Near-hydrodynamic flow according to the linearized electron Boltzmann equation

Near-hydrodynamic electron flows have been realized in a number of recent experiments, where momentum conserving collisions dominate the flow behavior. We present a matched asymptotic expansion of the governing Boltzmann equation to second order in the rarefaction parameter—the Knudsen number—for steady near-hydrodynamic electron flows with arbitrary diffusely scattering boundaries. We find corrections to the bulk governing equations and boundary corrections unreported in the literature. The developed theory is used to solve two-dimensional Poiseuille flow in the near-hydrodynamic regime. Non-hydrodynamic corrections are found to compete with the classical Hall viscosity. Our results are in excellent agreement with high-fidelity numerical solutions of the linearized Boltzmann equation.