Diamagnetic suspension with variable compliance for force sensing devices

Abstract

Diamagnetic levitation is applied to attain the smallest possible effective spring constant suitable for detection of weak and continuous forces relevant to various phenomena including biological ones. A Nd-Fe-B permanent magnet was suspended under aerial conditions with lifting force from a multi-layered solenoid and stabilized horizontally via repulsive interaction with a diamagnetic substance. The effective spring constant of the suspensions was analyzed via a ringdown measurement of the electromotive force caused by oscillation while changing the magnitude of the DC current in the solenoid. Measured minimum spring constant beyond which the potential energy minima along plumb direction vanishes was 26 mN/m for a ∅1.5 mm x 1.5 mm cylindrical permanent magnet in a Bi cylindrical diamagnetic pore. A variable-sized diamagnetic cavity composed of four mobile graphite slabs adaptable to cubic permanent magnets of arbitrary size was introduced to attain a smaller spring constant. The measured minimum spring constant for a 1 mm cubic permanent magnet levitated in this cavity was approximately 6 mN/m. Although the spring constant for a smaller 0.5 mm cubic magnet was not detectable with the present ringdown setup, its minimum possible value was evaluated from its volume to be below 1 mN/m, which can lead to the detection of a force below 1 nN if combined with an adequate optical displacement detection method. The measured spring constants were compared with the calculated results.

Keywords

• diamagnetic levitation
• magnetic gradient
• spring constant
• earnshaw’s theorem
• ringdown
• bismuth
• graphite