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## I. INTRODUCTION 

If the surface of a spherical liquid drop is briefly deformed, by a puff of air, for example, it vibrates, ringing at several different frequencies. The eigenfrequencies of these shape oscillations were determined by Lord Rayleigh, 

<img src='content_image/354730.jpg'>

where T is the surface tension, ρ is the density and a is the radius of the spherical drop at rest [1, 2]. By measuring σ , we can determine the surface tension of the liquid. Beaugnon et al. used diamagnetic levitation to measure σ of the lowest order ( l = 2) mode of a diamagnetically levitated liquid droplet [3] and, recently, we used diamagnetic levitation to investigate dynamics of a spinning water droplet [4]. A diamagnetically-levitated droplet is confined within a magnetogravitational potential trap [5, 6]. The trap acts as an addi- tional cohesive force on the drop, perturbing its eigenfrequency spectrum. Beaugnon et al. observed the shift to higher frequency of the lowest-order l = 2 mode, and determined an expression for the increase in terms of an enhanced effective surface tension [3]. However, their result cannot be generalized to the higher order modes. Here, we use diamagnetic levitation to measure the normal mode frequencies of a levitating drop, for l ≥ 2. We derive an expression for the eigenfrequencies of a liquid droplet confined by the magnetogravita- tional potential trap and compare it with our measured frequencies. Our analysis points the way to achieving accurate measurements of surface tension using this non-contact technique. We also consider the effect on the eigenfrequencies of the shape of the potential trap and consider analogies with the vibrations of a model ‘star’. 

## II. EXPERIMENTAL DETAILS 

We use a vertical-bore superconducting solenoid magnet with a room-temperature, 50 mm diameter bore to levitate droplets of water with radii ∼ 1 cm. The droplets levitate approx- imately 80 mm above the geometric center of the solenoid, where the diamagnetic force, proportional to B ∇ B , is equal in magnitude to, and opposite in direction to, the gravita- tional force on (i.e. the weight of) the droplet [5, 6]. The magnetic field is B ≈ 12 T and the vertical field gradient is ∂B/∂z ≈ 120 Tm − 1 at the levitation point. 

