Weber Number
Compute the Weber number We = (ρ·v²·L)/σ.
We
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Weber number: We = ρ·v²·L/σ
The Weber number is a dimensionless ratio of inertial forces to surface tension: We = ρ·v²·L/σ, where ρ is density (kg/m³), v is velocity (m/s), L is a characteristic length such as a droplet or jet diameter in m, and σ is surface tension (N/m). Take water (ρ = 1,000, σ = 0.072) at v = 2 m/s for a droplet of L = 1 cm: that works out to We ≈ 555, so inertia wins and the droplet tends to break apart. When We is low, surface tension is in charge and drops stay spherical and stable, the way a faucet drop forms slowly. When We is high, inertia takes over and drops shatter into smaller ones, which is atomization. A raindrop hitting the ground reaches We ~ 100–1,000 and bursts into a corona of secondary droplets. In sprays, the resulting droplet size scales inversely with We. Weber also ties into cavitation and the oscillation of bubbles in a liquid.
Applications
It shows up in fuel injection for diesel and GDI engines, where atomisation defines combustion; in agricultural pesticide spraying, where it governs drift control; in inkjet printing, where drop stability is everything; in microfluidics, for emulsion and droplet formation on a lab-on-a-chip; in cosmetic and pharmaceutical sprays; and in metal-casting atomisation.
FAQ
What is the critical We for breakup? For a droplet in an air stream, breakup starts around We ≈ 12, the so-called bag mode. Push past We > 350 and the droplet shatters catastrophically. The exact thresholds shift with the geometry and with viscosity, captured by the Ohnesorge number.
Weber vs Reynolds, when does each apply? Re weighs inertia against viscosity and rules pipe flow and external flow. We weighs inertia against surface tension and rules at interfaces, meaning drops, jets, sprays and bubbles. Atomisation is where both come into play at once.
Why is We critical in inkjet printing? Too low and the drop never detaches from the nozzle. Too high and it breaks into satellite drops that wreck the resolution. Industrial print heads have to stay inside a narrow window of We and Ohnesorge.
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