Regime
Re → 0 — creeping flow, inertia absent
Every figure drawn under this hypothesis — 259 of them — with the essay each one belongs to and the generator that drew it.
259 figure placements state this regime. The strip along the foot of every figure names two things — the model that produced it and the regime it holds in — and this listing is read back out of the finished drawing rather than from what produced it.
- A ball that bounces in water and not in oil — a sphere, Re on the diameter; the expansion itself is asymptotic as Re → 0 · creeping-flow
- A body with no lift, and a moment anyway — any Reynolds number — viscosity is absent, which is why the drag is zero · sphere-flow
- A bowed meniscus keeps most of its slip until the groove floods — creeping flow over a striped superhydrophobic wall; period 1, menisci pinned until the groove floods · extra-condition · hero
- A bowed meniscus keeps most of its slip until the groove floods — creeping flow over a striped superhydrophobic wall; period 1, menisci pinned until the groove floods · extra-condition
- A bowed meniscus keeps most of its slip until the groove floods — creeping flow over a striped wall; gas fraction 0.8, the pressure as dialled · extra-condition
- A bowed meniscus keeps most of its slip until the groove floods — creeping flow over a striped superhydrophobic wall; period 1, menisci pinned until the groove floods · extra-condition
- A bowed meniscus keeps most of its slip until the groove floods — creeping flow over a striped superhydrophobic wall; period 1, menisci pinned until the groove floods · extra-condition
- A bowed meniscus keeps most of its slip until the groove floods — creeping flow over a striped wall; gas fraction 0.8, menisci pinned · extra-condition
- A bowed meniscus keeps most of its slip until the groove floods — creeping flow over a striped wall; water, γ = 0.072 N/m, groove walls advancing at 120° · extra-condition
- A bowed meniscus keeps most of its slip until the groove floods — creeping flow over a striped superhydrophobic wall; period 1, menisci pinned until the groove floods · extra-condition
- A cap that slows a rising bubble stops a migrating one — Stokes flow; drag extrapolated past the cap edge, push checked by the reciprocal theorem · moving-surface · hero
- A cap that slows a rising bubble stops a migrating one — Stokes flow; drag extrapolated past the cap edge, push checked by the reciprocal theorem · moving-surface
- A cap that slows a rising bubble stops a migrating one — Reynolds and Marangoni numbers well below one; no gravity; insoluble surfactant, σ = σ₀ + (dσ/dT)T − RTΓ · moving-surface
- A cap that slows a rising bubble stops a migrating one — Reynolds and Marangoni numbers well below one; no gravity; insoluble surfactant, σ = σ₀ + (dσ/dT)T − RTΓ · moving-surface
- A cap that slows a rising bubble stops a migrating one — Reynolds and Marangoni numbers well below one; no gravity; insoluble surfactant, σ = σ₀ + (dσ/dT)T − RTΓ · moving-surface
- A cap that slows a rising bubble stops a migrating one — air in water at 20 °C, radius 20 µm; Marangoni number 0.42 at 1 K/mm; RTΓ∞ = 7.8 mN/m · moving-surface
- A cap that slows a rising bubble stops a migrating one — Reynolds and Marangoni numbers well below one; no gravity; insoluble surfactant, σ = σ₀ + (dσ/dT)T − RTΓ · moving-surface
- A cloud folds where a saddle is strong, not when — Stokes number 0.13 to 0.22 — linear drag, particle Reynolds number ≪ 1 · velocity-field · hero
- A cloud folds where a saddle is strong, not when — Stokes number 0.13 to 0.22 — linear drag, particle Reynolds number ≪ 1 · velocity-field
- A cloud folds where a saddle is strong, not when — Stokes number 0.13 to 0.22 — linear drag, particle Reynolds number ≪ 1 · velocity-field
- A cloud folds where a saddle is strong, not when — Stokes number 0.13 to 0.22 — linear drag, particle Reynolds number ≪ 1 · velocity-field
- A cloud folds where a saddle is strong, not when — Stokes number 0.05 — linear drag, particle Reynolds number ≪ 1 · velocity-field
- A cloud folds where a saddle is strong, not when — Stokes number 0.16 — linear drag, particle Reynolds number ≪ 1 · velocity-field
- A cloud folds where a saddle is strong, not when — Stokes number 0.13 to 0.22 — linear drag, particle Reynolds number ≪ 1 · velocity-field
- A drift made of two things that average to zero — steepness ak = 0.05, one fifth of a wavelength deep — second-order Stokes drift · what-a-parcel-remembers
- A drift made of two things that average to zero — steepness ak = 0.05, one fifth of a wavelength deep — second-order Stokes drift · what-a-parcel-remembers
- A drift made of two things that average to zero — steepness ak = 0.05 unless stated, one fifth of a wavelength deep — second-order Stokes drift · what-a-parcel-remembers
- A duct that forgets everything but one number — 2 mm above the wall in water — the kernel is exact, the Stokes layer · how-long-viscosity-remembers
- A force without the flow that makes it — creeping flow, Re → 0 — an unbounded fluid, so the tube wall is outside it · reciprocity · hero
- A force without the flow that makes it — creeping flow, Re → 0 — the average is exact for a quadratic ambient · reciprocity
- A force without the flow that makes it — creeping flow, Re → 0 — the theorem needs linearity and nothing else · reciprocity
- A force without the flow that makes it — creeping flow, Re → 0 — an unbounded fluid at rest at infinity · reciprocity
- A force without the flow that makes it — creeping flow, Re → 0 — an unbounded fluid, so the tube wall is outside it · reciprocity
- A force without the flow that makes it — creeping flow, Re → 0 — the average is exact for a quadratic ambient · reciprocity
- A force without the flow that makes it — creeping flow, Re → 0 — both fields satisfy μ∇²u = ∇p exactly · reciprocity
- A force without the flow that makes it — St = 0.3 · any Reynolds number for the flow; the particle drag is Stokesian · particle-paths
- A larger sphere overtakes its neighbour and leaves on the line it came in on — creeping flow, Re → 0; one sphere 2% larger, both of one material · reciprocity · hero
- A larger sphere overtakes its neighbour and leaves on the line it came in on — creeping flow, Re → 0; one sphere 2% larger, both of one material · reciprocity
- A larger sphere overtakes its neighbour and leaves on the line it came in on — creeping flow, Re → 0; spheres of one material, radii within a tenth · reciprocity
- A larger sphere overtakes its neighbour and leaves on the line it came in on — creeping flow, Re → 0; one sphere larger by the dialled share · reciprocity
- A larger sphere overtakes its neighbour and leaves on the line it came in on — creeping flow, Re → 0; one material, mismatch a half to ten per cent · reciprocity
- A larger sphere overtakes its neighbour and leaves on the line it came in on — creeping flow, Re → 0; spheres of one material, radii within a tenth · reciprocity
- A lattice of vortices folds a cloud at the saddles' quarter — Stokes number St = τ times the saddles' strain rate; heavy particles, no gravity; lengths in cell widths over π · velocity-field · hero
- A lattice of vortices folds a cloud at the saddles' quarter — Stokes number St = τ times the saddles' strain rate; heavy particles, no gravity; lengths in cell widths over π · velocity-field
- A lattice of vortices folds a cloud at the saddles' quarter — Stokes number St = τ times the saddles' strain rate; heavy particles, no gravity; lengths in cell widths over π · velocity-field
- A lattice of vortices folds a cloud at the saddles' quarter — Stokes number St = τ times the saddles' strain rate; heavy particles, no gravity; lengths in cell widths over π · velocity-field
- A lattice of vortices folds a cloud at the saddles' quarter — Stokes number St = τ times the saddles' strain rate; heavy particles, no gravity; lengths in cell widths over π · velocity-field
- A lattice of vortices folds a cloud at the saddles' quarter — Stokes number St = τ times the saddles' strain rate; heavy particles, no gravity; lengths in cell widths over π · velocity-field
- A lattice of vortices folds a cloud at the saddles' quarter — Stokes number St = τ times the saddles' strain rate; heavy particles, no gravity; lengths in cell widths over π · velocity-field
- A lattice of vortices folds a cloud at the saddles' quarter — Stokes number St = τ times the saddles' strain rate; heavy particles, no gravity; lengths in cell widths over π · velocity-field
- A layer that is an integral of everything upstream — 100 μm particle in air, released at 1 m/s — Stokes drag with a history term · how-long-viscosity-remembers
- A particle is a low-pass filter — Stokes drag · which-memory-a-number-decides
- A particle is a low-pass filter — Stokes drag · which-memory-a-number-decides
- A particle is a low-pass filter — water droplets in air · which-memory-a-number-decides
- A particle is a low-pass filter — Stokes drag · which-memory-a-number-decides
- A particle is a low-pass filter — water droplets in air · which-memory-a-number-decides
- A particle is a low-pass filter — Stokes drag on the droplet — honest below about 30 µm at these speeds · particle-paths
- A post holds liquid back by its radius, a stripe by its length — flat pinned menisci carrying no stress; lengths in periods; extrapolated to zero spacing · extra-condition · hero
- A post holds liquid back by its radius, a stripe by its length — flat pinned menisci carrying no stress; lengths in periods; extrapolated to zero spacing · extra-condition
- A post holds liquid back by its radius, a stripe by its length — flat pinned menisci carrying no stress; lengths in periods; extrapolated to zero spacing · extra-condition
- A post holds liquid back by its radius, a stripe by its length — flat pinned menisci carrying no stress; lengths in periods; extrapolated to zero spacing; φ = 0.1, grid 256 · extra-condition
- A post holds liquid back by its radius, a stripe by its length — flat pinned menisci carrying no stress; lengths in periods; extrapolated to zero spacing; φ = 0.1, grid 256 · extra-condition
- A post holds liquid back by its radius, a stripe by its length — flat pinned menisci carrying no stress; lengths in periods; extrapolated to zero spacing · extra-condition
- A post holds liquid back by its radius, a stripe by its length — flat pinned menisci carrying no stress; lengths in periods; extrapolated to zero spacing · extra-condition
- A scraper held flat is pushed off the wall it scrapes — creeping flow, Re → 0 in the corner; forces per μU ln(R/ε) · corner-eddy · hero
- A scraper held flat is pushed off the wall it scrapes — creeping flow, Re → 0 in the corner; forces per μU ln(R/ε) · corner-eddy
- A scraper held flat is pushed off the wall it scrapes — creeping flow, Re → 0 in the corner; blade angle as dialled · corner-eddy
- A scraper held flat is pushed off the wall it scrapes — creeping flow, Re → 0 in the corner; forces per μU ln(R/ε) · corner-eddy
- A scraper held flat is pushed off the wall it scrapes — creeping flow, Re → 0 in the corner; forces per μU ln(R/ε) · corner-eddy
- A scraper held flat is pushed off the wall it scrapes — creeping flow in the corner; paint of 1 Pa·s at 0.2 m/s, a blade 1 cm long and 10 cm wide · corner-eddy
- A scraper held flat is pushed off the wall it scrapes — creeping flow, Re → 0 in the corner; forces per μU ln(R/ε) · corner-eddy
- A stroke is worth the area it encloses — creeping flow, Re → 0 — the expansion is in kb, here 0.2 · moving-surface
- A stronger strain folds a cloud only if it lasts — Stokes number 0.15 to 0.26 — linear drag, particle Reynolds number ≪ 1 · velocity-field · hero
- A stronger strain folds a cloud only if it lasts — Stokes number 0.15 to 0.26 — linear drag, particle Reynolds number ≪ 1 · velocity-field
- A stronger strain folds a cloud only if it lasts — Stokes number 0.15 to 0.26 — linear drag, particle Reynolds number ≪ 1; St 0.21, a 0.3 · velocity-field
- A stronger strain folds a cloud only if it lasts — Stokes number 0.15 to 0.26 — linear drag, particle Reynolds number ≪ 1 · velocity-field
- A stronger strain folds a cloud only if it lasts — Stokes number 0.15 to 0.26 — linear drag, particle Reynolds number ≪ 1 · velocity-field
- A stronger strain folds a cloud only if it lasts — Stokes number 0.15 to 0.26 — linear drag, particle Reynolds number ≪ 1; St 0.17 · velocity-field
- A stronger strain folds a cloud only if it lasts — Stokes number 0.15 to 0.26 — linear drag, particle Reynolds number ≪ 1 · velocity-field
- A swimmer that cannot go backwards — creeping flow, Re → 0 — the expansion is in kb, here 0.2 · moving-surface · hero
- A swimmer that cannot go backwards — creeping flow, Re → 0 — the expansion is in kb, here 0.2 · moving-surface
- A swimmer that cannot go backwards — creeping flow, Re → 0 — a spherical clean interface, no surfactant · moving-surface
- A swimmer that cannot go backwards — creeping flow, Re → 0 — air in water at 20 °C, clean interface assumed · moving-surface
- A swimmer that cannot go backwards — creeping flow, Re → 0 — the expansion is in kb, here 0.05 · moving-surface
- A thousandth of a monolayer holds a bubble still — Reynolds number well below one; σ = σ₀ − RTΓ; drag in units of the clean bubble's 4πμUa · moving-surface · hero
- A thousandth of a monolayer holds a bubble still — Reynolds number well below one; σ = σ₀ − RTΓ; drag in units of the clean bubble's 4πμUa · moving-surface
- A thousandth of a monolayer holds a bubble still — Reynolds number well below one; σ = σ₀ − RTΓ; drag in units of the clean bubble's 4πμUa · moving-surface
- A thousandth of a monolayer holds a bubble still — Reynolds number well below one; σ = σ₀ − RTΓ; drag in units of the clean bubble's 4πμUa · moving-surface
- A thousandth of a monolayer holds a bubble still — Reynolds number well below one; σ = σ₀ − RTΓ; drag in units of the clean bubble's 4πμUa · moving-surface
- A thousandth of a monolayer holds a bubble still — Reynolds number well below one; σ = σ₀ − RTΓ; drag in units of the clean bubble's 4πμUa · moving-surface
- A thousandth of a monolayer holds a bubble still — Reynolds number well below one; σ = σ₀ − RTΓ; drag in units of the clean bubble's 4πμUa · moving-surface
- A velocity nobody has — creeping flow — the linear law holds below a pore Reynolds number of about ten · bed-flow · hero
- A velocity nobody has — creeping flow — the linear law holds below a pore Reynolds number of about ten · bed-flow
- A velocity nobody has — creeping flow — Darcy's law is a low-Reynolds statement · bed-flow
- A velocity nobody has — creeping flow — Poiseuille's law inside each tube · bed-flow
- A velocity nobody has — creeping flow — both sides are low-Reynolds results · bed-flow
- A velocity nobody has — creeping flow — Darcy's law is a low-Reynolds statement · bed-flow
- A velocity nobody has — creeping flow — the linear law holds below a pore Reynolds number of about ten · bed-flow
- A velocity nobody has — creeping flow — Poiseuille's law inside each tube · bed-flow
- A velocity nobody has — creeping flow — both sides are low-Reynolds results · bed-flow
- A viscosity made of particles — creeping flow, Re → 0 — rigid neutrally buoyant spheres, no Brownian motion · what-viscosity-is · hero
- A viscosity made of particles — creeping flow, Re → 0 — the ambient has been subtracted, so this is the addition · what-viscosity-is
- A viscosity made of particles — creeping flow, Re → 0 — the theorem needs linearity and nothing else · reciprocity
- A viscosity made of particles — creeping flow, Re → 0 — one rigid sphere in an unbounded straining field · what-viscosity-is
- A viscosity made of particles — creeping flow, Re → 0 — rigid neutrally buoyant spheres, no Brownian motion · what-viscosity-is
- A viscosity made of particles — creeping flow, Re → 0 — one rigid sphere in an unbounded straining field · what-viscosity-is
- A viscosity made of particles — creeping flow, Re → 0 — rigid neutrally buoyant spheres, no Brownian motion · what-viscosity-is
- A viscosity that depends on the question — creeping flow, Re → 0 — rigid neutrally buoyant spheres, no Brownian motion · what-viscosity-is
- A wall that is not quite there — creeping flow — Darcy's law is a low-Reynolds statement · bed-flow
- An oscillation with somewhere to go — f = 100 Hz, ν = 0.000015 m²/s · laminar, no mean flow · oscillating-wall
- An oscillation with somewhere to go — deep water, steepness 0.1 — the drift is second order and the field is first · mean-field
- An oscillation with somewhere to go — laminar — the layer is thinner than any turbulence it might sit under · oscillating-wall
- Drag decides whether a cloud folds, and the air decides at what — Stokes number St = τ times the cloud's fastest rate of convergence; lengths and times in the cloud's own units · velocity-field · hero
- Drag decides whether a cloud folds, and the air decides at what — still air; initial velocity −sin a, so the fastest convergence rate is one · velocity-field
- Drag decides whether a cloud folds, and the air decides at what — still air; the one-dimensional cloud, fastest convergence rate one · velocity-field
- Drag decides whether a cloud folds, and the air decides at what — still air; the one-dimensional cloud · velocity-field
- Drag decides whether a cloud folds, and the air decides at what — still air; the seeded two-dimensional cloud · velocity-field
- Drag decides whether a cloud folds, and the air decides at what — air converging as −sin x, strain rate one at the line; runs stop at the first crossing · velocity-field
- Drag decides whether a cloud folds, and the air decides at what — Stokes number St = τ times the cloud's fastest rate of convergence; lengths and times in the cloud's own units · velocity-field
- Drag decides whether a cloud folds, and the air decides at what — Stokes number St = τ times the cloud's fastest rate of convergence; lengths and times in the cloud's own units · velocity-field
- Everything about the start, except one vector — laminar — the layer is thinner than any turbulence it might sit under · oscillating-wall
- How long a fluid takes to forget it was not rotating — water — the exponent is the diffusion equation's, the Stokes layer · how-long-viscosity-remembers
- How small is small enough — a sphere, Re on the diameter; the expansion itself is asymptotic as Re → 0 · creeping-flow · hero
- How small is small enough — a sphere, Re on the diameter; the expansion itself is asymptotic as Re → 0 · creeping-flow
- How small is small enough — Re → 0, rooms from 4 to 1024 radii · creeping-flow
- How small is small enough — Re → 0, rooms from 4 to 1024 radii · creeping-flow
- The cell draws a larger cylinder — a Hele-Shaw cell: gap small against the body, reduced Reynolds number small · ideal-cylinder · hero
- The cell draws a larger cylinder — a Hele-Shaw cell: gap small against the body, reduced Reynolds number small · ideal-cylinder
- The cell draws a larger cylinder — a Hele-Shaw cell: gap small against the body, reduced Reynolds number small · ideal-cylinder
- The cell draws a larger cylinder — a Hele-Shaw cell: gap small against the body, reduced Reynolds number small · ideal-cylinder
- The cell draws a larger cylinder — a Hele-Shaw cell: gap small against the body, reduced Reynolds number small · ideal-cylinder
- The cell draws a larger cylinder — a Hele-Shaw cell: gap small against the body, reduced Reynolds number small · ideal-cylinder
- The cell draws a larger cylinder — a Hele-Shaw cell: gap small against the body, reduced Reynolds number small · ideal-cylinder
- The cheapest shape the walls allow — creeping flow — inertia is absent, and nothing outside the corner enters the answer · corner-eddy
- The drag that integrates a whole history — 100 μm at 2500 kg/m³ in air — Stokes regime, particle time constant 77 ms · how-long-viscosity-remembers · hero
- The drag that integrates a whole history — 100 μm at 2500 kg/m³ in air — Stokes regime, particle time constant 77 ms · how-long-viscosity-remembers
- The drag that integrates a whole history — 100 μm particle in air, released at 1 m/s — Stokes drag with a history term · how-long-viscosity-remembers
- The drag that integrates a whole history — 100 μm particle in air, released at 1 m/s — Stokes drag with a history term · how-long-viscosity-remembers
- The drag that integrates a whole history — 100 μm particle in air, beyond two particle time constants — Stokes drag with a history term · how-long-viscosity-remembers
- The drag that integrates a whole history — 100 μm particle in air — 1,200 steps over 0.4 s, Stokes drag with a history term · how-long-viscosity-remembers
- The drag that integrates a whole history — 100 μm at 2500 kg/m³ in air, released at 1 m/s · how-long-viscosity-remembers
- The drag that integrates a whole history — air, ν = 1.5e-5 m²/s — a 1 mm sphere, amplitude irrelevant · oscillating-wall
- The drift a closed box will not allow — the same wave in a closed channel · kinematic-exact · hero
- The drift a closed box will not allow — amplitude 0.1, wavenumber 1, depth 5 — a steepness of 0.1 · kinematic-exact
- The drift a closed box will not allow — twenty thousand depth points · kinematic-exact
- The drift a closed box will not allow — the same wave in a closed channel · kinematic-exact
- The drift in a wave that has none — deep water, steepness 0.1 — the drift is second order and the field is first · mean-field
- The drift in a wave that has none — deep water, steepness 0.05 — the drift is second order and the field is first · mean-field
- The drift in a wave that has none — laminar — the layer is thinner than any turbulence it might sit under · oscillating-wall
- The eddies nobody stirs — creeping flow — inertia is absent, and nothing outside the corner enters the answer · corner-eddy · hero
- The eddies nobody stirs — creeping flow — inertia is absent, and nothing outside the corner enters the answer · corner-eddy
- The eddies nobody stirs — creeping flow — the exponent is a property of the geometry alone · corner-eddy
- The eddies nobody stirs — creeping flow — the ratios are geometry and carry no velocity in them · corner-eddy
- The eddies nobody stirs — creeping flow — inertia is absent, and nothing outside the corner enters the answer · corner-eddy
- The eddies nobody stirs — creeping flow — the comparison is of boundary conditions, not of regimes · corner-eddy
- The eddies nobody stirs — creeping flow — inertia is absent, and nothing outside the corner enters the answer · corner-eddy
- The exact theory, drawn by viscosity — gap Reynolds number 4.0e+1, reduced 1.6e+0 · ideal-cylinder · hero
- The exact theory, drawn by viscosity — gap Reynolds number 4.0e+1, reduced 1.6e+0 · ideal-cylinder
- The exact theory, drawn by viscosity — the profile the depth average is an average of · ideal-cylinder
- The flow with no solution — a unit cylinder inside a boundary at R · viscous-limit
- The flow with no solution — R/a from ten to 10¹² · viscous-limit
- The flow with no solution — a unit cylinder inside a boundary at R · viscous-limit
- The flow with no solution — a circular cylinder at low Reynolds number · viscous-limit
- The groups are not the only groups — Reynolds numbers from 0.05 to 10⁴ — holds before any experiment · constraint-and-freedom
- The layer that stops at a depth — f = 1 Hz, ν = 0.000001 m²/s · laminar, no mean flow · oscillating-wall
- The mean is not the flow — deep water, steepness 0.1 — the drift is second order and the field is first · mean-field
- The outlet is the inlet, a while ago — creeping flow — the linear law holds below a pore Reynolds number of about ten · bed-flow
- The pump that is better the more it squeezes — creeping flow: long wavelength, no inertia, a sinusoidal wave on a symmetric two-dimensional channel · velocity-field · hero
- The pump that is better the more it squeezes — creeping flow: long wavelength, no inertia, a sinusoidal wave on a symmetric two-dimensional channel · velocity-field
- The pump that is better the more it squeezes — creeping flow: long wavelength, no inertia, a sinusoidal wave on a symmetric two-dimensional channel · velocity-field
- The pump that is better the more it squeezes — creeping flow: long wavelength, no inertia, a sinusoidal wave on a symmetric two-dimensional channel · velocity-field
- The pump that is better the more it squeezes — creeping flow: long wavelength, no inertia, a sinusoidal wave on a symmetric two-dimensional channel · velocity-field
- The pump that is better the more it squeezes — creeping flow: long wavelength, no inertia, a sinusoidal wave on a symmetric two-dimensional channel · velocity-field
- The pump that is better the more it squeezes — creeping flow: long wavelength, no inertia, a sinusoidal wave on a symmetric two-dimensional channel · velocity-field
- The pump that is better the more it squeezes — creeping flow: long wavelength, no inertia, a sinusoidal wave on a symmetric two-dimensional channel · velocity-field
- The pump that is better the more it squeezes — creeping flow: long wavelength, no inertia, a sinusoidal wave on a symmetric two-dimensional channel · velocity-field
- The surface that moves with the flow — creeping flow, Re → 0 — a spherical clean interface, no surfactant · moving-surface · hero
- The surface that moves with the flow — creeping flow, Re → 0 — a clean interface, viscosity ratio 0.5 · moving-surface
- The surface that moves with the flow — creeping flow, Re → 0 — a spherical clean interface, no surfactant · moving-surface
- The surface that moves with the flow — creeping flow, Re → 0 — a clean interface with no surfactant on it · moving-surface
- The surface that moves with the flow — creeping flow, Re → 0 — air in water at 20 °C, clean interface assumed · moving-surface
- The surface that moves with the flow — creeping flow, Re → 0 — a clean interface with no surfactant on it · moving-surface
- The surface that moves with the flow — creeping flow, Re → 0 — rigid neutrally buoyant spheres, no Brownian motion · what-viscosity-is
- The surface that moves with the flow — creeping flow, Re → 0 — a clean interface, viscosity ratio 0.02 · moving-surface
- The tangent that sizes a plant — creeping flow — Darcy's law is a low-Reynolds statement · bed-flow
- The theory that solves everything — gap Reynolds number 4.0e+1, reduced 1.6e+0 · ideal-cylinder
- The theory with no memory in it — f = 100 Hz, ν = 0.000015 m²/s · laminar, no mean flow · oscillating-wall
- The three that never converge — Reynolds numbers from 0.1 to 10⁻²⁰, creeping flow past a cylinder · regime-exact
- The tracer that is not one — Stokes drag, small particle Reynolds number, no history term — stated, not solved · particle-paths · hero
- The tracer that is not one — Stokes drag, small particle Reynolds number, no history term — stated, not solved · particle-paths
- The tracer that is not one — Stokes drag on the droplet — honest below about 30 µm at these speeds · particle-paths
- The tracer that is not one — Stokes drag, small relaxation time, a steady swirling flow — no history term · particle-paths
- The tracer that is not one — any Reynolds number for the flow; the particle drag is Stokesian by assumption · particle-paths
- The tracer that is not one — St = 1 · any Reynolds number for the flow; the particle drag is Stokesian · particle-paths
- The tracer that is not one — any Reynolds number for the flow; Stokes drag on the particle · particle-paths
- The wall that shakes — f = 100 Hz, ν = 0.000015 m²/s · laminar, no mean flow · oscillating-wall · hero
- The wall that shakes — f = 100 Hz, ν = 0.000015 m²/s · laminar, no mean flow · oscillating-wall
- The wall that shakes — f = 100 Hz, ν = 0.000015 m²/s · laminar by construction, no mean flow · oscillating-wall
- The wall that shakes — laminar — the layer is thinner than any turbulence it might sit under · oscillating-wall
- The wall that shakes — f = 1000 Hz, ν = 0.000015 m²/s · laminar, no mean flow · oscillating-wall
- The wall that shakes — f = 100 Hz · laminar; no mean flow, so nothing here is a boundary layer · oscillating-wall
- The wall that shakes — air, ν = 1.5e-5 m²/s — a 1 mm sphere, amplitude irrelevant · oscillating-wall
- The wall the fluid is listening to — 2 mm above the wall in water — the kernel is exact, the Stokes layer · how-long-viscosity-remembers · hero
- The wall the fluid is listening to — 2 mm above the wall in water — the kernel is exact, the Stokes layer · how-long-viscosity-remembers
- The wall the fluid is listening to — 2 mm above the wall in water — the Stokes layer · how-long-viscosity-remembers
- The wall the fluid is listening to — 2 mm above the wall in water — the Stokes layer · how-long-viscosity-remembers
- The wall the fluid is listening to — water — the exponent is the diffusion equation's, the Stokes layer · how-long-viscosity-remembers
- The wall the fluid is listening to — water; the oscillating case at one radian a second — the Stokes layer · how-long-viscosity-remembers
- The wall the fluid is listening to — 2 mm above the wall in water unless stated — the Stokes layer · how-long-viscosity-remembers
- The wall the fluid is listening to — f = 100 Hz, ν = 0.000015 m²/s · laminar, no mean flow · oscillating-wall
- The wall the fluid is listening to — 100 μm particle in air, beyond two particle time constants — Stokes drag with a history term · how-long-viscosity-remembers
- 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 world with no inertia — Re → 0, rooms from 4 to 1024 radii · creeping-flow
- The world with no inertia — a sphere, Re on the diameter; the expansion itself is asymptotic as Re → 0 · creeping-flow
- Three dimensions are kinder — any Reynolds number — viscosity is absent, which is why the drag is zero · sphere-flow · hero
- Three dimensions are kinder — any Reynolds number — viscosity is absent, which is why the drag is zero · sphere-flow
- Three dimensions are kinder — any Reynolds number — the argument is topological and carries no velocity · sphere-flow
- Twice as slippery along as across — flat menisci that carry no stress · extra-condition
- Twice as slippery along as across — Stokes flow; velocities in units of shear rate × period · extra-condition
- Twice as slippery along as across — Stokes flow; 240 modes, heights in periods · extra-condition
- Twice as slippery along as across — Stokes flow over flat stripes; any period · extra-condition
- Twice as slippery along as across — Stokes flow — first-order in mode count, extrapolated · extra-condition
- Two drags, or nothing swims — a slender filament at a wavelength of 2.3 µm — creeping flow, no filament-to-filament interaction · moving-surface
- Two drags, or nothing swims — a slender filament at a wavelength of 2.3 µm — creeping flow, no filament-to-filament interaction · moving-surface
- Two drags, or nothing swims — a 7 µm filament, a 0.5 µm body and a 100 Hz motor — creeping flow throughout · moving-surface
- Two drags, or nothing swims — creeping flow, Re → 0 — the expansion is in kb, here 0.2 · moving-surface
- Two drags, or nothing swims — a sphere, Re on the diameter; the expansion itself is asymptotic as Re → 0 · creeping-flow
- Two rings leapfrog only if they start alike — core 0.06, core volume conserved; coaxial thin-cored filaments, Γ equal, exact mutual field; inviscid · vortex-ring
- Two spheres settling at a slant keep their slant for ever, and three do not — creeping flow, Re → 0; equal spheres 2 to 30 radii apart · reciprocity · hero
- Two spheres settling at a slant keep their slant for ever, and three do not — creeping flow, Re → 0; equal spheres 2 to 30 radii apart · reciprocity
- Two spheres settling at a slant keep their slant for ever, and three do not — creeping flow, Re → 0; separation as dialled · reciprocity
- Two spheres settling at a slant keep their slant for ever, and three do not — creeping flow, Re → 0; equal spheres 3 to 50 radii apart · reciprocity
- Two spheres settling at a slant keep their slant for ever, and three do not — creeping flow, Re → 0; three equal spheres ten radii apart · reciprocity
- Two spheres settling at a slant keep their slant for ever, and three do not — creeping flow, Re → 0; three equal spheres ten radii apart · reciprocity
- Two spheres settling at a slant keep their slant for ever, and three do not — creeping flow, Re → 0; equal spheres 2 to 30 radii apart · reciprocity
- What a fluid takes out of a swing — air, ν = 1.5e-5 m²/s — a 1 mm sphere, amplitude irrelevant · oscillating-wall · hero
- What a fluid takes out of a swing — air, ν = 1.5e-5 m²/s — the layer is √(2ν/ω) thick throughout · oscillating-wall
- What a fluid takes out of a swing — air, ν = 1.5e-5 m²/s — a 1 mm sphere, amplitude irrelevant · oscillating-wall
- What a fluid takes out of a swing — f = 100 Hz, ν = 0.000015 m²/s · laminar, no mean flow · oscillating-wall
- What a fluid takes out of a swing — air, ν = 1.5e-5 m²/s — spheres standing in for real shapes · oscillating-wall
- What a fluid takes out of a swing — air, ν = 1.5e-5 m²/s — the layer is √(2ν/ω) thick throughout · oscillating-wall
- What a fluid takes out of a swing — f = 100 Hz, ν = 0.000015 m²/s · laminar by construction, no mean flow · oscillating-wall
- What a fluid takes out of a swing — air, ν = 1.5e-5 m²/s — a 1 mm sphere, amplitude irrelevant · oscillating-wall
- Whether the droplet turns — St = 1 · any Reynolds number for the flow; the particle drag is Stokesian · particle-paths · hero
- Whether the droplet turns — St = 1 · any Reynolds number for the flow; the particle drag is Stokesian · particle-paths
- Whether the droplet turns — any Reynolds number for the flow; the particle drag is Stokesian by assumption · particle-paths
- Whether the droplet turns — any Reynolds number for the flow; Stokes drag on the particle · particle-paths
- Whether the droplet turns — St = 0.08 · any Reynolds number for the flow; the particle drag is Stokesian · particle-paths
- Whether the droplet turns — St = 4 · any Reynolds number for the flow; the particle drag is Stokesian · particle-paths
- Whether the droplet turns — Stokes drag on the droplet — honest below about 30 µm at these speeds · particle-paths
- Whether the droplet turns — Stokes drag, small relaxation time, a steady swirling flow — no history term · particle-paths
- Whether the droplet turns — Re → 0, rooms from 4 to 1024 radii · creeping-flow
- Wobbling saddles keep the quarter, and raise it — Stokes number St = τ × strain rate; a fold when tr Z < −50; 100–144 particles a cloud · velocity-field · hero
- Wobbling saddles keep the quarter, and raise it — Stokes number St = τ × strain rate; a fold when tr Z < −50; 100–144 particles a cloud · velocity-field
- Wobbling saddles keep the quarter, and raise it — Stokes number St = τ × strain rate; ε = 1, ω = 3; one particle from (0.2, 1.3) · velocity-field
- Wobbling saddles keep the quarter, and raise it — Stokes number St = τ × strain rate; a fold when tr Z < −50; 100–144 particles a cloud · velocity-field
- Wobbling saddles keep the quarter, and raise it — Stokes number St = τ × strain rate; ω = 3; 144 particles over one cell · velocity-field
- Wobbling saddles keep the quarter, and raise it — Stokes number St = 0.2; cells of side π · velocity-field
- Wobbling saddles keep the quarter, and raise it — Stokes number St = τ × strain rate; a fold when tr Z < −50; 100–144 particles a cloud · velocity-field