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A diffuse-interface description of internal waves in a near-critical fluid D. M. Anderson and G. B. McFadden
 

Summary: ARTICLES
A diffuse-interface description of internal waves in a near-critical fluid
D. M. Anderson and G. B. McFadden
Mathematical and Computational Sciences Division, National Institute of Standards and Technology,
Gaithersburg, Maryland 20899
Received 30 August 1996; accepted 24 March 1997
We present a diffuse-interface treatment of the internal gravity waves which have been observed
experimentally by Berg et al. in xenon near its thermodynamic critical point. The results are
compared with theoretical predictions by Berg et al. that were obtained using separate models above
and below the critical temperature Tc . The diffuse-interface model applies both above and below
Tc , and is formulated by using the density as an order parameter. The diffuse interface is
represented as a transition zone of rapid but smooth density variation in the model, and density
gradients appear in a capillary tensor, or Korteweg stress term, in the momentum equation. We
obtain static density profiles, compute internal wave frequencies and compare with the experimental
data and theoretical results of Berg et al. both above and below the critical temperature. The results
reveal a singularity in the diffuse-interface model in the limit of incompressible perturbations.
S1070-6631 97 03007-9
I. INTRODUCTION
The singular behavior of the material properties of a
liquid­vapor system near the thermodynamic critical point1

  

Source: Anderson, Daniel M. - Department of Mathematical Sciences, George Mason University

 

Collections: Mathematics