  The size effect in the gas of impuritons of the superfluid mixtures of helium
isotopes is investigated by taking into consideration the contribution of
thermal excitations. The solution is obtained for the set of kinetic equations
describing a non-equilibrium state of the phonon-impuriton system of a
superfluid mixture situated in the volume filled with the macroparticles. It
allows to find the condition describing a steady, thermodynamically
non-equilibrium state of $^3{He}-^4{He}$ mixture in confined geometry. The
Knudsen effect in the gas of impuritons of a superfluid mixture is investigated
by taking into account the contribution of phonons. A model for the collision
operator has been proposed to analyze the exact results in the context of the
concrete physical situations. An experiment for the investigation of the
Knudsen effect in a superfluid mixture of helium isotopes is proposed.
