Mathematical modeling of fluid energy milling based on a stochastic approach

Abstract In this study, the stochastic method is used to simulate the grinding process in a fluid energy mill: the product particle size distribution is regarded as the result of repeating elementary breakage events, i.e. M p = M 0 [ T m ] m , where M 0 is the row vector of the size distribution of feed particles, M p is the row vector of the size distribution of product particles, m is the number of elementary steps, and T m is the matrix of transition probabilities representing the elementary breakage event. The matrix of transition probabilities can be related to the breakage rate function and the breakage distribution function of the elementary breakage event. A specially designed apparatus, named single-event fluid mill, was employed to experimentally estimate those two breakage functions of the elementary breakage event with a breakage rate correction factor θ . The classification effect is taken into consideration by defining a cutting size under which the particle will not break any more. Using this strategy, the product particle size distribution is calculated. The good consistency between the simulation and the experimental results indicates that this model is valid to quantitatively estimate the grinding performance of the fluid energy mill.

[1]  Henri Berthiaux Analysis of grinding processes by Markov chains , 2000 .

[2]  Vadim Mizonov,et al.  Application of the theory of Markov chains to model different processes in particle technology , 2005 .

[3]  P. C. Kapur An improved method for estimating the feed-size breakage distribution functions , 1982 .

[4]  P. C. Kapur,et al.  Approximate solutions to the discretized batch grinding equation , 1970 .

[5]  F. Müller,et al.  Model-based evaluation of grinding experiments , 1999 .

[6]  Henri Berthiaux,et al.  Validation of a model of a stirred bead mill by comparing results obtained in batch and continuous mode grinding , 1996 .

[7]  B. Dobson,et al.  Particle size reduction in a fluid energy mill , 1969 .

[8]  P. Nair Breakage parameters and the operating variables of a circular fluid energy mill , 1999 .

[9]  Peng Wang,et al.  Experimental and numerical analysis of a lab-scale fluid energy mill , 2009 .

[11]  B. Mohanty,et al.  Fluid energy grinding , 1982 .

[12]  Wolfgang Peukert,et al.  Modelling of Grinding in an Air Classifier Mill Based on a Fundamental Material Function , 2003 .

[13]  Rob Morrison,et al.  The future of comminution modelling , 2007 .

[14]  Leonard G. Austin,et al.  An analysis of some cases of non-first-order breakage rates , 1977 .

[15]  Leonard G. Austin,et al.  Introduction to the mathematical description of grinding as a rate process , 1971 .

[16]  Leonard G. Austin,et al.  An analysis of fine dry grinding in ball mills , 1981 .

[17]  Leonard G. Austin,et al.  A discussion of equations for the analysis of batch grinding data , 1999 .

[18]  John A. Dodds,et al.  Approximate calculation of breakage parameters from batch grinding tests , 1996 .

[19]  C. L. Prasher,et al.  Crushing and Grinding Process Handbook , 1987 .

[20]  N Midoux,et al.  Micronization of pharmaceutical substances in a spiral jet mill , 1999 .

[21]  Leonard G. Austin,et al.  Methods for determination of breakage distribution parameters , 1972 .

[22]  Ecevit Bilgili,et al.  Formulation of a non-linear framework for population balance modeling of batch grinding : Beyond first-order kinetics , 2006 .

[23]  H.J.C. Gommeren,et al.  Modelling and control of a jet mill plant , 2000 .

[24]  D. Venkateswarlu,et al.  Studies in fluid energy grinding , 1969 .

[25]  Ecevit Bilgili,et al.  Nano-milling of pigment agglomerates using a wet stirred media mill: Elucidation of the kinetics and breakage mechanisms , 2006 .