Great Bards of QbD: Lewis Fry Richardson

Integration in time (and space) of the equations of mass, momentum and energy conservation plays a growing role in QbD.  An early contributor to this field was Lewis Fry Richardson, whose 1922 book, Weather Prediction by Numerical Process, laid the basis for modern weather prediction techniques.  Richardson also occupied himself with understanding turbulence and like Corrsin, was briefly moved to write a verse about his ideas.  Corrsin was inspired by Shakespeare; Richardson by Jonathan Swift and Augustus de Morgan to write about the cascade of energy from large to small scales:

  Big whorls have little whorls,
  Which feed on their velocity;
  And little whorls have lesser whorls,
  And so on to viscosity
  (in the molecular sense).

Many subsequent students of turbulence and mixing built on Richardson's work, and the Richardson Number is named in his honour. He also analyzed wars using mathematics and had early ideas about fractals while studying the lengths of shared borders between countries. Recipients of the Lewis Fry Richardson Medal have included Benoit Mandelbrot.

De Morgan had written:

  Great fleas have little fleas upon their backs to bite 'em,
  And little fleas have lesser fleas, and so ad infinitum.
  And the great fleas themselves, in turn, have greater fleas to go on;
  While these again have greater still, and greater still, and so on.

Swift originally wrote (in 1733):

  So, naturalists observe, a flea
  Hath smaller fleas that on him prey;
  And these have smaller still to bite 'em;
  And so proceed ad infinitum.
  Thus every poet, in his kind,
  Is bit by him that comes behind.

Great Bards of QbD: Stanley Corrsin

When we calculate mixing timescales in reactors and crystallizers [Liquid mixing: batch and fed batch mixing times], we leverage the work of Stanley Corrsin, one of many pre-Internet scientists who laid foundations for our predictive abilities.  His paper, [Simple theory of an idealized turbulent mixer,  AIChE Journal, Volume 3, Issue 3, pages 329–330, September 1957] showed how the time constant for mixing depended on the rate of dissipation of turbulent kinetic energy.  

Stanley loved his subject so much that he was moved to poetry.  He is responsible for the following sonnet, inspired by one of Shakespeare's (Sonnet 18 Shall I compare thee to a Summer's day?): 

SONNET TO TURBULENCE by S. Corrsin ^[1]
For Hans Liepmann ^[2] on the occasion of his 70th birthday, with apologies to Bill S. and Liz B.B.

Shall we compare you to a laminar flow?

You are more lovely and more sinuous.

Rough winter winds shake branches free of snow,

And summer’s plumes churn up in cumulus.

How do we perceive you? Let me count the ways.

A random vortex field with strain entwined.

Fractal? Big and small swirls in the maze

May give us paradigms of flows to find.

Orthonormal forms non-linearly renew

Intricate flows with many free degrees

Or, in the latest fashion, merely few —

As strange attractor. In fact, we need Cray 3’s ^[3].

Experiment and theory, unforgiving;

For serious searcher, fun ... and it’s a living!

Registration open for DynoChem User Meetings 2011: Chicago, London and Mumbai

Registration has opened for the DynoChem 2011 User Meetings, taking place in Chicago, London and Mumbai, where pharmaceutical companies will share 'Recipes for Success' in April and May 2011.  More details at http://www.scale-up.com/UGM11.html.

Population balance modeling in crystallization - discussion

There's a LinkedIn discussion going an at present on population balance modeling in crystallization.  I posted there today as follows: 

Building a population balance model / framework is quick and easy, especially if you start from a readymade template. Making the model fit your data is more time-consuming and the quality of fit (and confidence ellipsoids) may be reasonable, though the relevant 'kernels' may be too simple or too averaged to fit really well. Making accurate predictions with your model, especially with a change of scale and equipment configuration, adds a further layer of effort to be successful, as the balance among the important phenomena may shift away from your original conditions. In some industries, this level of effort may be indulged; in the fast moving pharmaceutical development project, it usually will not, depending on the phase of development and the questions that need to be answered.

Common sense tallies with our experience in this area, that users need to understand / model first the mass balance, then the energy balance and then possibly the number / population balance. In many projects, trying to start at the wrong end (the population balance) only reveals that the mass and energy balance are not understood. On the other hand, starting with mass (concentration, addition rate, solubility) and energy (temperature, cooling / evaporation rate) alongside a basic evaluation of equipment characteristics (agitation, solids suspension, heat transfer resistance) often leads to insight that solves problems without requiring a population balance approach.

In these more routine projects, on-line size data (such as FBRM) are useful as a diagnostic and to provide trend information.

AIChE 2010: List of papers by and of interest to DynoChem users

Next week 7-12 November sees the AIChE 2010 Annual Meeting take place in Salt Lake City.  You can find an updated list of papers at AIChE by and of interest to DynoChem users at http://bit.ly/ceiS1r.

AIChE to Award Lilly’s Seibert, Pfizer’s Garcia-Munoz for Moving QbD Forward

Congratulations to Kevin Seibert and Sal Garcia-Munoz on receiving AIChE's new awards for Excellence in QbD.  The drug substance award is sponsored by DynoChem and the drug product award by Pfizer.  See the news item at PharmaQbD.com, http://bit.ly/bYBive.

In QbD or elsewhere, experiments are no substitute for thinking

Terry Redman posted an article on PharmaQbD.com recently entitled 'If QbD is the Map, Then PAT Is the GPS' and I posted a reply that I am reproducing here; you can add your own thoughts on the PharmaQbD site if you like.

Analogies are useful when trying to understand new concepts and Terry’s is witty and readable. It’s a shame that these analogies appear to be needed when we are several years down the line with QbD. I tend to think of both maps and GPS in a positive light, although both can be misleading from time to time.
If I had to use travel metaphors to explain QbD and PAT I would say:
- QbD is a way of driving safely and defensively, so that quality targets are met;
- The human / engineer / scientist / organization provides the map, steering, fuel and the motive power;
- Software and hardware tools may allow a change of gears;
- PAT instrumentation is the rear view mirror, telling us what has happened, after it has happened;
- Predictive modeling tools are the windscreen and the headlights, leveraging other information to predict the future, i.e. before it happens. That is what enables design.
You could summarize by saying that measurements, however numerous, sophisticated and timely, are not a substitute for thinking.