涡量决定作用在流体中物体上的力
Vorticity Determines the Force on Bodies Immersed in Active Fluids
摘要：
当浸入主动布朗粒子的流体中时，被动体可能开始根据其形状进行线性或角向运动。在这里，我们利用发散定理，将导致这种运动的力与密度和电流联系起来，这些力是由物体引起的，但距离物体很远。一般来说，力由两个贡献组成：由于偶极场分量的强度和由于粒子离开边界，产生非零的极化涡度。我们推导和数值证实结果的周期性系统，这是从根本上不同的无界系统的力量，规模与系统的面积。我们表明，涡是本地化接近的身体和点的局部曲率的变化，使合理的设计粒子的形状与所需的推进性能。
英文摘要：
When immersed into a fluid of active Brownian particles, passive bodies might start to undergo linear or angular directed motion depending on their shape. Here we exploit the divergence theorem to relate the forces responsible for this motion to the density and current induced by--but far away from--the body. In general, the force is composed of two contributions: due to the strength of the dipolar field component and due to particles leaving the boundary, generating a non-vanishing vorticity of the polarization. We derive and numerically corroborate results for periodic systems, which are fundamentally different from unbounded systems with forces that scale with the area of the system. We demonstrate that vorticity is localized close to the body and to points at which the local curvature changes, enabling the rational design of particle shapes with desired propulsion properties.
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