Extended Stokesian dynamics for the calculation of active particles dynamics in an arbitrary confined space

The analysis of active particle dynamics in their confined suspensions provides valuable insights into a range of fields, including biology and medical engineering; it would be useful in understanding bacterial distribution in the gut and in optimizing the design of microrobots for use in drug delivery systems. In the present study, a novel methodology combining the Stokesian dynamics method (SDM) and the boundary element method (BEM) was developed for calculating the motion of active particles in a confined boundary. The SDM was adopted to calculate the motion of the particles, while the BEM was integrated into the SDM to calculate the fluid dynamics in the presence of a boundary wall. The accuracy of the developed method was validated and guaranteed by comparing the velocities of an active particle moving near a flat wall obtained by the present method with those obtained only by the BEM. It was also demonstrated that the number of particles that can be handled can be increased from 10 to 100 times that of BEM for the same calculation time, and the calculation time can be reduced by one-tenth for the same number of particles. The proposed method is applied to some problem settings where many active particles swim in a complex closed geometry, which illustrates the strength of the proposed methodology.