Article révisé par les pairs
| Résumé : | The hydrodynamics of a fluid consisting of several components can be formulated in two different ways by applying the methods of the thermodynamics of irreversible processes. The first formulation is obtained if Gibbs' fundamental formula for the entropy per unit of mass of the system is assumed to be still valid when applied to the movement of the center of gravity of the system; statistically this corresponds to an approximate equilibrium velocity distribution function around the mean mass velocity, that is, to a normal transfer of impulse between the various components. This first formulation contains the classical Stokes-Navier equation for the hydrodynamics of a fluid. A second formulation is obtained if we assume the transfer of impulse between the various components to be a small perturbation or even negligible. This corresponds statistically to approximate equilibrium velocity distribution function around the macroscopical velocity of each component or "fluid" as we say in this case. Assuming therefore Gibbs' formula for the entropy sα per unit of mass of each fluid to be still valid when applied to the macroscopical movement of each fluid, we can derive a new set of hydrothermodynamical relations. When specialising, these equations to the two fluid model of liquid Helium II, Gorter's equations of motion for the normal and the superfluid are obtained. © 1951. |
