  Transport coefficients associated with the mass flux of a binary mixture of
Maxwell molecules under uniform shear flow are exactly determined from the
Boltzmann kinetic equation. A normal solution is obtained via a
Chapman--Enskog-like expansion around a local shear flow distribution that
retains all the hydrodynamics orders in the shear rate. In the first order of
the expansion the mass flux is proportional to the gradients of mole fraction,
pressure, and temperature but, due to the anisotropy induced in the system by
the shear flow, mutual diffusion, pressure diffusion and thermal diffusion
tensors are identified instead of the conventional scalar coefficients. These
tensors are obtained in terms of the shear rate and the parameters of the
mixture (particle masses, concentrations, and force constants). The description
is made both in the absence and in the presence of an external thermostat
introduced in computer simulations to compensate for the viscous heating. As
expected, the analysis shows that there is not a simple relationship between
the results with and without the thermostat. The dependence of the three
diffusion tensors on the shear rate is illustrated in the tracer limit case,
the results showing that the deviation of the generalized transport
coefficients from their equilibrium forms is in general quite important.
Finally, the generalized transport coefficients associated with the momentum
and heat transport are evaluated from a model kinetic equation of the Boltzmann
equation.
