💧 Droplet · Bubble · Jet Duel
Two contenders, each a droplet, soap bubble or liquid jet with its own radius and surface tension. Tap the one with the higher internal (excess) pressure. Remember: a bubble has two surfaces, a jet only a curved one.
droplet p = 2σ/r · soap bubble p = 4σ/r · liquid jet p = σ/r
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Why the factors differ
Balancing the bursting pressure force against the surface-tension pull around the cut gives the excess pressure. A droplet has one surface in tension → p = 2σ/r. A soap bubble has two surfaces (inner and outer) → p = 4σ/r, twice the droplet for the same r and σ. A liquid jet is curved in only one direction → p = σ/r. In every case the pressure rises as the radius shrinks, so the tiniest droplets carry surprisingly high internal pressures.