Tuning bubble coalescence rates over orders of magnitude in liquid mixtures of simple surface thermodynamics: Experiments and theory

Abstract

The coalescence time of bubbles in a liquid depends on the nature of the liquid, which determines both its surface thermodynamics and the molecular interactions between the gas/liquid interfaces, and on the geometry, prescribed by the curvature of the bubbles. Coalescence is well described in pure liquids that have the same composition in bulk and at interfaces and in which the interactions are attractive. In contrast, the mechanisms are poorly understood in more complex liquids in which coalescence times are orders of magnitudes larger than in pure liquids and are unpredictable. To provide insight on these mechanisms, we use model systems: binary mixtures of miscible oils. In these liquids, interfaces have purely attractive molecular interactions and the surface thermodynamics can simply be described using a well-determined Gibbs elastic modulus, which is controlled by the composition of the mixture. We measure the coalescence rate by forming periodic trains of bubbles in millifluidic tubes whose radius varies over 1.5 decade. We report coalescence times spanning more than three decades and, for a given composition, varying according to a power law with curvature, with an exponent larger than that reported in pure liquids and independent of Gibbs elasticity. The experimental behavior is in excellent agreement with a numerical solution of the coupled thermodynamical and hydrodynamical equations, performed in the simple geometry of a suspended liquid film. Our results clearly reveal how geometry and surface thermodynamics modify the coalescence process of bubbles in the limit of small Gibbs elasticity.