The dynamics of confined droplets

The dynamics of confined droplets has been extensively studied during the last decades, in the footsteps of the development of digital microfluidics. In the field of oil recovery, numerous phenomena lead to the emulsification of petroleum while transported across a reservoir, e.g. viscous fingering or snap-off. The understanding of the peculiar dynamics of confined droplets and emulsions is thus of crucial importance.
In a first part, we will discuss the shapes and velocities of completely wetting droplets of oil sliding under gravity between closely spaced parallel walls (Hele-Shaw cell). Viscous dissipation opposing the motion takes place both in the bulk of the liquid and in the vicinity of contact lines. In this model geometry, bulk and line effects may be measured independently. We investigate contact line dissipation by studying the motion of droplets on pre-wetted surfaces, a way to regularize the contact line singularity in a controlled way.

In a second part, we focus on the dynamics of non-wetting droplets of oil confined in a vertical Hele-Shaw cell filled with a much less viscous surfactant solution. The oil droplets are denser than the aqueous solution and move at constant speed driven by gravity. The surfactant solution completely wets the walls, and a thin lubrication film separates the oil droplets from the walls. For a cell with smooth walls, two main dynamical regimes are characterized as the gap between the walls is varied. Viscous dissipation is found to dominate either in the droplet or in the lubrication film. A sharp transition between both regimes is observed and successfully captured by asymptotic models. For a cell with rough walls, that transition is found to be dramatically altered. We show that droplets are generally much slower in a rough Hele-Shaw cell, in comparison with a similar smooth cell. Building up on the seminal work of Seiwert et al. (JFM, 2011) on film deposition by dip coating on a rough surface, we shed light on non-trivial friction processes resulting from the interplay of viscous dissipation at the front of the droplet, in the lubrication film and in the bulk of the droplet.

The dynamics of confined droplets has been extensively studied during the last decades, in the footsteps of the development of digital microfluidics. In the field of oil recovery, numerous phenomena lead to the emulsification of petroleum while transported across a reservoir, e.g. viscous fingering or snap-off. The understanding of the peculiar dynamics of confined droplets and emulsions is thus of crucial importance.

In a first part, we will discuss the shapes and velocities of completely wetting droplets of oil sliding under gravity between closely spaced parallel walls (Hele-Shaw cell). Viscous dissipation opposing the motion takes place both in the bulk of the liquid and in the vicinity of contact lines. In this model geometry, bulk and line effects may be measured independently. We investigate contact line dissipation by studying the motion of droplets on pre-wetted surfaces, a way to regularize the contact line singularity in a controlled way.

In a second part, we focus on the dynamics of non-wetting droplets of oil confined in a vertical Hele-Shaw cell filled with a much less viscous surfactant solution. The oil droplets are denser than the aqueous solution and move at constant speed driven by gravity. The surfactant solution completely wets the walls, and a thin lubrication film separates the oil droplets from the walls. For a cell with smooth walls, two main dynamical regimes are characterized as the gap between the walls is varied. Viscous dissipation is found to dominate either in the droplet or in the lubrication film. A sharp transition between both regimes is observed and successfully captured by asymptotic models. For a cell with rough walls, that transition is found to be dramatically altered. We show that droplets are generally much slower in a rough Hele-Shaw cell, in comparison with a similar smooth cell. Building up on the seminal work of Seiwert et al. (JFM, 2011) on film deposition by dip coating on a rough surface, we shed light on non-trivial friction processes resulting from the interplay of viscous dissipation at the front of the droplet, in the lubrication film and in the bulk of the droplet.