2007/07/10 by Vishwajeet Mehandia, VISHWAJEET MEHANDIA, Prabhu R. Nott +1 · 1 citation
Engineering · Materials Science · Physics and Astronomy · #Constant (computer programming) #Dipole #Drag #Magnetosphere particle motion #Micro and Nano Robotics #Modular Robots and Swarm Intelligence #Newtonian fluid #Orientation (vector space) #Particle (ecology) #Pickering emulsions and particle stabilization #Range (aeronautics) #Stokes flow #Suspension (topology) #cond-mat.soft #cond-mat.stat-mech
paper · pdf · doi:10.1017/s0022112007009184
25 pages, 19 figures, under review in J. Fluid. Mech
arxiv created 2007/07/10 · openalex publication_date 2008/01/08 · arxiv updated 2015/05/12 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We propose a method for the dynamic simulation of a collection of self-propelled particles in a viscous Newtonian fluid. We restrict attention to particles whose size and velocity are small enough that the fluid motion is in the creeping flow regime. We propose a simple model for a self-propelled particle, and extended the Stokesian Dynamics method to conduct dynamic simulations of a collection of such particles. In our description, each particle is treated as a sphere with an orientation vector p , whose locomotion is driven by the action of a force dipole S p of constant magnitude S 0 at a point slightly displaced from its centre. To simplify the calculation, we place the dipole at the centre of the particle, and introduce a virtual propulsion force F p to effect propulsion. The magnitude F 0 of this force is proportional to S 0 . The directions of S p and F p are determined by p . In isolation, a self-propelled particle moves at a constant velocity u 0 p , with the speed u 0 determined by S 0 . When it coexists with many such particles, its hydrodynamic interaction with the other particles alters its velocity and, more importantly, its orientation. As a result, the motion of the particle is chaotic. Our simulations are not restricted to low particle concentration, as we implement the full hydrodynamic interactions between the particles, but we restrict the motion of particles to two dimensions to reduce computation. We have studied the statistical properties of a suspension of self-propelled particles for a range of the particle concentration, quantified by the area fraction φ a . We find several interesting features in the microstructure and statistics. We find that particles tend to swim in clusters wherein they are in close proximity. Consequently, incorporating the finite size of the particles and the near-field hydrodynamic interactions is of the essence. There is a continuous process of breakage and formation of the clusters. We find that the distributions of particle velocity at low and high φ a are qualitatively different; it is close to the normal distribution at high φ a , in agreement with experimental measurements. The motion of the particles is diffusive at long time, and the self-diffusivity decreases with increasing φ a . The pair correlation function shows a large anisotropic build-up near contact, which decays rapidly with separation. There is also an anisotropic orientation correlation near contact, which decays more slowly with separation. Movies are available with the online version of the paper.