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Blending Bulk Solids by the Numbers
Mixing, segregation, feeding and sampling of powders and pellets, worked through one compounding plant's colour, filler and additive blends
How well a blend can be mixed, how to measure it, why it unmixes, how feeders and extruders smooth or pass on variation, and how to sample and prove a blend without fooling yourself.
Start readingAbout this book
Most manufactured products contain a blend somewhere: a colour masterbatch in a plastic, a filler in a compound, a vitamin in a feed, an active ingredient in a tablet, cement and sand in a dry mortar. A blend is good if every portion its user takes contains the right proportions, and it fails if some portions do not. Whether that happens depends on how the blend was mixed, how it was moved and stored afterwards, how it was fed into the process, and how it was sampled and tested. Each of those steps can be understood with a small number of ideas from probability and the physics of particles.
This book teaches those ideas for practical use. It starts by defining what “well mixed” means and showing that even a perfect random mixture has a limit to its uniformity, set by counting statistics. It then covers measuring mixedness, mixing as a random walk, the scale-up of blenders, the mechanisms that unmix a blend, and segregation in hoppers and transfers. The later chapters deal with continuous blending by feeders and extruders, minor ingredients and premixes, sampling, and the plans and charts that prove a blend.
It is for process, production and quality engineers, plant supervisors, laboratory staff and students. It assumes algebra, logarithms and introductory statistics: means, standard deviations and the normal distribution. Each chapter works the running case with real numbers, includes one plausible mistake and how it was found, and ends with an exercise and its worked answer.
The running case
Every chapter follows one fictional plant. This is an illustration. Plant C compounds polypropylene with calcium carbonate filler and sells the result as pellets. Three blends run through it.
- Colour. The plant’s own moulding cell makes 60 g lids from natural polypropylene pellets, each about 24 mg, coloured by adding 2% of a black masterbatch, pellets of about 20 mg carrying 40% carbon black. A volumetric doser at the moulding machine’s throat adds the masterbatch.
- Filler. The extrusion line makes a 30% filled compound at 1,500 kg/h. Loss-in-weight feeders deliver polypropylene at 1,035 kg/h, calcium carbonate at 450 kg/h and an additive premix at 15 kg/h into the extruder. The product specification is 30.0 ± 1.0% filler by ash content.
- Additives. The premix is 20% of a stabiliser powder in polypropylene powder, made in 200 kg batches in a 500 L ribbon blender. At 1% addition it gives 0.20% stabiliser in the compound.
The plant, its equipment, materials, specifications and every measurement are invented. None describes KEVOS® work, a real plant or a real supplier’s product.
How to use the book
Read Chapters 1 to 4 in order: they define mixedness, its random limit, how to measure it and how mixing proceeds. Chapters 5 to 7 cover batch blenders, segregation and what happens to a blend after it leaves the blender. Chapters 8 and 9 deal with continuous feeding and minor ingredients, and Chapters 10 and 11 with sampling and proving a blend.
KEVOS® tools are linked where they perform a step of the method, with a note of exactly what each calculates. The statistical tools follow the methods in the NIST/SEMATECH e-Handbook of Statistical Methods.
Source limits and professional responsibility
The statistics in this book are exact for the models stated; the physical models of mixing and segregation are simplifications that capture the main behaviour and are checked against measurement in each chapter. Specifications, test methods and acceptance criteria for real products are set by customers, standards and, for regulated products such as food, feed, medicines and agricultural chemicals, by regulators. They are named where relevant and not quoted.
Blending involves rotating machinery, dust and, for many materials, combustible or hazardous powders. The design and operation of real blending, feeding and sampling systems are matters for competent people under the equipment makers’ instructions and Australian work health and safety law. This book is educational. It explains how blends behave and how the standard calculations work; it is not a validation of any process or a substitute for testing a real blend.
Who this book is for
Process, production and quality engineers, plant supervisors, laboratory staff and students who blend, feed, dose or test powders, pellets and granules and need blends that stay within specification.
What you will learn
- Define a blend's quality at the scale its user experiences, and calculate the best uniformity a random mixture can reach.
- Measure mixedness from sample results, compare blenders and blend times, and estimate the time a blender needs.
- Explain the main segregation mechanisms, predict where a blend will unmix, and choose handling that prevents it.
- Work out how feeder fluctuations and extruder back-mixing combine to set the variation in a continuous blend.
- Size particles, premixes and samples for minor ingredients using counting statistics.
- Plan sampling and acceptance of a blend, and monitor it with charts and capability indices.
Inside this book
Chapters
- 01What well mixed meansA blend's quality depends on the scale at which its user takes it. Define the scale of scrutiny, the composition variance and the perfectly segregated and random limits, and set the let-down ratio.
- 02The random-mixture limit: counting particlesWhy even a perfect random blend varies from sample to sample, how the variance follows from counting particles, why the tails matter more than the average, and what changes the limit.
- 03Measuring mixedness: variance, Lacey's index and comparing blendersTurn sample results into a measure of mixedness, compare it with the random limit, see why Lacey's index can mislead, and compare blend times or blenders with confidence intervals and an F test.
- 04Mixing as a random walk: how fast a blend approaches randomMixing mechanisms, why the excess variance of a blend decays exponentially, how to fit the decay rate and predict a blend time, and what a dispersion coefficient says about a blender.
- 05Batch blenders and scale-upTumbling, convective and high-shear blenders, the Froude number that sets a tumbler's flow regime, and why a blend time found in one blender does not carry to a larger one without a test.
- 06Why blends unmix: segregation mechanismsSifting, trajectory, air and vibration-driven segregation in blends, the balance between segregation drift and mixing that sets a concentration profile, and how to test and design against unmixing.
- 07After the blender: bags, bins and discharge orderHow filling a container builds a segregated heap and discharging it delivers the blend in a changing sequence, how to measure that sequence, and how a packaging change was proved with a planned trial.
- 08Continuous blending: feeders, fluctuations and back-mixingHow feeder fluctuations become composition variation, how an extruder's back-mixing filters them by their time scale, how refill floods and slow drifts get through, and how capability is proved.
- 09Minor ingredients and premixesWhy ingredients at fractions of a per cent fail by counting statistics, how to calculate the particle size a minor ingredient needs, and how premixes and carrier strategies put it in every unit.
- 10Sampling without fooling yourselfWhy sampling particulate material adds its own error, the rules for a fair sample from a stream or container, sample dividing, how many samples a decision needs, and a scoop that rejected good premix.
- 11Proving a blend: acceptance plans and monitoringDesign a blend acceptance plan and work out how often it passes good and poor blends, monitor a continuous blend with an EWMA chart for small drifts, and bring Plant C's three blends under control.
Apply This in Practice
Use these KEVOS® tools to try the method from this reading with your own numbers.
Applies this method
Capability Confidence Check (Cp, Cpk and Their Lower Confidence Bounds, Sample Size)
Gives Cp and Cpk with their lower confidence bounds and the sample size to prove a required Cpk; used for the compound’s filler content before and after the feeder refill changes.
Used in Continuous blending: feeders, fluctuations and back-mixing
Applies this method
EWMA Control Chart Check (Weighted Moving Average, Control Limits, Small Shifts)
Calculates an EWMA chart from up to twenty readings with control limits and the first signal; used to catch a small sustained drift in filler content that Shewhart limits missed.
Applies this method
Linear Calibration Check (Straight-Line Fit, Calibrated Value, Calibration Interval)
A least-squares straight-line fit with standard errors and inverse prediction, built for instrument calibration; used here to fit the log of excess blend variance against time and predict a blend time.
Used in Mixing as a random walk: how fast a blend approaches random
Applies this method
Mixture Cost and Blending (Alligation)
Gives the proportions of two ingredients that blend to a target value by alligation, and a blend’s cost or property as a weighted average; used for the masterbatch let-down and the tracer concentrate in the masterbatch.
Used in What well mixed means
Applies this method
p-Chart Check (Fraction Defective, Control Limits, Samples Out of Control)
Gives the fraction defective per sample, the binomial control limits and samples outside them; used to show the shade rejects were a stable rate matching the random-mixture prediction.
Applies this method
Process Change Trial (Sample Size, Welch t-Test, Improvement Decision)
Plans the sample size for a before-and-after trial and evaluates it with a Welch t-test and confidence interval; used to prove that a premix packaging change fixed the stabiliser shortfall.
Applies this method
Sample Size to Estimate a Mean
Gives the number of results needed to estimate a mean within a margin at a confidence level; used to plan how many filler and premix tests a decision needs.
Applies this method
Two-Variance F Test (Compare the Spread of Two Machines, Batches or Methods)
Compares two sample standard deviations with an F test, p-value and a confidence interval for their ratio; used to decide whether a longer blend time reduces the scatter.
Used in Measuring mixedness: variance, Lacey's index and comparing blenders
References and source notes
The manuscript and worked examples are original KEVOS® writing. References inform particular concepts; their authors do not endorse this book. Web references were consulted on 31 October 2026.
- L. P. Kadanoff, World Scientific, Singapore (ISBN 981 02 3758 8). Statistical Physics: Statics, Dynamics and Renormalization (2000). Supplied source, in copyright. Read only as a subject map: random walks, diffusion, Gaussian distributions and the central limit theorem, fluctuations in large and small systems, the barometer formula and drift with diffusion. It is a physics text; no text, equations, figures, examples or exercises are reproduced or adapted, and the engineering treatment, running case and numbers in this book are original.
- P. V. Danckwerts, Applied Scientific Research, vol. 3, pp. 279–296. The definition and measurement of some characteristics of mixtures (1952). Origin of the scale of scrutiny and the intensity of segregation used in Chapters 1 and 3. Described, not quoted.
- P. V. Danckwerts, Chemical Engineering Science, vol. 2, pp. 1–13. Continuous flow systems: distribution of residence times (1953). Residence time distributions, the basis of the back-mixing and smoothing model in Chapter 8.
- P. M. C. Lacey, Journal of Applied Chemistry, vol. 4, pp. 257–268. Developments in the theory of particle mixing (1954). Mixing as a random process, the random-mixture variance and the mixing index used in Chapters 2 to 4. Described, not quoted.
- A. Rosato, K. J. Strandburg, F. Prinz and R. H. Swendsen, Physical Review Letters, vol. 58, pp. 1038–1040. Why the Brazil nuts are on top: size segregation of particulate matter by shaking (1987). Simulation study of size segregation under shaking, used qualitatively in Chapter 6.
- J. C. Williams, Powder Technology, vol. 15, pp. 245–251. The segregation of particulate materials. A review (1976). Review of segregation mechanisms used for the classification in Chapter 6. Described, not quoted.
- H. M. Jaeger, S. R. Nagel and R. P. Behringer, Reviews of Modern Physics, vol. 68, pp. 1259–1273. Granular solids, liquids, and gases (1996). Review of granular physics including convection and size segregation in vibrated beds, used for the physical explanations in Chapters 4 and 6.
- P. Gy, John Wiley & Sons, Chichester (ISBN 0 471 97956 2). Sampling for Analytical Purposes (1998). The theory of sampling particulate materials, including the fundamental sampling error and its dependence on particle size and sample mass, used qualitatively in Chapter 10. No formulas or factors are reproduced.
- National Institute of Standards and Technology. NIST/SEMATECH e-Handbook of Statistical Methods (2012). Reference for the confidence interval of a variance, the F test for two variances, EWMA control charts and capability indices used in Chapters 3, 8 and 11, and by the KEVOS® tools linked there.
- International Organization for Standardization. ISO 3451-1, Plastics: Determination of ash, Part 1: General methods (Current edition). Named by number and scope only, as the type of method used to measure filler content in a compound by ashing, in Chapters 8 and 11. No values are quoted.
- ASTM International. ASTM D6940, Standard practice for measuring sifting segregation tendencies of bulk solids (Current edition). Named by number and scope only in Chapter 6, as a laboratory test that ranks a blend's tendency to segregate by sifting.