Don’t Bet on the Spherical Horse

spherical horseHappy New Year!

An old physicist’s joke goes something like this:




Many years ago, a professor in the theoretical physics department at Caltech was asked if his group could develop a mathematical model to predict whether a given horse might win the Kentucky Derby. He thought about the complexity of the situation and the many points of variability that would have to be considered: environmental factors such as air temperature, humidity, speed and direction of the wind throughout the race; ground conditions including the size distribution, moisture content and cohesive properties of the dirt on the track; and the numerous properties of the horses themselves that could come into play – including their weight, height, density, present health, recent diet and energy reserves.

After considerable thought, he confidently declared that he could come up with a working theoretical model that could accurately predict each horse’s flight around the track with an accuracy of 0.001 seconds.

First, he said, we just have to assume that the horse is a perfect sphere…

I’m not sure if the joke or the physicist is older, but this joke has long been used to highlight the limitations of theoretical modeling when dealing with real-life physical systems. It continues to ring true when considering the measurement of particle size distributions and especially crystallization systems, where complex three dimensional structures are routinely simplified to a “single characteristic dimension” such as a spherical equivalent diameter. (Of course, even a spherical equivalent diameter is not definitive and has to be defined based on the root method of measurement.)

It has long been projected that as computer power increases, modeling will become capable of getting closer to reality. And Computational Fluid Dynamics is an area that has made dramatic progress in the modeling, prediction and optimization of liquid mixing patterns in vessels and pipelines, but the industrial application of CFD still seems to reach rather hard limits when it comes to successfully modeling the mixing of suspensions or other multiphase flow problems.

Even with relatively new PSA techniques using image analysis, where multi-dimensional measurements are readily captured from the 2D projections of individual particles, it is fairly common practice to convert the information to one of many possible spherical equivalent diameters – such as spherical equivalent diameter of the projected area. Perhaps one saving grace is that we can also come up with a separate one-dimensional measurement that can report the shape of the particle as a single number (such as sphericity or convexity). At least getting to two (or more) independent characteristic measurements offers the ability to create scatter plots that can distinguish between “good” and “bad” particles. Is this good enough for today’s practical applications? Or is there still a need for a higher level of detail in a real-life particle system measurement?

It does seem that we still have an overdependence on simplified math and the use of spherical equivalent diameters to characterize most particle systems – even where it is clearly not appropriate. Is this still due to a lack of computing power, is it a lack of ability to conceptually visualize multi-dimensional particle systems, or is it just a force of habit engrained by the old physicists that laid the groundwork and the old measurements that were designed to reproduce sieve distributions?

Or do you disagree and feel that recent examples of modeling are capable of dealing with real-life particle systems in multi-dimensional distributions that cover size and shape – and that these models are already being used to improve real industrial processes?

What is your opinion on the real needs of industry and academia for dealing with the most complex particle systems in the chemical process industries?

What are the current limiting factors in being able to measure, analyze, and make use of multi-dimensional particle system characterization measurements?

Additional Resources
Best Practices for Inline Particle Size Characterization
Seeding a Crystallization Process
Best Practices for Crystallization Development
Scale-up of Batch Crystallization from Lab to Plant
In Situ Monitoring and Control of Complex Particle and Droplet Systems

Should we assume all particles are spheres?

Should we assume all particles are spheres?