Rational extension of the Boussinesq approximation to a two-component fluid

This note extends the Boussinesq approximation to a two-component fluid, in a manner consistent with the conservation law of mass. It is shown that the governing equations for a two-component fluid can systematically be formulated, with the aid of the conservation law of energy, on the following assumption: the density of the fluid is a function solely of the concentration of one component, but the thermal expansion coefficient of the fluid does not vanish. It is also shown that the velocity of the fluid cannot in general be solenoidal under the extended approximation