Skip to main content Accessibility help

Extensions of extremum principles for slow viscous flows

  • Richard Skalak (a1)


Several generalizations of theorems of the types originally stated by Helmholtz concerning the dissipation of energy in slow viscous flow have been given recently by Keller, Rubenfeld & Molyneux (1967). These generalizations included cases in which the fluid contains one or more solid bodies and drops of another liquid assuming the drops do not change shape. Some further extensions are given herein which allow for drops which may be deformed by the flow and include the effect of surface tension. The admissible boundary conditions have also been extended and particular theorems applicable to infinite domains, spatially periodic flows and to flows in infinite cylindrical pipes are derived. Uniqueness theorems are also proved.



Hide All
Courant, R. & Hilbert, D. 1962 Methods of Mathematic Physics, vol. 2, New York: Interscience.
Duffin, R. J. 1956 J. Rat. Mech. and Anal. 5, 939950.
Gurtin, M. E. & Sternberg, E. 1961 Arch. Rat. Mech. and Anal. 8, 99119.
Keller, J. B., Rubenfeld, L. A. & Molyneux, J. E. 1967 J. Fluid Mech. 30, 97125.
Landau, L. D. & Lifshitz, E. M. 1959 Fluid Mechanics. London: Pergamon.
Thomas, T. Y. 1942 Am. J. Math. 64, 75467
MathJax is a JavaScript display engine for mathematics. For more information see


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed