Viscous Flow of Two-Component Electron Fluid in Magnetic Field

In pure conductors with a low density of defects, frequent electron-electron collisions can lead to the formation of a viscous fluid consisting of conduction electrons. In this work, is studied magnetotransport in a viscous fluid consisting of two types of electrons, for which some of their parameters are different. The difference between such system and the one-component electron fluid is as follows. The scattering of electrons with their transitions from one component to another can lead to an imbalance in flows and concentrations, which affects the flow as a whole. In this work, the balance transport equations for such a system are constructed and solved for the case of a long sample with rough edges. The equation for the flow of the unbalance value towards the edges contains the bulk viscosity term. It is shown that in sufficiently wide samples, the transformation of particles into each other during scattering leads to the formation of a single viscous fluid flowing as a whole, while in narrow samples the two components flow as two independent fluids. The width of the sample at which this transition occurs is determined by the internal parameters of the fluid and the magnitude of magnetic field. The distributions of the flow of the fluid components over a sample cross section and the magnetoresistance of a sample are calculated. The latter turns out to be positive and saturating, corresponding to the transition with increasing of magnetic field from independent Poiseuille flows of the two components to the Poiseuille flow of a uniform fluid.