Deformation and necking of liquid droplets in a magnetic field

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 analyzed in terms of an apparent surface tension γapp or an effective density ρeff. 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 T2 m−1 deform the droplets and lead to changes of ρeff that are negative for diamagnetic solutions (buoyancy effect) and positive for paramagnetic solutions. The droplet profile of strongly paramagnetic 0.1 molar DyCl3 solution is analyzed, treating the nonuniform vertical field gradient as a spatial variation of gravity. The influence of Maxwell stress on the droplet shape is discussed. In dynamic measurements, the droplet shape at pinch-off is recorded by high-speed photography and analyzed in terms of a relative change of dynamic surface tension in the presence of a magnetic field. The surface-tension-dependent prefactor 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.