Change in Particle Size Distribution of Fractal Agglomerates during Brownian Coagulation in the Free-Molecule Regime

Taylor series expansion scheme applied for solving population balance equation

Population balance equations (PBE) are widely applied to describe many physicochemical processes such as nanoparticle synthesis, chemical processes for particulates, colloid gel, aerosol dynamics, and disease progression. The numerical study for solving the PBE, i.e. population balance modeling, is undergoing rapid development. In this review, the application of the Taylor series expansion scheme in solving the PBE was discussed. The theories, implement criteria, and applications are presented here in a universal form for ease of use. The aforementioned method is mathematically economical and applicable to the combination of fine-particle physicochemical processes and can be used to numerically and pseudo-analytically describe the time evolution of statistical parameters governed by the PBE. This article summarizes the principal details of the method and discusses its application to engineering problems. Four key issues relevant to this method, namely, the optimization of type of moment sequence, selection of Taylor series expansion point, optimization of an order of Taylor series expansion, and selection of terms for Taylor series expansion, are emphasized. The possible direction for the development of this method and its advantages and shortcomings are also discussed.

Investigations on the semi-batch precipitation of silica

The semi-batch precipitation process of silica from sodium silicate and sulphuric acid has been structured into a primary particle production stage, an aggregation process until the gel point is reached and finally a gel fragmentation and compaction process. The progress of aggregation was analyzed by photon correlation spectroscopy. The reaction limited aggregation kernel was found to be proportional to B'(t)(q(p - q))A/2, where A assumes the value of one. The quantity B'(t) varies between 3.4 x 10(-20) and 2.6 x 10(-20) 1/min and is only a weak function of time. The stability ratio W for the aggregation process decreases with increasing aggregate size. During the period after the gel point the gel fragmentates. The gel clusters have an initial fractal dimension of approximately 1.8 which rapidly increases to 2.4 and stays roughly constant until the end of the process. The specific surface area decreases from 480 to 300 m2/g. The primary particles have a uniform size of 22.7 nm.