Symbolic Computation Group

David R. Cheriton School of Computer Science
University of Waterloo, Waterloo, Ontario, Canada

Thermodynamics of Van der Waals Mixtures; Symbolic and numerical computations, visualizations using Maple
A.H.M. Levelt, University of Nijmegen, The Netherlands
Friday, May 3, 2002, at U. of Waterloo.


The physicst J.D. van der Waals is best known for his equation of state for fluids (1873), which incorporates the liquid-vapor transition and criticality. In 1890, he proposed a generalization to fluid mixtures, the first time the complex phase behavior of mixtures could be modeled. Special cases of the Van der Waals binary mixtures equation were studied by the mathematician D.J. Korteweg (1891), he of the Korteweg-de Vries equation, and by J.J. van Laar (1903-1906). In both cases, huge symbolic computations were performed with paper and pencil.

Only around 1970, when electronic computers became widely available, was the study resumed by the chemist R.L. Scott at UCLA. He and his student Van Konynenburg studied the general case extensively, formulating the starting equations using paper and pencil, and performing all further calculations numerically, while plotting the results using a Calcomp plotter. The availability of these "global" results provides a framework for understanding the older work. The calculation of phase separations in multicomponent mixtures by means of equations of state is now widespread throughout the chemical process industry.

My attention was drawn to the work of Korteweg and Van Laar by the physicist Paul Meijer (CUA, Washington, DC). In particular, he noticed several exact results in Van Laar's work, which he and I then confirmed, using Maple. He also alerted me to the differential geometry applied to thermodynamic surfaces by Korteweg, and the resulting complex graphs. Presently, my sister, J.M.H. Levelt Sengers (NIST, Gaithersburg, MD) and I, are trying to understand Korteweg's work from a modern physical and mathematical point of view.

In my talk, I give a limited overview of this field, and discuss some mathematical details. But the emphasis will be on my applications of Maple to the required symbolic computations, as well as to the visualization of surfaces in 3-D, of which examples will be given in the talk. No previous knowledge of thermodynamics is required; the necessary minimum will be explained.


Last modified on Sunday, 04 November 2012, at 15:42 hours.