A bar-joint model based on the corrected resistive force theory for artificial flagellated micro-swimmers propelled by acoustic waves

In this work, we proposed a bar-joint model based on the corrected resistive force theory (CRFT) for studying artificial flagellated micro-swimmers (AFMSs) propelled by acoustic waves in a two-dimensional (2D) flow field or with a rectangular cross-section. Note that the classical resistive-force theory for 3D cylindrical flagellum leads to over 90% deviation in terminal velocity from those of 2D fluid-structure interaction (FSI) simulations, while the proposed CRFT bar-joint model can reduce the deviation to below 5%; hence, it enables a reliable prediction of the 2D locomotion of an acoustically actuated AFMS with a rectangular cross-section, which is the case in some experiments. Introduced in the CRFT is a single correction factor K determined by comparing the linear terminal velocities under acoustic actuation obtained from the CRFT with those from simulations. After the determination of K, detailed comparisons of trajectories between the CRFT-based bar-joint AFMS model and the FSI simulation were presented, exhibiting an excellent consistency. Finally, a numerical demonstration of the purely acoustic or magneto-acoustic steering of an AFMS based on the CRFT was presented, which can be one of the choices for future AFMS-based precision therapy.