ten Hagen Borge, Wittkowski Raphael, Takagi Daisuke, Kümmel Felix, Bechinger Clemens, Löwen Hartmut
Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, D-40225 Düsseldorf, Germany.
J Phys Condens Matter. 2015 May 20;27(19):194110. doi: 10.1088/0953-8984/27/19/194110. Epub 2015 Apr 29.
The self-propulsion of artificial and biological microswimmers (or active colloidal particles) has often been modelled by using a force and a torque entering into the overdamped equations for the Brownian motion of passive particles. This seemingly contradicts the fact that a swimmer is force-free and torque-free, i.e. that the net force and torque on the particle vanish. Using different models for mechanical and diffusiophoretic self-propulsion, we demonstrate here that the equations of motion of microswimmers can be mapped onto those of passive particles with the shape-dependent grand resistance matrix and formally external effective forces and torques. This is consistent with experimental findings on the circular motion of artificial asymmetric microswimmers driven by self-diffusiophoresis. The concept of effective self-propulsion forces and torques significantly facilitates the understanding of the swimming paths, e.g. for a microswimmer under gravity. However, this concept has its limitations when the self-propulsion mechanism of a swimmer is disturbed either by another particle in its close vicinity or by interactions with obstacles, such as a wall.
人工和生物微游动体（或活性胶体粒子）的自推进通常通过引入一个力和一个扭矩来建模，该力和扭矩进入被动粒子布朗运动的过阻尼方程。这似乎与游动体不受力和扭矩的事实相矛盾，即粒子上的净力和扭矩为零。通过使用不同的机械和扩散泳动自推进模型，我们在此证明，微游动体的运动方程可以通过形状依赖的广义阻力矩阵以及形式上的外部有效力和扭矩映射到被动粒子的运动方程。这与关于自扩散泳动驱动的人工不对称微游动体圆周运动的实验结果一致。有效自推进力和扭矩的概念极大地促进了对游动路径的理解，例如对于重力作用下的微游动体。然而，当游动体的自推进机制受到其附近另一个粒子或与障碍物（如壁）的相互作用干扰时，这个概念有其局限性。
