On the steady-state size distribution of dispersions in breakage processes

• Published in: Chemical engineering science Vol. 52; no. 8; pp. 1285 - 1299
• Main Authors: Kostoglou, M., Dovas, S., Karabelas, A.J.
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 01.04.1997; Elsevier
• Subjects: Applications of mathematics to chemical engineering. Modeling. Simulation. Optimization; Applied sciences; Breakage; Chemical engineering; Exact sciences and technology; population balances; size distribution; steady state; steady state; population balances; Breakage; size distribution; Monte Carlo method; Particle size; Rupture; Theoretical study; Immiscible fluid; Grain size distribution; Modeling; Dispersion; Population balance; Inverse problem; Breakage function; Fluid fluid; Analytical method; Numerical simulation; Mathematical model
• DOI: 10.1016/S0009-2509(96)00488-5
• ISSN: 0009-2509

Breakage processes are considered in the absence of agglomeration or coagulation. A new method is proposed, based on a population balance type of formulation, applicable to systems (such as dispersions) that may be characterized by a maximum stable particle size. In this method, considerable simplification is achieved by means of a transformation that effectively eliminates the breakage frequency, thus allowing the convenient computation of steady state through solution of an integral equation. To compute the steady state, apart from the maximum size and the breakage kernel, only an estimate of the initial distribution is required. Two functional forms of binary breakage kernels which can represent a large variety of possible breakage mechanisms are proposed (by an appropriate selection of parameter values). For the sake of completeness, analytical solutions are also presented for several, relatively simple kernels. Finally, a study is made to assess the influence of initial conditions on the steady-state size distribution, which is helpful in tackling the inverse problem of determining the breakage kernel using limited experimental data.