Major themes in Ben Widom’s work, such as fluid and fluid mixture criticality, critical end points, mean-field and actual critical exponents, capillarity and interfacial tension had 19th century roots in my native country. I first met Ben during his year at the University of Amsterdam in 1962. Our paths have since crossed at many happy occasions. Van der Waals published his equation of state in 1873 – it was the first closed-form equation of state to yield a vapor- liquid critical point. It resulted in the law of corresponding states of 1880, which would enable Leiden cryogenic physicist Kamerlingh Onnes to liquefy helium in 1908. 1n 1890 van der Waals’s generalization to binary mixtures saw the light – a key to understanding the complexities of phase behavior of fluid mixtures. Van der Waals published his square-gradient theory of capillarity in 1894. In the course of testing his predictions for the critical behavior of surface tension Van der Waals defined and calculated mean-field critical exponents in the modern sense of the word. Before 1900 he was aware that that the experimental critical exponent for surface tension violated mean-field theory in an essential way. Little could he have guessed that the problem would take more than sixty years to be resolved by scientists such as Ben Widom.

Van der Waals disappointed: First experimental tests of mean-field theory

254th National Meeting (2017)

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