Coalescence of bubbles & drops
Coalescence of Bubbles & Drops
Coalescence is a process where two or more droplets or bubbles merge during contact to form a single daughter droplet or bubble. This phenomenon is crucial in various fields, including emulsion technology, mineral flotation, foam stability, and oil recovery.
Understanding Coalescence
When two droplets or bubbles come into contact, the thin film of fluid between them starts to drain due to various forces. If this film becomes unstable and ruptures, the droplets or bubbles will merge. This process can be influenced by several factors, including surface tension, viscosity, and the presence of surfactants.
Factors Affecting Coalescence
- Surface Tension: The tendency of a fluid surface to shrink into the minimum surface area possible.
- Viscosity: A measure of a fluid's resistance to deformation at a given rate.
- Surfactants: Substances that reduce the surface tension of a fluid, affecting the stability of the film between droplets or bubbles.
Coalescence Process
- Approach: Droplets/bubbles move towards each other, often due to external forces like gravity or flow.
- Film Drainage: The liquid film between the droplets/bubbles starts to drain.
- Film Instability: Instabilities in the film may develop, leading to thin spots.
- Film Rupture: The film ruptures when the thickness reaches a critical value.
- Coalescence: The contents of the droplets/bubbles merge to form a larger entity.
Mathematical Description
The drainage of the film between two approaching droplets or bubbles can be described by the Reynolds lubrication theory. The time it takes for the film to drain to a critical thickness, $h_c$, before rupture can occur is given by:
$$ t = \frac{\mu R^2}{\Delta P h_c} $$
where:
- $t$ is the drainage time,
- $\mu$ is the viscosity of the fluid,
- $R$ is the radius of the droplets/bubbles,
- $\Delta P$ is the pressure difference driving the drainage.
Differences Between Bubbles and Drops Coalescence
| Aspect | Bubbles | Drops |
|---|---|---|
| Medium | Typically in a liquid | Typically in a gas or another immiscible liquid |
| Surface Tension | Influences the bubble's stability | Influences the drop's shape and stability |
| Viscosity | Affects the drainage rate of the liquid film | Affects the coalescence rate |
| Influence of Gravity | Less significant due to buoyancy | More significant, leading to sedimentation |
| Surfactants | Can stabilize or destabilize the bubble film | Can stabilize or destabilize the drop film |
Examples
Example 1: Coalescence in Emulsions
In an oil-in-water emulsion, oil droplets can coalesce to form larger oil droplets. The presence of surfactants can stabilize the emulsion by preventing coalescence.
Example 2: Bubble Coalescence in Foam
In a foam, bubbles tend to coalesce over time, leading to the collapse of the foam. Surfactants can be added to stabilize the foam by creating a rigid film around the bubbles.
Example 3: Raindrop Formation
As small droplets in a cloud collide and coalesce, they form larger raindrops. This process continues until the drops become large enough to fall to the ground due to gravity.
Conclusion
Coalescence of bubbles and drops is a complex process influenced by various factors. Understanding these factors and the conditions that promote or inhibit coalescence is essential for controlling and manipulating emulsions, foams, and other colloidal systems.