Turn a jar of honey and a bottle of water upside down at the same moment. Exactly the same gravity acts on both liquids, yet they behave nothing alike: the water leaves its container almost instantly and splashes across the counter, while the honey forms a thick, stately thread that lazily creeps downward. That difference does not come from density — it comes from the liquid's internal friction, a physical property called dynamic viscosity.
Dynamic viscosity is an invisible brake that governs the motion of every fluid, liquid or gas. It decides how blood circulates through your vessels, how oil keeps an engine from seizing, and why ketchup first resists and then suddenly lands on your plate. Understanding it takes us from the kitchen counter, through nineteenth-century laboratories, all the way to an experiment that has been running without a break for nearly a hundred years.
The two-plate model: what viscosity really is
To define viscosity precisely, we have to drop the everyday "thick" and "sticky" and look at a fluid as a stack of layers. Picture a liquid as a deck of many parallel, molecular layers. When the fluid flows, those layers slide past one another at different speeds, and every such sliding meets resistance. Dynamic viscosity is simply the measure of that resistance.
The classic picture is the two-plate model, going back to Newton. We trap a fluid between two parallel plates of area A, separated by a distance y. The bottom plate is fixed; we drag the top one horizontally at a constant speed v by applying a force F. The layer of fluid touching the top plate clings to it and moves at speed v; the layer at the bottom plate stays still. In between, the speed changes linearly — from zero to v.
Experiment shows the required force is directly proportional to the plate area and to the velocity gradient v/y:
F = η · A · (v / y)
The constant of proportionality is exactly the dynamic viscosity, denoted by the Greek letter η (eta) or μ (mu). Dividing force by area gives the shear stress τ = F/A, which lets us write Newton's law of viscosity in differential form:
τ = η · (du / dy)
where du/dy is the shear rate (the velocity gradient perpendicular to the flow). Dynamic viscosity is therefore the ratio of shear stress to shear rate. Its SI unit is the pascal-second (Pa·s), equal to a kilogram per metre per second:
1 Pa·s = 1 kg / (m·s)
It is worth separating dynamic from kinematic viscosity right away. The former describes internal friction on its own. Kinematic viscosity ν (nu) also folds in the liquid's weight — it is the dynamic viscosity divided by density: ν = η / ρ. Its SI unit is m²/s, and in engineering practice the stokes (St) and centistokes (1 cSt = 1 mm²/s). In short: dynamic viscosity tells you how hard it is to shove the layers with an external force, while kinematic viscosity tells you how easily the fluid runs under its own weight.
From blood to the poise: Poiseuille's legacy
Precise units of viscosity were born not at an engineer's bench but at a medical one. The key figure was the French physician and physicist Jean Léonard Marie Poiseuille (1797–1869), fascinated by the mechanics of blood flowing through the capillaries.
In his doctoral work, defended in 1828, Poiseuille built a haemodynamometer — a U-shaped mercury manometer connected straight to arteries to measure blood pressure (he filled the tubes with sodium carbonate so the blood would not clot). Wanting to isolate the effect of a vessel's geometry on resistance, he moved his experiments outside living bodies: he built apparatus with extremely narrow glass capillaries, inner diameters from 0.015 to 0.6 mm, and timed how water flowed through them.
That is how he formulated the relationship for the volumetric flow rate Q, known today as the Hagen–Poiseuille law:
Q = π · r⁴ · ΔP / (8 · η · L)
where r is the capillary radius, ΔP the pressure difference across its ends, L the tube length, and η the dynamic viscosity. The crucial part is the fourth power of the radius: halving a vessel's diameter cuts the flow at the same pressure by a factor of sixteen (2⁴ = 16). That is why even a slight narrowing of an artery burdens the heart so dramatically.
In recognition of Poiseuille's work, the old CGS system (centimetre-gram-second) named the unit of viscosity the poise (P), defined as 1 g/(cm·s). Converting to SI is simple — swapping grams for kilograms and centimetres for metres gives:
1 P = 0.1 Pa·s, so 1 Pa·s = 10 P
In everyday lab work, though, the hundredth of a poise reigns — the centipoise (cP), identical to the millipascal-second: 1 cP = 1 mPa·s = 10⁻³ Pa·s. That choice is no accident. It is physically anchored: distilled water at 20 °C has a viscosity of almost exactly 1.002 cP. Thanks to that, every result reads intuitively — 84 cP means "84 times more friction than water," and 1500 cP means "1500 times more." All of these units — Pa·s, poise, centipoise, and millipascal-second — are converted between one another by the dynamic-viscosity converter on this site.
The scale of viscosity: from air to pitch
Viscosity in nature spans well over a dozen orders of magnitude. The table below lines up typical values — from the most fluid to the nearly solid — with their multiple relative to water at 20 °C.
| Substance | Temperature | Viscosity [mPa·s = cP] | Viscosity [Pa·s] | Multiple (water 20 °C = 1) |
|---|---|---|---|---|
| Air | 20 °C | 0.0182 | 1.82 × 10⁻⁵ | ~0.018× (gas, exceptional fluidity) |
| Boiling water | 100 °C | 0.282 | 2.82 × 10⁻⁴ | ~0.28× |
| Water | 20 °C | 1.002 | 1.00 × 10⁻³ | 1× (reference point) |
| Mercury | 20 °C | 1.55 | 1.55 × 10⁻³ | ~1.5× (dense but thin) |
| Human blood | 37 °C | 3–4 | ~3.5 × 10⁻³ | ~3.5× |
| Olive oil | 25 °C | 84 | 8.4 × 10⁻² | ~84× |
| SAE 30 engine oil | 40 °C | ~100 | ~0.10 | ~100× |
| Glycerol | 20 °C | ~1450 | ~1.45 | ~1450× |
| Honey (liquid) | 20 °C | ~10,000 | ~10 | ~10,000× (rapeseed several times more) |
| Ketchup (at rest) | 25 °C | ~50,000 | ~50 | ~50,000× (non-Newtonian) |
| Pitch (bitumen) | 20–25 °C | ~2.3 × 10¹¹ | ~2.3 × 10⁸ | ~230 billion × |
The bottom of the table is the most surprising. Substances we treat every day as solids — road asphalt or pitch — are, from a physicist's point of view, liquids of gigantic viscosity in which flow plays out over decades. We will come back to them, because they hide one of the most beautiful experiments in the history of science.
Heat and cold: why temperature changes everything
Viscosity is almost never a constant — it depends strongly on temperature, and in a way that is both non-linear and asymmetric: heating thins liquids but thickens gases.
In liquids the molecules are packed close together, and the resistance to sliding layers comes from cohesive forces — intermolecular attraction (hydrogen bonds, van der Waals interactions). When a liquid is heated, the supplied energy turns into kinetic energy of the molecules; they vibrate more violently and break away from their neighbours more easily. Cohesion weakens, the layers slide more freely, and viscosity drops sharply. For Newtonian liquids this is described by the exponential Arrhenius–Andrade equation:
η(T) = A · exp( Eₐ / (R · T) )
where A is a material constant, Eₐ the activation energy of flow, R the gas constant, and T the absolute temperature in kelvins. For honey Eₐ is about 85 kJ/mol — one of the highest values among foods. The effect is tangible: honey's viscosity roughly halves for every 6–8 °C of warming. Honey straight from the fridge is nearly impossible to spread, while warmed in a water bath to 40 °C it loses internal friction many times over and pours like syrup. Water content matters too: according to Yanniotis (2006), each extra 1% of moisture lowers honey's viscosity by about 35%. That is why honeys above the moisture limit (USDA: 18.6%) are rarer — excess water invites fermentation.
In gases the mechanism is entirely different. The molecules are far apart, their attraction negligible, and the friction comes from momentum carried by molecules wandering between layers of different speed. A heated gas means faster molecules, more collisions, and more intense momentum exchange between layers — and that hinders orderly flow. Macroscopically, a gas's viscosity rises. The viscosity of dry air climbs from about 17.1 μPa·s at 0 °C to 21.3 μPa·s at 100 °C.
Non-Newtonian fluids: ketchup and oobleck
Fluids whose viscosity stays constant regardless of the shearing force (at a given temperature) are called Newtonian — water, air, alcohols, light oils. No matter how fast you stir water, its internal resistance does not change. But there is a huge family of liquids that break this rule: for them, viscosity depends on the shear stress or on how long the shearing lasts.
Ketchup is the classic shear-thinning (pseudoplastic) fluid. At rest, tomato particles and long polymer chains (pectins, xanthan gum) form a dense, tangled three-dimensional network that blocks flow — hence a viscosity on the order of 50,000 mPa·s and the fact that ketchup will not pour from an upturned bottle. But hit the base or squeeze the sides and you apply a large shear stress; the tangled chains straighten and line up along the flow, the network breaks, viscosity collapses — and the whole portion lands on your plate. Good emulsion paints work the same way: under a brush (high shear) they are thin and spread smoothly, and the moment you stop they thicken again so they do not run down the wall.
The opposite mechanism rules shear-thickening (dilatant) fluids. The most famous example is a suspension of corn starch in water, roughly two parts starch to one of water — popularly known as oobleck. Under slow stirring (low shear rate) water surrounds the starch grains and acts as a lubricant — the fluid pours between your fingers like thick milk. But punch it, and the sudden force squeezes the water out from between the grains; stripped of their coating, the particles jam into a tight, locked structure (hydroclustering). Viscosity jumps by several orders of magnitude in a fraction of a second — the fluid briefly turns into a solid that a fist bounces off. Once the pressure stops, water returns between the grains and the oobleck flows like an ordinary liquid again.
Three myths worth defusing
The physics of fluids is full of intuitive traps. Three of them have grown especially stubborn myths.
Myth 1: "Viscosity is the same as density." In everyday speech "dense" and "viscous" travel together, but they are two entirely independent quantities. Density is mass per unit volume (ρ = m/V); viscosity is internal friction. The best counterexample is mercury: its density is a whopping 13,590 kg/m³ — more than thirteen times that of water (1000 kg/m³) and fifteen times that of olive oil (~910 kg/m³). If density ruled flow, mercury should ooze. Yet its viscosity is a mere 1.55 mPa·s — mercury flows almost as easily as water and is more than fifty times thinner than light olive oil (84 mPa·s). Dense does not mean viscous.
Myth 2: "The codes on engine oil, like 10W-40, are the viscosity value itself." They are not pascal-seconds or centipoises but viscosity grades under the SAE J300 standard, describing how the oil behaves at extreme temperatures. In "10W," the letter W stands for winter: a 10W-grade oil must, in the cold-crank test (CCS, −25 °C), stay below 7000 cP so the starter can turn the crankshaft, and pass the pumpability test (MRV, −30 °C) below 60,000 cP. The number "40" describes the hot engine: kinematic viscosity at 100 °C must fall between 12.5 and 16.3 cSt, and the high-shear dynamic viscosity (HTHS, 150 °C) must be at least 3.5–3.7 cP. To make one oil meet both specs at once, polymer viscosity modifiers are added: at low temperatures their chains coil into tight balls and stay out of the way, and at high temperatures they unfurl, swell, and brake the oil's natural thinning.
Myth 3: "Pitch and glass are solids." Asphalt and pitch at room temperature seem hard as stone — struck with a hammer they shatter into sharp, glassy shards. And yet physics classifies them as liquids of colossal viscosity. The proof is the longest-running laboratory experiment in the world, entered in the Guinness Book of Records: the pitch drop experiment, set up in 1927 by Professor Thomas Parnell at the University of Queensland in Brisbane. Parnell wanted to show his students that apparently solid substances flow, given enough time. He heated the pitch, poured it into a glass funnel with a sealed stem, and let it settle for three years. In 1930 he cut off the bottom, and gravity began slowly pulling the pitch downward.
| Drop | Date | Formation time [years] | Details |
|---|---|---|---|
| 1 | December 1938 | 8.1 | first drop, no witnesses |
| 2 | February 1947 | 8.2 | the postwar years |
| 3 | April 1954 | 7.2 | shortest formation time |
| 4 | May 1962 | 8.1 | Prof. John Mainstone takes over |
| 5 | August 1970 | 8.3 | — |
| 6 | April 1979 | 8.7 | last drop before air conditioning |
| 7 | 3 July 1988 | 9.2 | Mainstone stepped out for coffee just as it fell |
| 8 | 28 November 2000 | 12.3 | first after air conditioning; camera recording failed |
| 9 | 24 April 2014 | 13.4 | a jolt while swapping the beaker detached the drop |
From the data, the pitch's viscosity was calculated at about 2.3 × 10⁸ Pa·s — some 230 billion times that of water. Interestingly, installing air conditioning in the 1990s lowered the average temperature by a few degrees and so raised the pitch's viscosity that the interval between drops stretched from about 8 years to over 12 — a beautiful illustration of the exponential dependence on temperature. For decades no one saw a drop fall live; the breakthrough came in a sister experiment at Trinity College Dublin, where on 11 July 2013 a falling drop of pitch was captured on video for the first time.
And those old stained-glass windows that supposedly "flowed" and are thicker at the bottom? A myth. Silica glass at room temperature is a solid with an amorphous structure, and the time needed for it to sag noticeably exceeds the age of the universe. The uneven thickness of old panes comes purely from how they were made — craftsmen deliberately mounted the thicker edge at the bottom of the frame.
Everything flows, just at its own pace
Dynamic viscosity teaches humility toward intuition. First: density and viscosity are different things — mercury is dense yet flows like water. Second: viscosity is not a physical constant but a value strongly dependent on temperature and on how we mechanically work the fluid. That knowledge pays off daily — from warming honey, through shaking ketchup, to consciously choosing a multigrade oil. And in the background waits the longest experiment in the world, patiently reminding us that even "solids" flow — just at a pace a single human life will never quite catch in the act.
Further reading
- M. Dziubiński, T. Kiljański, J. Sęk, Podstawy reologii i reometrii płynów, Łódź University of Technology Press, Łódź 2009 — an academic introduction to non-Newtonian fluids and measurement methods.
- D. Halliday, R. Resnick, J. Walker, Fundamentals of Physics — the classic treatment of hydrodynamics and Newton's law of viscosity.
- R. Edgeworth, B. J. Dalton, T. Parnell, The pitch drop experiment, "European Journal of Physics" 5, no. 4 (1984), pp. 198–200 — the original paper on the world's longest-running experiment.