Winkler Roland G, Wysocki Adam, Gompper Gerhard
Theoretical Soft Matter and Biophysics, Institute for Advanced Simulation and Institute of Complex Systems, Forschungszentrum Jülich, D-52425 Jülich, Germany.
Soft Matter. 2015 Sep 7;11(33):6680-91. doi: 10.1039/c5sm01412c.
The pressure of suspensions of self-propelled objects is studied theoretically and by simulation of spherical active Brownian particles (ABPs). We show that for certain geometries, the mechanical pressure as force/area of confined systems can be equally expressed by bulk properties, which implies the existence of a nonequilibrium equation of state. Exploiting the virial theorem, we derive expressions for the pressure of ABPs confined by solid walls or exposed to periodic boundary conditions. In both cases, the pressure comprises three contributions: the ideal-gas pressure due to white-noise random forces, an activity-induced pressure ("swim pressure"), which can be expressed in terms of a product of the bare and a mean effective particle velocity, and the contribution by interparticle forces. We find that the pressure of spherical ABPs in confined systems explicitly depends on the presence of the confining walls and the particle-wall interactions, which has no correspondence in systems with periodic boundary conditions. Our simulations of three-dimensional ABPs in systems with periodic boundary conditions reveal a pressure-concentration dependence that becomes increasingly nonmonotonic with increasing activity. Above a critical activity and ABP concentration, a phase transition occurs, which is reflected in a rapid and steep change of the pressure. We present and discuss the pressure for various activities and analyse the contributions of the individual pressure components.
通过对球形活性布朗粒子（ABP）进行理论研究和模拟，我们研究了自推进物体悬浮液的压力。我们表明，对于某些几何形状，作为受限系统的力/面积的机械压力可以同样由体性质来表示，这意味着存在非平衡状态方程。利用维里定理，我们推导了由固体壁限制或暴露于周期性边界条件下的ABP的压力表达式。在这两种情况下，压力都包含三个贡献：由白噪声随机力引起的理想气体压力、一个活性诱导压力（“游动压力”），它可以用裸粒子速度和平均有效粒子速度的乘积来表示，以及粒子间力的贡献。我们发现，受限系统中球形ABP的压力明确取决于限制壁的存在和粒子 - 壁相互作用，这在具有周期性边界条件的系统中没有对应情况。我们对具有周期性边界条件的系统中的三维ABP进行的模拟揭示了压力 - 浓度依赖性，随着活性增加，这种依赖性变得越来越非单调。在临界活性和ABP浓度以上，会发生相变，这反映在压力的快速和急剧变化中。我们给出并讨论了各种活性下的压力，并分析了各个压力分量的贡献。
