Capillary Number

Definition

The capillary number is a dimensionless number that describes the relative effect of viscous forces to surface tension forces in a fluid flow. It is defined as the ratio of the viscous forces, characterized by the fluid's viscosity and velocity, to the surface tension acting at the interface of two fluids. This number helps in understanding how fluids behave in small geometries, where surface tension becomes significantly influential compared to viscous effects.

5 Must Know Facts For Your Next Test

1. The capillary number is typically expressed as Ca = \frac{\mu U}{\sigma}, where \mu is the dynamic viscosity, U is the flow velocity, and \sigma is the surface tension.
2. As the capillary number increases, the influence of viscous forces becomes more dominant compared to surface tension forces, leading to different flow behaviors.
3. Capillary numbers less than 1 indicate that surface tension forces dominate over viscous forces, which is crucial in microfluidic applications.
4. In processes like oil recovery or inkjet printing, understanding the capillary number helps in optimizing performance and fluid distribution.
5. The concept of capillary number is significant in various fields, including biology, material science, and chemical engineering, influencing phenomena like droplet formation and spreading.

Review Questions

• How does the capillary number influence fluid behavior in small-scale flows?
  • The capillary number significantly impacts fluid behavior in small-scale flows by determining whether viscous forces or surface tension forces are more dominant. When the capillary number is low (less than 1), surface tension plays a crucial role, which is often seen in microfluidic devices where precise control over fluid movement is necessary. Conversely, as the capillary number increases, viscous forces become more influential, altering flow patterns and potentially leading to different outcomes in processes like mixing or droplet formation.
• Discuss the practical implications of capillary number in applications such as inkjet printing and oil recovery.
  • In applications like inkjet printing, maintaining an optimal capillary number ensures that droplets form correctly and spread as intended on surfaces. A low capillary number allows surface tension to control droplet formation, leading to high-resolution prints. In oil recovery processes, understanding the capillary number can help engineers optimize the flow of oil through porous media by balancing viscous drag with surface tension effects, ultimately improving extraction efficiency and yield.
• Evaluate how changes in viscosity or surface tension affect the capillary number and subsequent fluid dynamics.
  • Changes in viscosity or surface tension directly affect the capillary number, altering fluid dynamics significantly. For instance, increasing viscosity while keeping surface tension constant raises the capillary number, promoting more viscous flow behavior that may overshadow surface tension effects. Conversely, lowering surface tension while keeping viscosity constant decreases the capillary number, enhancing surface tension's influence and potentially leading to different flow regimes. Understanding these relationships is critical for predicting fluid behavior in various engineering applications and natural systems.

Related terms

Surface Tension:

The force that acts at the surface of a liquid, causing it to behave as if it has an elastic 'skin' due to cohesive forces between liquid molecules.

Viscosity:

A measure of a fluid's resistance to flow, indicating how thick or thin a fluid is, influencing how it deforms under shear stress.

Wetability: The ability of a liquid to maintain contact with a solid surface, influenced by adhesive and cohesive forces, which can be described using contact angle measurements.