Webergetal

Webergetal, or the Weber number, is a dimensionless parameter used in fluid mechanics to describe the relative importance of inertial forces to interfacial tension forces in flows with free surfaces or interfaces between immiscible fluids. It is commonly applied to droplets, jets, bubbles, and sprays.

The Weber number is defined as We = (ρ v^2 L) / σ, where ρ is the fluid density, v is a characteristic velocity, L is a characteristic length scale (such as droplet diameter or nozzle diameter), and σ is the interfacial surface tension. In gas–liquid problems, ρ is typically the liquid density and σ the liquid–air surface tension. The choice of L and v depends on the specific problem and can significantly affect the computed value.

Interpretation of the Weber number centers on regimes of dominance. When We is large (We >> 1), inertial forces dominate and interfaces are prone to deformation, break-up, or fragmentation. When We is small (We << 1), surface tension resists deformation and tends to maintain smoother, more spherical shapes. In many practical problems, gravity and viscosity also influence outcomes, and the Weber number is often considered together with other nondimensional numbers such as the Ohnesorge number and the Bond number.

Applications of the Weber number include predicting atomization and spray formation, droplet breakup in fuel-injection systems, inkjet printing, emulsification, and bubble breakup. It serves as a guide for selecting operating conditions to achieve desired droplet sizes and spray characteristics and for mapping breakup regimes in regime diagrams.

Limitations should be noted: We is a simplified descriptor and real flows depend on viscosity, density contrasts, turbulence, gravity, and surrounding conditions.