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We develop a flux-conservative formalism for a Newtonian multi-fluid system,including dissipation and entrainment (i.e. allowing the momentum of one fluidto be a linear combination of the velocities of all fluids). Maximum use ismade of mass, energy, and linear and angular momentum conservation to specifythe equations of motion. Also used extensively are insights gleaned from aconvective variational action principle, key being the distinction between eachvelocity and its canonically conjugate momentum. Dissipation is incorporated tosecond order in the ``thermodynamic forces'' via the approach pioneered byOnsager. An immediate goal of the investigation is to understand better thenumber, and form, of independent dissipation terms required for a consistentset of equations of motion in the multi-fluid context. A significant, butseemingly innocuous detail, is that one must be careful to isolate ``forces''that can be written as total gradients, otherwise errors can be made inrelating the net internal force to the net externally applied force. Ourlong-range aim is to provide a formalism that can be used to model dynamicalmulti-fluid systems both perturbatively and via fully nonlinear 3D numericalevolutions. To elucidate the formalism we consider the standard model for aheat-conducting, superfluid neutron star, which is believed to be dominated bysuperfluid neutrons, superconducting protons, and a highly degenerate,ultra-relativistic gas of normal fluid electrons. We determine that in thiscase there are, in principle, 19 dissipation coefficients in the final set ofequations.Comment: 21 pages, uses Revtex

A flux-conservative formalism for convective and dissipative multi-fluid systems, with application to Newtonian superfluid neutron stars