手性活性物质：微观“扭矩偶极子”具有一种以上的流体动力学描述
Chiral active matter: microscopic `torque dipoles' have more than one hydrodynamic description
摘要：
许多生物系统，如细菌悬浮液和肌动球蛋白网络，形成极性液晶。这些系统是“活跃的”或远离平衡，由于溶剂的组成颗粒的局部强制。在许多情况下，活动的来源是手征性的;由于强迫是内部产生的，因此局部存在某种“扭矩偶极子”。但是，在描述系统的流体动力学方程中如何对“扭矩偶极子”进行编码并不明显：不同的作者在这个问题上得出了相互矛盾的结论。在这项工作中，我们解决的悖论提出了一个仔细的推导，从线性不可逆热力学，一般的运动方程的单组分手性活性流体的自旋自由度。我们发现，有没有独特的流体动力学描述这样的流体中存在的扭矩偶极子的一个给定的强度。相反，至少出现了三种不同的流体动力学描述，这取决于我们是否将每个扭矩偶极子分解为两个点扭矩，两个力对，或者一个点扭矩和一个力对-其中点扭矩产生手性物体的内角动量（自旋），而力对赋予有助于流体速度的质心运动。通过考虑一个一般的扩展的Onsager系数，我们还得到了一个新的剪切伸长参数和交叉耦合粘度，这可能会导致不可预测的现象，即使在被动极性液晶。最后，消除角变量给出了一个有效的极地流体动力学与重整化的主动应力，粘度和动力学系数。值得注意的是，这可以包括手性活性对极性序参量的运动方程的直接贡献，其甚至在流体速度设置为零的“干”活性系统中仍然存在。
英文摘要：
Many biological systems, such as bacterial suspensions and actomyosin networks, form polar liquid crystals. These systems are `active' or far-from-equilibrium, due to local forcing of the solvent by the constituent particles. In many cases the source of activity is chiral; since forcing is internally generated, some sort of `torque dipole' is then present locally. But it is not obvious how `torque dipoles' should be encoded in the hydrodynamic equations that describe the system at continuum level: different authors have arrived at contradictory conclusions on this issue. In this work, we resolve the paradox by presenting a careful derivation, from linear irreversible thermodynamics, of the general equations of motion of a single-component chiral active fluid with spin degrees of freedom. We find that there is no unique hydrodynamic description for such a fluid in the presence of torque dipoles of a given strength. Instead, at least three different hydrodynamic descriptions emerge, depending on whether we decompose each torque dipole as two point torques, two force pairs, or one point torque and one force pair -- where point torques create internal angular momenta of the chiral bodies (spin), whereas force pairs impart centre of mass motion that contributes to fluid velocity. By considering a general expansion of the Onsager coefficients, we also derive a new shear-elongation parameter and cross-coupling viscosity, which can lead to unpredicted phenomena even in passive polar liquid crystals. Finally, elimination of the angular variables gives an effective polar hydrodynamics with renormalized active stresses, viscosities and kinetic coefficients. Remarkably, this can include a direct contribution of chiral activity to the equation of motion for the polar order parameter, which survives even in `dry' active systems where the fluid velocity is set to zero.
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