Characterization of Feeder Effects On Continuous Powder Mixing Using Fourier Series Analysis

Continuous powder mixing attenuates feeding fluctuations while reduces transverse heterogeneity of initial segregated components [1]. Although the capacity of the mixer to smooth out feeder fluctuations can be generally characterized by the variance reduction ratio (VRR) at the input and output of the mixer [2-4], few studies are performed quantitatively in illustrating this attenuation process. This leads to inconveniency in selection or improvement of integrated feeder-mixer system if it is not optimal.

In this study, the feeder effects on the solid mixer are investigated through Fourier series analysis. The VRR is deduced using the Fourier series of the feed rate and the residence time distribution (RTD), which facilitate the VRR to be explicitly decomposed into different frequency components. By analyzing the feeding variance and the filtering ability of the mixer to reduce the variance in different frequency domains, the model provides a novel method to determine whether the integrated feeder-mixer system satisfies specific powder mixing performance criteria, and provides specific guidelines for system improvement.

Based on the developed method, the influence of Peclet number (Pe) and the mean residence time (¦") of the Taylor dispersion model on the filtering ability is investigated. The results suggest that large ¦" and small Pe lead to good filtering ability. The method also provides general feeder performance criteria, which can be effectively used in the improvement of feeder design.  Experimental results are used  to illustrate how specific guidelines can be suggested based on the proposed  Fourier series method.

Reference

1.         Pernenkil, L. and C.L. Cooney, A review on the continuous blending of powders. Chemical Engineering Science, 2006. 61(2): 720-742.

2.         Danckwerts, P.V., Continuous flow systems : Distribution of residence times. Chemical Engineering Science, 1953. 2(1): 1-13.

3.         Williams, J.C. and M.A. Rahman, Prediction of the performance of continuous mixers for particulate solids using residence time distributions : Part II. Experimental. Powder Technology, 1972. 5(5): 307-316.

4.         Ralf Weineköter, L.R., Continuous Mixing of Fine Particles. Particle and Particle Systems Characterization, 1995. 12(1): 46-53.