomeration are theoretically proved from Eqs.(52) and (53).
i)
CD increases, as γ, cosθ and ψ
B, increase, and as γ andε decrease. The effect of these factors on the
CD is larger in
R>λν than in
R>λν.
ii) On the fixed condition of
N, agglomerates growth rate becomes faster, as γ, cosθ and ψ
B and
N (0)
V increase, and as ε decreases. ln the cases resulting the same
CD at different
N, the higher
N, the faster in agglomerates growth rate.
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