Set by the Bond or Weber number — surface tension against weight or inertia

• A breaking strength that is the size of a flaw — homogeneous, flat-interface surface tension — an estimate, not a solution · absolute-pressure
• An edge holds any angle it is given — static liquid, surface tension against gravity — no flow, no evaporation, the edge perfectly sharp · wall-jet · hero
• An edge holds any angle it is given — static liquid, surface tension against gravity — no flow, no evaporation, the edge perfectly sharp · wall-jet
• An edge holds any angle it is given — static liquid, surface tension against gravity — no flow, no evaporation, the edge perfectly sharp · wall-jet
• An edge holds any angle it is given — static liquid, surface tension against gravity — no flow, no evaporation, the edge perfectly sharp · wall-jet
• An edge holds any angle it is given — static liquid, surface tension against gravity — no flow, no evaporation, the edge perfectly sharp · wall-jet
• An edge holds any angle it is given — static liquid, surface tension against gravity — no flow, no evaporation, the edge perfectly sharp · wall-jet
• An edge holds any angle it is given — static liquid, surface tension against gravity — no flow, no evaporation, the edge perfectly sharp · wall-jet
• How far apart a ceiling drips — air below of negligible density; lengths in capillary lengths · shear-instability · hero
• How far apart a ceiling drips — air below of negligible density; lengths in capillary lengths · shear-instability
• How far apart a ceiling drips — air below of negligible density; lengths in capillary lengths · shear-instability
• How far apart a ceiling drips — air below of negligible density; lengths in capillary lengths · shear-instability
• How far apart a ceiling drips — air below of negligible density; lengths in capillary lengths · shear-instability
• How far apart a ceiling drips — air below of negligible density; lengths in capillary lengths · shear-instability
• How far apart a ceiling drips — air below of negligible density; lengths in capillary lengths · shear-instability
• The air shortens a jet's fastest ripple, and the drops follow — ripples on a round jet; time in capillary units √(ρa³/σ); Oh, gas Weber number on the diameter · jet-breakup · hero
• The air shortens a jet's fastest ripple, and the drops follow — ripples on a round jet; time in capillary units √(ρa³/σ); Oh, gas Weber number on the diameter · jet-breakup
• The air shortens a jet's fastest ripple, and the drops follow — ripples on a round jet; time in capillary units √(ρa³/σ); Oh, gas Weber number on the diameter; inviscid · jet-breakup
• The air shortens a jet's fastest ripple, and the drops follow — ripples on a round jet; time in capillary units √(ρa³/σ); Oh, gas Weber number on the diameter; inviscid · jet-breakup
• The air shortens a jet's fastest ripple, and the drops follow — ripples on a round jet; time in capillary units √(ρa³/σ); Oh, gas Weber number on the diameter · jet-breakup
• The air shortens a jet's fastest ripple, and the drops follow — ripples on a round jet; time in capillary units √(ρa³/σ); Oh, gas Weber number on the diameter · jet-breakup
• The drop falls at a fold — static — Bond number of order one, quasi-static filling, contact line pinned at the rim · drop-profile · hero
• The drop falls at a fold — static — Bond number of order one, quasi-static filling, contact line pinned at the rim · drop-profile
• The drop falls at a fold — static — Bond number of order one, quasi-static filling, contact line pinned at the rim · drop-profile
• The drop falls at a fold — static — Bond number of order one, quasi-static filling, contact line pinned at the rim · drop-profile
• The drop falls at a fold — static — Bond number of order one, quasi-static filling, contact line pinned at the rim · drop-profile
• The drop falls at a fold — static — Bond number of order one, quasi-static filling, contact line pinned at the rim · drop-profile
• The drop falls at a fold — static — Bond number of order one, quasi-static filling, contact line pinned at the rim · drop-profile
• The drop that is not a tear — a two-dimensional sheet, so one curvature; depths in capillary lengths, and no drop size anywhere in it · drop-profile
• The fastest finger is set by the gap and one number — any gap, tension and viscosities; Ca from the viscosity difference · ideal-cylinder
• The meniscus slows the finger and hardly moves it — capillary number at onset; any fluids, any gap · ideal-cylinder
• The number that cannot break a drop — Ca = μ_c γ̇a/σ in simple shear — creeping flow, no inertia anywhere · regime-collapse · hero
• The number that cannot break a drop — Ca = μ_c γ̇a/σ in simple shear — creeping flow, no inertia anywhere · regime-collapse
• The number that cannot break a drop — Ca = μ_c γ̇a/σ in simple shear — creeping flow, no inertia anywhere · regime-collapse
• The number that cannot break a drop — Ca = μ_c γ̇a/σ in simple shear — creeping flow, breakup threshold · regime-collapse
• The number that cannot break a drop — Ca → ∞ in simple shear — the saturation, not a threshold in Ca · regime-collapse
• The number that cannot break a drop — Ca = μ_c γ̇a/σ in simple shear — creeping flow, breakup threshold · regime-collapse
• The number that cannot break a drop — Ca → ∞ in simple shear — the saturation, not a threshold in Ca · regime-collapse
• The number that cannot break a drop — Ca = μ_c γ̇a/σ — creeping flow, planar linear flows only · regime-collapse
• The size a drop is allowed — a two-dimensional sheet, so one curvature; depths in capillary lengths, and no drop size anywhere in it · drop-profile
• The size a drop is allowed — a two-dimensional sheet, so one curvature; depths in capillary lengths, and no drop size anywhere in it · drop-profile
• The warm side pulls a bubble with no force on it — conduction only — the drop's motion carries no heat; κ the drop's conductivity over the liquid's · moving-surface
• The warm side pulls a bubble with no force on it — Reynolds and Marangoni numbers well below one; σ = σ₀ + (dσ/dT)(T − T₀), dσ/dT < 0 · moving-surface
• The warm side pulls a bubble with no force on it — Reynolds and Marangoni numbers well below one; σ = σ₀ + (dσ/dT)(T − T₀), dσ/dT < 0 · moving-surface
• Viscosity lets a jet break, later and into bigger drops — ripples on a round jet; time in capillary units √(ρa³/σ); Oh, gas Weber number on the diameter · jet-breakup · hero
• Viscosity lets a jet break, later and into bigger drops — ripples on a round jet; time in capillary units √(ρa³/σ); Oh, gas Weber number on the diameter · jet-breakup
• Viscosity lets a jet break, later and into bigger drops — ripples on a round jet; time in capillary units √(ρa³/σ); Oh, gas Weber number on the diameter · jet-breakup
• Viscosity lets a jet break, later and into bigger drops — ripples on a round jet; time in capillary units √(ρa³/σ); Oh, gas Weber number on the diameter · jet-breakup
• Viscosity lets a jet break, later and into bigger drops — ripples on a round jet; time in capillary units √(ρa³/σ); Oh, gas Weber number on the diameter · jet-breakup
• Viscosity lets a jet break, later and into bigger drops — ripples on a round jet; time in capillary units √(ρa³/σ); Oh, gas Weber number on the diameter · jet-breakup
• What a plate takes with it — a two-dimensional sheet, so one curvature; depths in capillary lengths, and no drop size anywhere in it · drop-profile
• Where a jet stops being a jet — set by the Weber number — a liquid jet issuing into a gas at rest · jet-breakup · hero
• Where a jet stops being a jet — set by the Weber number — a liquid jet issuing into a gas at rest · jet-breakup
• Where a jet stops being a jet — set by the Weber number — the gas's inertia against the jet's surface tension · jet-breakup
• Where a jet stops being a jet — set by the Weber number — the branch ends at a borrowed transition · jet-breakup
• Where a jet stops being a jet — set by the Weber number — this nozzle is in the Rayleigh break-up regime · jet-breakup
• Where a jet stops being a jet — set by the Weber number — the regime names and their thresholds are borrowed · jet-breakup
• Where a jet stops being a jet — set by the Weber number — a liquid jet issuing into a gas at rest · jet-breakup
• Where a jet stops being a jet — set by the Weber number — the gas's inertia against the jet's surface tension · jet-breakup
• Where a jet stops being a jet — set by the Weber number — this nozzle is in the Rayleigh break-up regime · jet-breakup
• The drop a no-slip wall would never let spread — water in air — Ca from 10⁻⁶ to 1, the upper end outside Stokes flow · coating-film
• What a plate takes with it — water at 20 °C — Ca from 10⁻⁶ to 10⁻², the last three outside the range · coating-film · hero
• What a plate takes with it — water at 20 °C — Ca from 10⁻⁶ to 10⁻², the last three outside the range · coating-film
• What a plate takes with it — Ca between 10⁻⁶ and 10⁻¹ — the last of these is outside the derivation · coating-film
• The drop a no-slip wall would never let spread — water — Ca = 1.4 × 10⁻⁵, Stokes flow in the corner · coating-film · hero
• The drop a no-slip wall would never let spread — water — Ca = 1.4 × 10⁻⁵, Stokes flow in the corner · coating-film
• The meniscus slows the finger and hardly moves it — capillary number 10⁻⁴ to 0.3; glycerol against air, gap 1 mm · ideal-cylinder · hero
• The meniscus slows the finger and hardly moves it — capillary number 10⁻⁴ to 0.3; glycerol against air, gap 1 mm · ideal-cylinder
• The meniscus slows the finger and hardly moves it — capillary number 10⁻⁴ to 0.3; glycerol against air, gap 1 mm · ideal-cylinder
• The meniscus slows the finger and hardly moves it — capillary number 10⁻⁴ to 0.3; glycerol against air, gap 1 mm · ideal-cylinder
• The meniscus slows the finger and hardly moves it — capillary number 10⁻⁴ to 0.3; glycerol against air, gap 1 mm · ideal-cylinder
• A law that is exact as an average — static — Bond number from 10⁻³ to 10², contact angle fixed at the wall · drop-profile · hero
• A law that is exact as an average — static — Bond number from 10⁻³ to 10², contact angle fixed at the wall · drop-profile
• A law that is exact as an average — static — Bond number from 10⁻³ to 10², contact angle fixed at the wall · drop-profile
• A law that is exact as an average — static — Bond number from 10⁻³ to 10², contact angle fixed at the wall · drop-profile
• A law that is exact as an average — static — Bond number from 10⁻³ to 10², contact angle fixed at the wall · drop-profile
• A law that is exact as an average — static — Bond number from 10⁻³ to 10², contact angle fixed at the wall · drop-profile
• A law that is exact as an average — static — Bond number from 10⁻³ to 10², contact angle fixed at the wall · drop-profile
• A thin fibre coats by its own radius, and beads by it — silicone oil, 20 mPa·s; ripple 10⁻³; capillary number Ca ≪ 1, complete wetting, coat thin against the fibre · coating-film
• What a plate takes with it — Ca below 10⁻³ — a long bubble, no gravity, and a film thin against the radius · coating-film
• A sliding drop is held harder the faster it goes — capillary numbers below 0.03, inertia neglected; slip length 1 nm on a ridge 2 mm across · drop-profile · hero
• A sliding drop is held harder the faster it goes — capillary numbers below 0.03, inertia neglected; slip length 1 nm on a ridge 2 mm across · drop-profile
• A sliding drop is held harder the faster it goes — capillary numbers below 0.03, inertia neglected; slip length 1 nm on a ridge 2 mm across · drop-profile
• A sliding drop is held harder the faster it goes — capillary numbers below 0.03, inertia neglected; slip length 1 nm on a ridge 2 mm across · drop-profile
• A sliding drop is held harder the faster it goes — capillary numbers below 0.03, inertia neglected; slip length 1 nm on a ridge 2 mm across · drop-profile
• A sliding drop is held harder the faster it goes — capillary numbers below 0.03, inertia neglected; slip length 1 nm on a ridge 2 mm across · drop-profile
• A sliding drop is held harder the faster it goes — capillary numbers below 0.03, inertia neglected; slip length 1 nm on a ridge 2 mm across · drop-profile
• A sloping ceiling drips downhill, or not at all — water: σ 0.072 N/m, capillary length 2.7 mm; paint: σ 0.035 N/m, ρ 1300 kg/m³, 1.66 mm · shear-instability
• The fastest finger is set by the gap and one number — air into oil of 0.1 Pa·s; gap 1 mm; tension 0.02 N/m · ideal-cylinder · hero
• The fastest finger is set by the gap and one number — air into oil of 0.1 Pa·s; gap 1 mm; tension 0.02 N/m · ideal-cylinder
• The fastest finger is set by the gap and one number — air into oil of 0.1 Pa·s; gap 1 mm; tension 0.02 N/m · ideal-cylinder
• The fastest finger is set by the gap and one number — air into oil of 0.1 Pa·s; gap 1 mm; tension 0.02 N/m; injection 0.31 cm²/s per unit gap · ideal-cylinder
• The fastest finger is set by the gap and one number — a displacing fluid into oil of 0.1 Pa·s; gap 1 mm; tension 0.02 N/m · ideal-cylinder
• The fastest finger is set by the gap and one number — air into oil of 0.1 Pa·s; gap 1 mm; tension 0.02 N/m · ideal-cylinder
• A drop rings like a bell — amplitude swept from 0.2 to 8 per cent of the radius · drop-profile
• A drop rings like a bell — small amplitude, Ohnesorge number small — water drops of 0.3 to 6 mm · drop-profile · hero
• A drop rings like a bell — small amplitude, Ohnesorge number small — water drops of 0.3 to 6 mm · drop-profile
• A drop rings like a bell — small amplitude, Ohnesorge number small — water drops of 0.3 to 6 mm · drop-profile
• A drop rings like a bell — small amplitude, Ohnesorge number small — water drops of 0.3 to 6 mm · drop-profile
• A drop rings like a bell — small amplitude, Ohnesorge number small — water drops of 0.3 to 6 mm · drop-profile
• A drop rings like a bell — small amplitude, Ohnesorge number small — water drops of 0.3 to 6 mm · drop-profile
• A thin fibre coats by its own radius, and beads by it — capillary number Ca ≪ 1, complete wetting, coat thin against the fibre · coating-film · hero
• A thin fibre coats by its own radius, and beads by it — capillary number Ca ≪ 1, complete wetting, coat thin against the fibre · coating-film
• A thin fibre coats by its own radius, and beads by it — capillary number Ca ≪ 1, complete wetting, coat thin against the fibre · coating-film
• A thin fibre coats by its own radius, and beads by it — capillary number Ca ≪ 1, complete wetting, coat thin against the fibre · coating-film
• A thin fibre coats by its own radius, and beads by it — capillary number Ca ≪ 1, complete wetting, coat thin against the fibre · coating-film
• A thin fibre coats by its own radius, and beads by it — capillary number Ca ≪ 1, complete wetting, coat thin against the fibre · coating-film
• A thin fibre coats by its own radius, and beads by it — capillary number Ca ≪ 1, complete wetting, coat thin against the fibre · coating-film
• The drop a no-slip wall would never let spread — Ca ≪ 1 and no inertia — the solution has no length in it at all · coating-film
• The drop a no-slip wall would never let spread — Ca ≪ 1 — every check in the thin-film and Stokes-flow range · coating-film
• The drop that is not a tear — linear in the distortion, so quantitative below We ≈ 1 and indicative above; the poles meet at We = 32/3 · drop-profile · hero
• The drop that is not a tear — linear in the distortion, so quantitative below We ≈ 1 and indicative above; the poles meet at We = 32/3 · drop-profile
• The drop that is not a tear — linear in the distortion, so quantitative below We ≈ 1 and indicative above; the poles meet at We = 32/3 · drop-profile
• The meniscus slows the finger and hardly moves it — Hele-Shaw cell — gap Reynolds number ≪ 1; small capillary number · ideal-cylinder
• The number that cannot break a drop — Ca = μ_c γ̇a/σ in simple shear — creeping flow, viscosity ratio 1 · regime-collapse
• The size a drop is allowed — linear in the distortion, so quantitative below We ≈ 1 and indicative above; the poles meet at We = 32/3 · drop-profile
• What a plate takes with it — Ca ≪ 1 — the equation has no parameter in it, so neither has the constant · coating-film
• The force a contact line holds is a range — static; the lifted volume is exactly 2πR cos θ in capillary lengths, so the ratio holds for a tube of any radius · drop-profile
• The force a contact line holds is a range — static, a two-dimensional ridge; lengths in capillary lengths, 2.71 mm for water · drop-profile · hero
• The force a contact line holds is a range — static, gravity and surface tension only; lengths in capillary lengths, 2.71 mm for water · drop-profile
• The force a contact line holds is a range — static, gravity and surface tension only; lengths in capillary lengths, 2.71 mm for water · drop-profile
• The force a contact line holds is a range — static, a two-dimensional ridge; lengths in capillary lengths, 2.71 mm for water · drop-profile
• The force a contact line holds is a range — static, a two-dimensional ridge; lengths in capillary lengths, 2.71 mm for water · drop-profile
• The force a contact line holds is a range — static, gravity and surface tension only; lengths in capillary lengths, 2.71 mm for water · drop-profile
• The number that cannot break a drop — Ca = 3 throughout — the flow type is the variable, not the strength · regime-collapse
• A threshold that is also a duration — a 5 micron air bubble in water at one atmosphere · how-long-a-machine-remembers · hero
• A threshold that is also a duration — a 5 micron air bubble in water at one atmosphere · how-long-a-machine-remembers
• A threshold that is also a duration — a bubble whose rest radius is 5 microns · how-long-a-machine-remembers
• The warm side pulls a bubble with no force on it — air in 10 cSt silicone oil, dσ/dT = -0.06 mN/(m·K); buoyant Reynolds number one near 300 µm · moving-surface · hero
• The warm side pulls a bubble with no force on it — air in 10 cSt silicone oil, dσ/dT = -0.06 mN/(m·K); buoyant Reynolds number one near 300 µm · moving-surface
• The warm side pulls a bubble with no force on it — air in 10 cSt silicone oil; the gradient weak enough that the layer does not convect · moving-surface
• A breaking strength that is the size of a flaw — water at 20 °C — below a nanometre a continuum surface tension is itself in doubt · absolute-pressure
• A rounded edge spills before its line goes round — water at 20 °C, capillary length 2.73 mm; a plateau turning down through 90° over a rounding of radius r · wall-jet · hero
• A rounded edge spills before its line goes round — water at 20 °C, capillary length 2.73 mm; a plateau turning down through 90° over a rounding of radius r · wall-jet
• A rounded edge spills before its line goes round — water at 20 °C, capillary length 2.73 mm; a plateau turning down through 90° over a rounding of radius r · wall-jet
• A rounded edge spills before its line goes round — water at 20 °C, capillary length 2.73 mm; a plateau turning down through 90° over a rounding of radius r · wall-jet
• A rounded edge spills before its line goes round — water at 20 °C, capillary length 2.73 mm; a plateau turning down through 90° over a rounding of radius r · wall-jet
• A rounded edge spills before its line goes round — water at 20 °C, capillary length 2.73 mm; a plateau turning down through 90° over a rounding of radius r; a coin 19.05 mm across · wall-jet
• A rounded edge spills before its line goes round — water at 20 °C, capillary length 2.73 mm; a plateau turning down through 90° over a rounding of radius r · wall-jet
• A thin fibre coats by its own radius, and beads by it — silicone oil, 20 mPa·s, 20 mN/m; capillary number Ca ≪ 1, complete wetting, coat thin against the fibre · coating-film
• The vorticity a clean surface cannot refuse — air in water at 20 °C; spherical bubbles only, Weber number below one · extra-condition · hero
• The vorticity a clean surface cannot refuse — air in water at 20 °C; spherical bubbles only, Weber number below one · extra-condition
• The air that breaks a siphon nothing else can — vertical tube, Eötvös 21.0 — surface tension neglected in the drift · siphon-profile
• The drop a no-slip wall would never let spread — a 100 cSt silicone oil, perfect wetting — Ca ≪ 1, gravity neglected · coating-film
• The size a drop is allowed — a sessile drop at 100° contact angle; no flow anywhere in the picture · drop-profile
• The size a drop is allowed — a sessile drop at 140° contact angle; no flow anywhere in the picture · drop-profile
• The drop that is not a tear — a sessile drop at 180°; the Bond number is formed on the equivalent sphere · drop-profile
• The drop that is not a tear — a sessile drop at 180° contact angle; no flow anywhere in the picture · drop-profile
• The size a drop is allowed — a sessile drop at 180°; the Bond number is formed on the equivalent sphere · drop-profile · hero
• The size a drop is allowed — a sessile drop at 180°; the Bond number is formed on the equivalent sphere · drop-profile
• The size a drop is allowed — a sessile drop at 180° contact angle; no flow anywhere in the picture · drop-profile
• The drop that is not a tear — water in air at 1.204 kg/m³, Re from 60 to 5,000 — the drag law's own range · drop-profile
• The size a drop is allowed — water in air at 1.204 kg/m³, Re from 60 to 5,000 — the drag law's own range · drop-profile

Every regime · All figures · All essays