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A variational principle applied to the dynamics of a liquid with diffusing gas bubbles
Arch. Mech. 58 (4-5), 363-380, 2006
Keywords: Hamilton’s principle; dynamical balance equations; immiscible mixtures; bubbly liquids
Abstract
The dynamic balance equations for bubbly liquids are deduced by evaluating the variation of a spatial Hamiltonian functional for immiscible mixtures. The constraint of incompressibility for the liquid is considered by choosing suitable "paths" of variation for the functions which describe the motion of the mixture and, although this appears to be a novelty, the equations obtained are in agreement with those derived from other theories, except for an inviscid drag term due to inertia forces and depending on changes of the radius of bubbles.