Dry mixing plays an important role in many processes. The operation can take place at different stages of a process, for example at the beginning to mix raw materials or at the end to disperse additives into a product. Regardless, the purpose of the mixer remains the same: creating a mixture homogeneous enough for the intended application.
This article aims to help process designers and plant operators understand what homogeneity in solids processing is, how to characterize it, and how to validate a dry mixing operation by measuring the degree of mixing.
A perfect degree of homogeneity, or mixture quality, means ingredients appear in the same proportions in any sample taken at any point of a mixture. Of course, this ideal result doesn’t occur in the real world. Instead, differences between components, mainly in terms of particle sizes, always will constitute a natural limit to homogenization. (We won’t consider coating effects in this article.) Additionally, the sample size matters when checking homogeneity — assessing the same mix using two different sample sizes may lead to different conclusions.
As a consequence, discussing the homogeneity of a mix of solids demands care. The nature of the solids being mixed and the sample size significantly affect the confidence you should place in any measurement of homogeneity. Sample size is a critical parameter (Figure 1). So, always reflect upon what represents a meaningful sample size for an application; selecting too small a size will make it difficult to determine if the mix is homogeneous, while too large a size almost certainly will make the mix appear homogeneous. For example, if a mixture is intended to be consumed (such as a pharmaceutical or food), the appropriate sample size is the serving size.
The mixing quality is defined in regards to a specific property the processor wants to be equal at any point in the mixture. This sometimes is a physical property like particle size distribution but more often is ingredient composition. Here, we will focus only on composition.
For practical use in processing, the notion of homogeneity must be translated mathematically using statistics. This usually is done by calculating a sample variance (S2) of the concentration of one component from an analysis of samples taken from the mixer.
The analysis is performed on a tracer, a component of the mixture whose distribution is taken as representative of the state of the mixture. Getting meaningful results, i.e., rather narrow confidence intervals, generally requires a minimum of 30 samples from the mix, with a sampling methodology that doesn’t leave part of the mix unsampled.
The lower the sample variance is, the higher the degree of mixing or homogeneity and the better the quality of the mix.
Achieving valid insights from samples requires careful attention to three key preliminaries: the desired target value, the choice of tracer and the sampling procedure.
Setting the target value. Measuring mixture quality only makes sense if a processor has set sample variance targets to enable comparing the measurement to an objective. Such targets depend upon the application. Consider two examples:
1. The mixture is used internally for another unit operation on site; the company itself defines the specifications, which may allow quite a large variation to ensure a smooth operation.
2. The mixture is sold directly, e.g., as a pharmaceutical tablet; the specifications must meet legal regulations, which may be very narrow.
This highlights a general point. If the mixture is used in an intermediate process step, the quality of the mix may not be critical and relatively high composition variations may be acceptable. However, if the mixture is an end product subject to strict regulation (such as a pharmaceutical or food), much more stringent control of the mix quality is required and the validation of the mixer must ensure the mix always will be within specifications.
Let’s now look at how to validate the mixture quality and compare the actual state of the mix to a target.
Choosing a tracer. Determining the composition of complex samples (beyond a binary mixture) sometimes is difficult, if not impossible. That’s why analysis often is done only on a single component, the tracer.
Selection of the tracer demands care. It shouldn’t be a major ingredient, except if the mixture contains only major components. It usually is chosen from small/minor ingredients that often are of interest in the mix (nutrient, active substance, etc.). Because of its low concentration, that component will take longer to homogenize, and thus represents a worst case among all the ingredients.
The tracer should lend itself to easy analysis. It’s better if the tracer is part of the mix formula (vitamin, active substance, reactive chemical, etc.). However, sometimes adding another component as the tracer can make sense to ease the mixer validation exercise, for example, adding salt.