Ferrofluidic Manipulator: Theoretical Model for Single-Particle Velocity

Theoretical models have crucial importance in the design of algorithms for feedback control of robotic micromanipulation platforms. More importantly, theoretical models provide an understanding of the limits of each manipulation approach along with the identification of the key parameters that influence motion performance. Here, we provide a mathematical framework and numerical implementation of the velocity field for a single diamagnetic particle pinned at the air–ferrofluid interface when it is actuated by one or more inclined electromagnets in a system previously introduced as the ferrofluidic manipulator (Cenev et al., 2021). The theoretical model uses a magnetic dipole approximation for a dipole located between the tip of a solenoid and the end of the coil. The model reveals that the forces due to gravitation, the applied magnetic field, and the capillary action have decreasing contributions to the overall velocity field, respectively. The model assumes overdamped dynamics, and therefore, it is time-independent. The model is valid for an infinite number of electromagnetic solenoids. The theoretical predictions are in good agreement with the estimations from experimental data realized for one and two actuated solenoids.