In pure conductors with a low density of defects, frequent electron-electron collisions can lead to formation of a viscous electron fluid. For the case of two-dimensional electrons with a quadratic energy spectrum, the resistance of samples with such fluid is proportional to the fluid viscosity. The dependence of the viscosity on the magnetic field, perpendicular to the electron layer, leads to a strong negative magnetoresistance. Apparently, such magnetoresistance has been recently observed in high-quality graphene, GaAs quantum wells and some other conductors. In this work, is studied magnetotransport in a viscous fluid consisting of electrons of two types, both of which have a quadratic energy spectrum, but different densities and viscosities. It is shown that a weak scattering of electrons with their conversion from one type to another can lead to an imbalance in flows and densities of the fluid components, affecting the flow as a whole. For the case of degenerate electrons in two Zeeman spin-splitted subbands, such effect is an example of the spin Hall effects in a viscous electron fluid. The balance hydrodynamic equations are constructed and solved for a long sample with rough edges. The equation for the current of the imbalance between the densities of electrons of the two types towards the sample edges contains the bulk viscosity term. The resulting imbalance current is “crumpled” in the direction of the normal to the edges. It is shown that in sufficiently wide samples, the transformation of electrons from one type into other during scattering leads to the formation of a single viscous fluid flowing as a whole, while in narrow samples the two components of the fluid flows independently. The width of the sample at which this transition occurs is determined by magnetic field and the internal parameters of the fluid, in particular, by the bulk viscosity. The distributions of the flows of the fluid components and the magnetoresistance of a sample are calculated. The latter turns out to be positive and saturating, reflecting the transition between the two described above regimes with the increase of magnetic field. Possibly, the studied effect is responsible for the damping of the giant negative magnetoresistance in GaAs quantum wells with application of an inclined magnetic field (its in-plane component leads to the appearance of the two fluid components in the spin-splitted Zeeman subbands).

This work has been supported by Russian Science Foundation (project #18-72-10111).