二维手性流体中的稳定基态。手性斯托克斯腔
Steady base states in a two-dimensional chiral fluid. The chiral Stokes cavity
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中文总结 AI 辅助
研究二维手性流体稳定基态，通过强制角动量守恒推导应力张量等，将经典通道与手性伙伴对应，给出手性斯托克斯腔相关系统及求解，得出无量纲组控制几何形状和转变，可定量预测并恢复文献现象学框架。
中文摘要 AI 辅助
我们从第一原理出发，发展了二维手性流体的流体动力学，即携带净微观角动量（自旋）场的流体。在不施加应力张量对称性的情况下强制角动量守恒，我们推导出应力张量和自旋通量的完整形式，并表明整个手性响应是由一个具有直接物理起源的单一操作从经典牛顿响应生成的——手性作用的90°旋转，在粒子层面由横向力反映。应用于不可约（偏量）分解时，该旋转为每个经典通道分配一个手性伙伴——压力到手性压力，体黏度和剪切黏度到它们的奇数对应物，自旋通量梯度到其旋转图像——每个通道一个系数和一个机械作用，没有进一步的交叉耦合。在这种表示中，稳定基态变得基本。静态状态由全纯手性复势组织，机械压力和手性压力形成一对共轭调和对，受拓扑存在条件约束；不均匀的活动力导致方位流；边界驱动的受限流，即手性斯托克斯腔，服从修正的亥姆霍兹 - 泊松系统，在圆形域中以封闭形式求解，在方形域中进行数值求解。一个单一的无量纲组控制两种几何形状，并设定从屏蔽单涡 regime 到一系列符号反转涡旋结构的转变。该理论产生定量预测，便于与气浮手性盘的实验直接比较，并作为特殊情况恢复了手性流体文献的现象学框架。
英文摘要
We develop from first principles the hydrodynamics of a two-dimensional chiral fluid, i.e. one carrying a net microscopic angular-momentum (spin) field. Enforcing angular-momentum conservation without imposing stress-tensor symmetry, we derive the full form of the stress tensor and of the spin flux, and we show that the entire chiral response is generated from the classical Newtonian one by a single operation of direct physical origin --- the $90^{\circ}$ rotation through which chirality acts, mirrored at the particle level by transverse forces (Caprini & Marini Bettolo Marconi 2025). Applied to the irreducible (deviatoric) decomposition, the rotation assigns to each classical channel a chiral partner --- pressure to chiral pressure, bulk and shear viscosities to their odd counterparts, the spin-flux gradient to its rotated image --- one coefficient and one mechanical action per channel, with no further cross-couplings. In this representation the steady base states become elementary. Quiescent states are organised by a holomorphic chiral complex potential, the mechanical and chiral pressures forming a conjugate harmonic pair subject to a topological existence condition; inhomogeneous activity forces azimuthal flows; and a boundary-driven confined flow, the chiral Stokes cavity, obeys a modified Helmholtz--Poisson system, solved in closed form in a circular domain and numerically in a square one. A single dimensionless group controls both geometries and sets the crossover from a screened, single-vortex regime to a sequence of sign-reversing vortical structures. The theory yields quantitative predictions, amenable to direct comparison with experiments on air-fluidised chiral disks (López-Castaño et al. 2022), and recovers the phenomenological frameworks of the chiral-fluid literature as particular cases.
