J. Soc. Cosmetic Chemists 21 3-36 (1070) •) 1970 Society of Cosmetic Chemists of Great Britain The continuous mixing of particulate solids J. C. WILLIAMS and M. A. RAHMAN* Presented at the symposium on "Powders", organised by the Pharmaceutical Society of Ireland and the Society of Cosmetic Chemists of Great Britain, at Dublin, on 17th April 1969. Synopsis•The present state of knowledge of CONTINUOUS MIXING is reviewed and the problems of applying the concepts developed for fluid_ mixing to PARTICULATE SOLIDS systems are discussed. The available EXPERIMENTAL techniques are considered and a simple method suitable for solids mixers is described. The performance of an inclined ROTATING DRUM mixer has been investigated by the DELTA-INPUT RESPONSE technique,•.using components of the same particle size but differ- ing in other properties. It is shown that this technique, which leads to the evaluation of the VARIANCE REDUCTION RATIO, is useful in assessing the performance of a mixer, and that it can be used to establish the best operating conditions for a given system. INTRODUCTION Most industrial mixing of particulate solids is carried out as a batch process, and in this respect those industries that involve the handling of solid materials lag behind processes involving fluids. When the solid particles to be mixed tend to segregate, because of differences in the physical properties, particularly particle size, it is not always easy to produce a mixture approaching randomness in a batch mixer, and the storage and subsequent handling of a batch of mixture almost always lead to some further segregation, so that the mixture supplied to the next part of the process is often unsatisfactory. In such cases consideration should be given to the possibility of using a continuous mixer, placed as near as possible to the next stage of the process, so that intermediate storage is eliminated and handling of the *Postgraduate School of Studies in Powder Technology, University of Bradford, Yorks. 3

JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS mixture is reduced to a minimum. In general, it is comparatively simple to produce transverse mixing between the components fed to the mixer, and the quality of mixing is, therefore, limited by the accuracy of the control of the feed rates of the separate components. The continuous mixer should, therefore, be designed so as to have an appreciable amount of back mixing, which will help to reduce fluctuations introduced by the feeders. A study of the problems involved in the characterisation of the per- formance of a continuous mixer for particulate solids is reported in this paper. The methods proposed have been used to investigate some aspects Of the performance of a rotating inclined drum as a continuous mixer. LITERATURE SURVEY Introduction The literature of continuous mixing, in general, shows two basically different approaches to the problem of deriving equations to describe the performance of a system. These are (1) the direct formulation and inte- gration of a mass balance equation, and (2) the application of the knowledge of the distribution of residence times obtained by indirect techniques. The first approach has proved to be successful when the flow pattern of a system is either plug flow or perfect mixing, because in these cases some simplifying approximations hold good and the problem becomes relatively easy. Direct approach Assuming perfect mixing Danckwerts and Sellers (1) showed that c• o 2/(yi2 = V/V e R(r)dr . . (I) o where (•o 2 = variance of the property of interest of the outgoing stream. (5 2 = variance of the property of interest of the ingoing stream v -- volumetric flow rate, assumed equal for inflow and outflow V -- volume of the vessel occupied by the material R(r) = the coefficient of autocorrelation of the ingoing stream for points separated by a distance r. Some typical systems In deriving equation (I) the authors assumed that the volumes of the inflow and outflow in any given time interval are fixed and equal. In