Coalescence of bubbles and drops in an outer fluid

Abstract: When two liquid drops touch, a microscopic connecting liquid bridge forms and rapidly grows as the two drops merge into one. Whereas coalescence has been thoroughly studied when drops coalesce in vacuum or air, many important situations involve coalescence in a dense surrounding fluid, such as oil coalescence in brine. Here we study the merging of gas bubbles and liquid drops in an external fluid. Our data indicate that the flows occur over much larger length scales in the outer fluid than inside the drops themselves. Thus we find that the asymptotic early regime is always dominated by the viscosity of the drops, independent of the external fluid. A phase diagram showing the crossovers into the different possible late-time dynamics identifies a dimensionless number that signifies when the external viscosity can be important.

Coalescence of Bubbles and Drops in an Outer Fluid

The paper authored by Joseph D. Paulsen et al. delves into the dynamics of bubble and droplet coalescence within an external fluid. This study is distinguished from previous works focusing on coalescence in vacuum or air, providing insights into scenarios where the merging occurs in a dense surrounding fluid such as oil in brine.

Key Findings

The research presents compelling evidence that fluid flows during coalescence occur over larger length scales in the outer fluid compared to flows within the drops themselves. It identifies that the early stages of coalescence are invariably dictated by the viscosity of the inner fluid, regardless of the viscosity of the surrounding fluid. A significant aspect of this study is the establishment of a phase diagram that illustrates the transition between various late-time dynamics. This diagram not only aids in understanding these transitions but also highlights a dimensionless number signifying when external fluid viscosity becomes significant.

Experimental Insights

Through a series of experiments, the authors coalesced hemispherical drops or bubbles of varied internal viscosities within silicone oils of diverse viscosities. Notably, despite large differences in outer fluid viscosity, the neck radii remained consistent at the same time after contact, suggesting the dominant influence of the inner fluid at early times.

In instances of air bubbles merging in an outer fluid, the study discerned two distinct regimes based on outer-fluid viscosity and inertia. The respective coalescence time scales correlated well with known dimensionless constants $C_1$ and $D_1$, pointing towards a clean separation of dynamics depending on whether viscosity or inertia predominates in the outer fluid.

Transition Between Regimes

The research further investigates the transition from an initial inertially-limited-viscous regime to a regime influenced by either the inner or outer fluid inertial forces. It concludes that the outer fluid gains control in scenarios of significantly larger external viscosities. These transitions are defined within the phase diagram in detail, and specific dimensionless numbers for different fluid parameters are provided.

Theoretical and Practical Implications

Theoretically, these findings refine existing models of coalescence by integrating the influence of external fluid dynamics. Practically, understanding such dynamics has implications for industries where bubble or droplet merging in a fluid medium is common, such as food processing or biopharmaceutical production.

Future Directions

Future research may focus on extending the analysis to scenarios with higher inner-fluid Ohnesorge numbers or exploring the finer perturbations introduced by the non-dominant fluid. Additionally, developing a comprehensive theory of bubble coalescence could elucidate flows external to the neck region more rigorously.

In essence, this paper contributes substantial clarity to the multifaceted dynamics of coalescence within a surrounding fluid, enhancing both theoretical understanding and practical applications in fluid dynamics and related fields.