Topography of the lubrication film under a pancake droplet travelling in a Hele-Shaw cell

Abstract

Understanding the dynamics of a droplet pushed by an external fluid in a confined geometry calls for the identification of all the dissipation mechanisms at play in the lubrication film between droplet and cell wall. Experimentally, reflection interference contrast microscopy has proven an efficient tool to measure the thickness of such lubrication films for microfluidic droplets, with a precision of a few nanometres (Huerre et al., Lab on a Chip, vol. 16 (5), 2016, pp. 911–916). The present work takes advantage of the high accuracy of this technique to chart quantitatively the lubrication film between oil droplets and the glass wall of a microfluidic chamber. We find that the lubrication films exhibit a complex three-dimensional shape, which we are able to rationalize using a hydrodynamical model in the lubrication approximation. We show that the complete topography cannot be recovered using a single model boundary condition along the whole interface. Rather, surface tension gradients are negligible at the front of the droplet, whereas they significantly modify the film profile at the rear, where surfactant accumulation induces local thickening of the lubrication film. The presence of ravines on the sides of the droplet is due to three-dimensional effects which can be qualitatively reproduced numerically. To our knowledge, this is the first experimental investigation of such local effects on travelling droplets.