Drops and bubbles in wedges

Abstract

We investigate experimentally the spontaneous motion of drops and bubbles confined between two plates forming a narrow wedge. Such discoidal objects migrate under the gradient in interfacial energy induced by the non-homogeneous confinement. The resulting capillary driving force is balanced by viscous resistance. The viscous friction on a drop bridging parallel plates is estimated by measuring its sliding velocity under gravity. The viscous forces are the sum of two contributions, from the bulk of the liquid and from contact lines, the relative strength of which depends on the drop size and velocity and the physical properties of the liquid. The balance of capillarity and viscosity quantitatively explains the dynamics of spontaneous migration of a drop in a wedge. Close the tip of the wedge, bulk dissipation dominates and the migrating velocity of drops is constant and independent of drop volume. The distance between the drop and the tip of the wedge is thus linear with time t: x(t) ∼ t 0 − t, where t 0 is the time at which the drop reaches the tip of the wedge. Far away from the apex, contact lines dominate the friction, the motion is accelerated toward the tip of the wedge and velocities are higher for larger drops. In this regime, it is shown that x(t) ∼ (t 0 −t) 4/13 . The position and time of the crossover between the two dissipation regimes are used to write a dimensionless equation of motion. Plotted in rescaled variables, all experimental trajectories collapse to the prediction of our model. In contrast to drops, gas bubbles in a liquid-filled wedge behave as non-wetting objects. They thus escape the confinement of the wedge to reduce their surface area. The physical mechanisms involved are similar for drops and bubbles, so that the forces acting have the same mathematical structures in both cases, except for the sign of the capillary driving force and a numerical factor. We thus predict and show experimentally that the trajectories of drops and bubbles obey the same equation of motion,except for a change in the sign of t 0 − t.

Washing wedges: capillary instability in a gradient of confinement

“…This prediction is, in particular, important in the dynamics of foams sliding against a wall (Cantat 2013). It also enables one to account for the motion of a drop bridging the walls of a Hele-Shaw cell and flowing under its own weight (Reyssat 2014). Equivalently, Park & Homsy (1984) have shown that in the case of a non-wetting fluid displacing a wetting phase in a Hele-Shaw cell, dynamic wetting modifies the interfacial pressure jump by adding a term of order (γ /h)Ca 2/3 w .…”

“…Conversely, Lorenceau & Quéré (2004) showed that a drop of wetting oil deposited on a conical fibre spontaneously moves away from the tip. More recently, gradients of confinement have been proposed as a solution to propel droplets in narrow channels (Renvoisé et al 2009) or as an elegant tool to produce and guide droplets in microfluidic devices (Dangla, Kayi & Baroud 2013), while Reyssat (2014) analysed the dynamics of drops and bubbles confined in wedges.…”

Influence of Bubbles on the Energy Conversion Efficiency of Electrochemical Reactors

“…145,146,147 This principle is based on capillary pressure gradients that evolve when bubbles are deformed by a tapered channel. 148 Another effective geometrical approach involves the use of hemispherical channels and wells which can capture traveling bubbles in a highly gas permeable microchannel (e.g., Poly-dimethyl siloxane, PDMS, channels), such that the bubbles trapped spontaneously dissipate. 149 This approach is limited by the permeability of the gas in the channel material and is effective when the gas evolution rate is slow.…”

Film thickness distribution in gravity-driven pancake-shaped droplets rising in a Hele-Shaw cell

“…The experimental data are plotted against the theoretical equation ( that for low Ca ranges, the dissipation in the thin film (Keiser et al 2018) and in the dynamic meniscus (Reyssat 2014) have to be taken into account.…”