Locally Induced Analog Casimir Force from a Self-propelling Vibrating Robot Boat

Active agents on fluid surfaces can perturb their surroundings by creating waves that reciprocally affect the agent. Inspired by the wave-mediated dynamics of surface-bouncing droplets, we study the motion and wave-field dynamics of a 5.9 cm radius, 8.8 cm tall, eccentric motor-driven vibrating robot boat on the surface of a 4 cm deep pool of water. The boat's vibration creates outwardly propagating surface waves with frequency range 10-63 Hz; a Schlieren method enables surface wave visualization with submillimeter resolution. Far from boundaries, the boat generates circular waves for frequencies below ~40 Hz with maximum amplitude 0.6 mm; above ~40 Hz, the waves gain subharmonic components. When held near a planar boundary by a thin 1.4 m wire, the wave field becomes complex, and the boat experiences a force analogous to the Casimir effect. Below the subharmonic threshold, the boat moves less than 0.5 mm toward/away from the wall; above the threshold, displacements grow to 0.5-1.5 mm. For all frequencies, a lower/higher initial distance skews the force toward attraction/repulsion. The effect is stable to slight perturbation: for repulsive cases, a boat perturbed toward the wall returns to a stable position; for attractive cases, a boat perturbed away accelerates toward the wall.