Abstract
We study the evolution of the growing volume of a droplet formed out of a capillary tube driven at a constant applied pressure by optical volume detection. A particular application aims at modeling the dynamic of the drop in the case of the injection of drugs in the middle-ear cavity using a small target drug delivery system. Various dispense tips such as a steel needle or silicone catheters and different t-BuOH aqueous solutions were used. A physical model based on the simplified Laplace–Young equation for a spherical droplet was developed to interpret the experimental results and model the observed deviation of the mean flow rate from the Poiseuille law when the drop radius is smaller than the capillary length. We emphasize the large influence of the surface tension which introduces a highly nonlinear effect at low applied pressure just above the capillary threshold pressure. The model fits well the evolution of the growing volume at various applied pressure up to a maximum diameter corresponding to the drop size close to the capillary length of the fluid, , based on the liquid density ρ, gravity g and surface tension γ. We demonstrate that the model can also be applied to non spherical pendant droplets providing the apex elongation over the drop height of a spherical cap of the same volume is kept in a 30% range.