Lisin E A, Vaulina O S, Lisina I I, Petrov O F
Joint Institute for High Temperatures, Russian Academy of Sciences, Moscow, 125412, Russia.
Phys Chem Chem Phys. 2021 Aug 4;23(30):16248-16257. doi: 10.1039/d1cp02511b.
Self-propelled colloids, active polymers and membranes, driven (vibrated) granular layers and hybrid synthetic-biological systems are striking examples of systems containing synthetic active Brownian particles. Such particles autonomously convert the available energy of the environment into their own directed mechanical motion. In most studies the self-propelled Brownian particles move in overdamped media. Recently, experiments with Janus particles in a low-pressure plasma have appeared. A distinctive feature of such a medium is an extremely low viscosity at which the inertial effects play a significant role, resulting in underdamped Brownian motion. At present, there is a lack of statistical theory describing the underdamped Brownian motion of self-propelled particles at all time scales. This paper presents the numerical simulation results of active Brownian motion in homogeneous media of different viscosities. The calculations are performed using a mathematical model of a self-propelled Brownian sphere with translational and rotational inertia. The time-dependent mean square displacement and mean linear displacement (the noise-averaged trajectory) of the particle are investigated as a function of medium viscosity, self-propulsion velocity and moment of inertia. Our simulation reveals that the dynamics of a self-propelled spherical particle significantly depends on two independent dimensionless parameters of the particle: the ratio of the self-propulsion velocity to the characteristic thermal velocity and the ratio of the friction coefficient to the rotational diffusion coefficient. The obtained statistical characteristics of active Brownian motion are compared with the known theoretical models in a wide range of medium viscosities. We propose simple corrections to the basic theory of overdamped active Brownian motion, which allow one to calculate the effective diffusion coefficient and the persistence length of a self-propelled Brownian particle in a medium with any dynamic viscosity. The results obtained are discussed in relation to active particles in a colloidal plasma and superfluid helium.
自驱动胶体、活性聚合物和膜、驱动（振动）颗粒层以及混合合成生物系统是包含合成活性布朗粒子的系统的显著例子。这类粒子能自主地将环境中的可用能量转化为自身的定向机械运动。在大多数研究中，自驱动布朗粒子在过阻尼介质中运动。最近，出现了在低压等离子体中对Janus粒子进行的实验。这种介质的一个显著特征是具有极低的粘度，在这种粘度下惯性效应起着重要作用，导致欠阻尼布朗运动。目前，缺乏能在所有时间尺度上描述自驱动粒子欠阻尼布朗运动的统计理论。本文给出了在不同粘度均匀介质中活性布朗运动的数值模拟结果。计算是使用具有平动和转动惯性的自驱动布朗球体的数学模型进行的。研究了粒子随时间变化的均方位移和平均线性位移（噪声平均轨迹）与介质粘度、自推进速度和转动惯量的函数关系。我们的模拟表明，自驱动球形粒子的动力学显著取决于粒子的两个独立无量纲参数：自推进速度与特征热速度的比值以及摩擦系数与转动扩散系数的比值。在很宽的介质粘度范围内，将所获得的活性布朗运动的统计特性与已知的理论模型进行了比较。我们对过阻尼活性布朗运动的基本理论提出了简单修正，这使得人们能够计算出自驱动布朗粒子在具有任何动态粘度的介质中的有效扩散系数和持久长度。讨论了所得结果与胶体等离子体和超流氦中的活性粒子的关系。
