The self-preserving size distribution of fractal aggregates coagulating by Brownian motion and simultaneous fluid shear at low Peclet numbers: Numerical solutions

•Deriving integro-differential coagulation equation of fractal aggregates.•Determining the conditions for obtaining self-preserving size distribution.•Obtaining weak self-preserving size distributions at low Peclet numbers.•The Peclet number of particles with the mean volume is a constant.•Self-preserving size distribution is close to a lognormal distribution.

The asymptotic size distribution of fractal particles undergoing Brownian and simultaneous shear-induced coagulation has not been investigated. We have addressed this issue by establishing and solving ordinary integro-differential coagulation equations. The self-preserving distribution (SPSD) requires a shear rate decreasing with time according to a formula, which we report, for various fractal dimensions. Under this condition, it is the Peclet number of primary particles that controls the self-preservative characteristics of coagulating aggregates. The size distribution of fractal aggregates at low Peclet numbers of primary particles was determined to be self-preserving. The SPSDs were calculated for aggregates of various fractal dimensions. An upper limit of the Peclet number exists where the SPSD could be obtained. This upper limit decreases with decreasing fractal dimension: from 1.1 for the fractal dimension of 3 to 0.14 for the fractal dimension of 1.8. The Peclet number of particles with the mean volume hydrodynamic radius is a constant during the coagulation process, and is proportional to the Peclet number of primary particles. As the Peclet number increases, the SPSDs will broaden, and the peak value will also increases and drifts to the left. The SPSD is close to a lognormal distribution. This represents a theoretical foundation for the size distribution evolution of coagulating fractal aggregates in flow fields and for the lognormal size distribution assumption of atmospheric aerosols.

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