Rotational invariance strongly constrains the viscosity tensor of classical fluids. When this symmetry is broken in anisotropic materials a wide array of novel phenomena become possible. We explore electron fluid behaviors arising from the most general viscosity tensors in two and three dimensions, constrained only thermodynamics and crystal symmetries. We find nontrivial behaviors in both two- and three-dimensional materials, including imprints of the crystal symmetry on the large-scale flow pattern. Breaking time-reversal symmetry introduces a non-dissipative Hall component to the viscosity tensor, and while this vanishes for 3D isotropic systems we show it need not for anisotropic materials. Further, for such systems we find that the electronic fluid stress can couple to the vorticity without breaking time-reversal symmetry. Our work demonstrates the anomalous landscape for electron hydrodynamics in systems beyond graphene, and presents experimental geometries to quantify the effects of electronic viscosity.

旋转不变性强烈约束经典流体的粘度张量。当各向异性材料的这种对称性被打破时，一系列新奇的现象就成为可能。我们探索由二维和三维中最常见的粘度张量产生的电子流体行为，仅约束热力学和晶体对称性。我们在二维和三维材料中发现了非平凡的行为，包括大尺度流动模式上晶体对称性的印记。打破时间反转对称性将非耗散霍尔分量引入到粘度张量中，虽然这对于 3D 各向同性系统消失，但我们表明对于各向异性材料来说不需要。此外，对于此类系统，我们发现电子流体应力可以耦合到涡度而不破坏时间反转对称性。我们的工作展示了石墨烯以外的系统中电子流体动力学的异常景观，并提出了量化电子粘度影响的实验几何结构。