论文标题
通过有限宽度缝隙的粘性流量：边界条件和耗散
Viscous flow through a finite-width slit: Boundary conditions and dissipation
论文作者
论文摘要
我们在二维样品中研究流体动力粘性电子传输，该样品通过一维无限屏障分为两个半侵入平面。半无限平面通过屏障中的有限大小缝隙进行电连接。我们通过缝隙计算电流，假设平面之间有限电压下降并忽略了障碍诱导的欧姆电阻，因此耗散和电阻纯粹是粘度引起的。我们发现，该几何形状中唯一的解决方案是在有限的电阻下产生有限的耗散（因此，并非自相矛盾），是一种同时满足无压力和无滑动边界条件的耗散。这是一个显着的结果，所获得的速度曲线满足了所谓的“部分滑坡”（Maxwell）边界条件，即滑动长度的任何值，这从所有最终结果中删除。我们还计算了小型和较大的热电导率的电子温度曲线，并在前一种情况下发现不对称（相对于屏障）温度模式。
We study the hydrodynamic viscous electronic transport in a two-dimensional sample separated into two semi-infinite planes by a one-dimensional infinite barrier. The semi-infinite planes are electrically connected via the finite-size slit in the barrier. We calculate the current through the slit assuming finite voltage drop between the planes and neglecting disorder-induced Ohmic resistance, so that dissipation and resistance are purely viscosity-induced. We find that the only solution to the Stokes equation in this geometry, which yields a finite dissipation at finite resistance (and, hence, is not self-contradictory), is the one that fulfills both the no-stress and no-slip boundary conditions simultaneously. As a remarkable consequence, the obtained velocity profile satisfies the so-called "partial-slip" (Maxwell) boundary condition for any value of the slip length, which drops out from all final results. We also calculate the electronic temperature profile for the small and large heat conductivity, and find asymmetric (with respect to the barrier) temperature patterns in the former case.
