Deformation and necking of liquid droplets in a magnetic field

TL;DR

This study investigates how magnetic fields influence the deformation, shape, and pinch-off dynamics of pendant liquid droplets, revealing minimal effects on surface tension but notable shape changes due to magnetic field gradients.

Contribution

It provides new insights into the effects of uniform and nonuniform magnetic fields on droplet shape, surface tension, and pinch-off behavior, including analysis of magnetic body forces and Maxwell stress.

Findings

Magnetic fields cause shape deformation but have negligible effect on surface tension.

Magnetic field gradients induce effective density changes in droplets.

Pinch-off dynamics are unaffected by magnetic fields in the small filament regime.

Abstract

Pendant droplets of water and paramagnetic solutions are studied in the presence of uniform and nonuniform magnetic fields produced by small permanent magnet arrays, both in static conditions and during dynamic pinch-off. Static measurements of the droplet shape are analysed in terms of an apparent surface tension {\gamma}app or an effective density \r{ho}eff. The change of surface tension of deionized water in a uniform field of 450 mT is insignificant, 0.19 - 0.21 mNm-1. Measurements on droplets of compensated zero-susceptibility solutions of Cu2+, Mn2+ and Dy3+ where the shape is unaffected by any magnetic body force show changes of surface tension of about -1% in 500 mT. Magnetic field gradients of up to 100 T2m-1 deform the droplets and lead to changes of \r{ho}eff that are negative for diamagnetic solutions (buoyancy effect) and positive for paramagnetic solutions. The droplet profile of strongly-paramagnetic 0.1 Dy M DyCl3 solution is analysed, treating the nonuniform vertical field gradient as a spatial variation of gravity. The influence of Maxwell stress on droplet shape is discussed. In dynamic measurements, the droplet shape at pinch-off is recorded by high-speed photography and analysed in terms of a relative change of dynamic surface tension in the presence of a magnetic field. The surface-tension-dependent pre-factor of the scaling law that governs the pinch-off dynamics shows no difference for pure water or 0.11 M DyCl3 solutions in the field. The nonuniform field has no influence in the pinch-off region because the filament diameter is much less than the capillary length.