Role of Laplace pressure in the equilibrium of a hanging drop by a mechanical loading

Abstract : For a very low feed rate, it can be assumedthat a hanging drop at the end of a capillary remains in near equilibrium just before breaking.The equilibrium condition indicates that the action of the capillary force must oppose the weight of the drop, to which should be added the force due to Laplace pressure.Thus, for a given fluid and a fixed wet perimeter, the maximum mass of a hanging drop should be constant if Laplace pressure is also constant.We modulated this pressure by modifying the main curvatures of the dropandwe observed that the mass of the drop is not constant.For three contrasting surface tension liquids, drops were made with five different needle diameters.They were loaded with glass beads of increasing mass respecting the axi-symmetry of the system.This loading induces a stretchingof the drop that modulates the main curvatures.The measurements of the volumesand curvature radii for different loadingratesare performedby image analysis.These loading experimentshighlight the increase of Laplace pressure with theloading and the non-linear decrease of the drop mass.However, we observethat the liquid mass in the loaded drop decreases linearly with the increase of the beadmasswithout verifyingthe mass balance.Such aresult isincluded ina master curve which highlights the role of the Laplace pressure in the equilibrium of a hanging drop just before its rupture.It challenges the validity of Tate's law and allows the setting of functional ranges for capillary micromanipulators.