Why is water like honey to a water flea?
― Shrink the body, and the same water becomes a different liquid
Give a good hard kick in a pool, let your legs stop, and your body keeps gliding on. But the small creatures living in that same water have never once felt that glide. Same water — but the smaller the body, the stickier and clingier that water becomes.
A swimming pool in summer. You take a breath and give one big stroke. Even after your arms stop, your body keeps sliding forward. Water feels like a light, slippery fluid that steps aside once you push it.
That same day, in a classroom aquarium, a water flea about a millimetre long is paddling its antennae up and down. Look closely, and the moment it stops paddling, it halts instantly, right where it is. No gliding "whoosh" for it.
Shrink further, down to a bacterium, and the distance it travels after it stops swimming is said to be less than the width of a single atom. Living in the very same water, we and they seem to be looking at a completely different character of liquid.
It comes down to just two things
A body that's already moving is hard to stop because it has mass packed inside it. This resistance to stopping scales with volume — length cubed. The bigger the body, the more it favours pushing water aside and coasting onward.
Water drags against the surface of a body as it flows past. This braking force scales only with surface area — length squared. Shrink the body, and its bulk shrinks faster than its surface does, so the braking force is all that's left.
In other words, whether water feels slippery or feels like honey depends entirely on which of these two forces wins. That contest is captured by a single number, which comes next.
The Reynolds number ― the one number that decides water's "character"
Multiply a body's length by its swimming speed, then divide by how sticky the water is: that gives you the Reynolds number. It's just a ratio, with no units. The bigger this number, the more the "pushing force" wins; the smaller it is, the more the "clinging force" wins.
Take a look at Figure 1. The horizontal axis is the Reynolds number, with larger creatures further to the right. A person swimming in a pool sits at around 1.7 million. A water flea is around 3. A bacterium is far below 1. The boundary sits at around 1 — cross it to the left, and water suddenly starts behaving like a thick, sticky liquid.
In a world where you stop the instant you stop, even swimming style must change
With no gliding available at all, creatures have to change how they swim altogether. We can swim breaststroke because we push water differently when our arms and legs spread than when they close, and we carry the momentum gained in between across the gap through inertia. Small creatures have no such carry-over.
Look at the left side of Figure 2. A motion that simply opens and closes, like a clam's shell, retraces exactly the same shape backward on the return stroke. In a world where stickiness wins, whatever progress you make on the way out is exactly cancelled on the way back, and the net movement is zero. This is known as the scallop theorem.
So small creatures instead choose a motion that never returns to its original shape, as shown on the right of Figure 2. Bacteria spin a corkscrew-shaped flagellum like a motor; sperm send waves rippling down their tail. Neither is an "open and close" motion — both are a "spin" or a "send a wave" motion. In a world dominated by stickiness, the paths available for moving forward turn out to be quite limited.
Pour honey into a bowl, stir it slowly with a spoon, and stop. In water, the swirl keeps spinning for a while; in honey, it stops almost the instant you do. Your hand, at that moment, is tracing the same resistance a water flea feels every single day.
Even a large fish like tuna lives in this "sticky water" during its first few millimetres of life, just after hatching. As it grows, the character of water changes around it, so it's thought to need to rebuild its swimming style partway through growing up.
Summary
The reason water feels slippery isn't a property of water itself — it's simply because our bodies happen to be big enough. The smaller a body gets, the more the clinging force wins over the pushing force, and water turns into a sticky liquid. Water fleas and bacteria are crossing that "sea of honey" using swimming styles completely unlike our own.
Water isn't slippery because of water.
It's slippery because your body happens to be big.
For more on turning surrounding flow to your advantage, see why migrating birds fly in a V formation and how aeroplanes fly. On the relationship between water and body surfaces, see also why water birds' feathers don't get wet.
- Fill a deep bowl with water and sprinkle a little pepper on the surface. Stir slowly with your finger, the same direction, ten times, then stop suddenly. The pattern of pepper keeps swirling for a while.
- In another bowl, put honey and stir it the same way with a spoon, then stop. The pattern should stop almost the instant you do.
- Finally, in the honey, slowly move the spoon to the right, then trace the exact same path back to the left. The swirl marks around it return almost to how they started — showing that a simple there-and-back motion carries nothing along with it.
You can't change your own body size, but by changing a liquid's stickiness, you can visit, first-hand, the world small creatures see every day.
Want to know more? ― Terms, formulas, and links to the curriculumWe label each part by level, from middle-school science to university specialist courses
- MSCovered in middle-school science
- HSCovered in high-school "Physics Basics / Physics"
- HS+High-school advanced content, or textbook sidebar material
- Univ.Not covered in high school — university specialist courses (fluid dynamics, biophysics)
- ResearchNot yet settled even at university level — an area researchers are actively investigating
MSTerms: this phenomenon has names
- Reynolds number: the ratio between how strongly the pushing force acts and how strongly the clinging force acts. It carries no units.
- Viscosity: how resistant a liquid's layers are to sliding past one another when they rub together. This is what we usually call "stickiness."
- Scallop theorem: the rule that in a world where stickiness wins, a simple back-and-forth open-close motion cannot produce forward progress.
MSHSCheck it with a formula: how different are the numbers for a swimmer and a water flea?
The Reynolds number is found by multiplying a body's length by its speed, then dividing by a number representing how sticky the water is. We'll skip the symbols and calculate directly, keeping the units consistent — length in metres, speed in metres per second.
| Swimmer's body length | 1.7 metres |
| Swimmer's speed | 1 metre per second |
| Water flea's body length | 0.001 metres |
| Water flea's swimming speed | 0.003 metres per second |
| Number representing water's stickiness (water at 20°C) | taken as 0.000001 |
| Person: length × speed | 1.7 × 1 = 1.7 |
| Person's Reynolds number | 1.7 ÷ 0.000001 = 1,700,000 |
| Water flea: length × speed | 0.001 × 0.003 = 0.000003 |
| Water flea's Reynolds number | 0.000003 ÷ 0.000001 = 3 |
Same water, same day, same tank — yet as numbers, the gap is more than 500,000-fold. That gap is the real identity behind the difference between "slippery" and "sticky."
HSHS+Laminar and turbulent flow ― the shape of the flow itself switches too
HSWhen the Reynolds number is large, flow rolls up everywhere into a chaotic mess of eddies — this is called turbulent flow. When it's small, layers of water stay neatly arranged and flow quietly — this is called laminar flow. Around small creatures, the flow is always laminar.
HS+In pure laminar flow, stirring barely mixes anything. So for small creatures, letting scent or nutrient molecules spread on their own can actually be faster than "carrying them by flow." Stirring itself simply doesn't pay off in that world.
Univ.An equation where the direction of time disappears
Drop the term corresponding to the pushing force from the equations describing flow, and time disappears entirely as a variable. This is called Stokes flow. If time drops out, it means "whether you move fast or slow, the path the water takes is exactly the same." That's why a simple open-close back-and-forth motion cancels out whatever progress it makes on the way out, on the way back, for zero net movement. This is thought to be why the tails of sperm and bacteria move not in a simple back-and-forth but in waves or corkscrew shapes.
ResearchWhat's still not fully understood
- Behaviour in large groups. When bacteria gather at high density, large swirling flows appear that can't be predicted just from the motion of individuals. Under what conditions this arises, and how far it can be predicted, is said to still be a work in progress.
- Swimming in liquids that are not just sticky but also springy. Substances like mucus inside the body combine stickiness with elasticity. Simple water-based reasoning doesn't directly apply in such liquids, and both faster and slower swimming have reportedly been observed as a result.
- Designing tiny machines that swim inside the body. How to build microscopic swimmers, such as ones that deliver drugs, so they move efficiently is strongly constrained by the physics of this world, and is said to remain an ongoing challenge.
In other words, even the contents of this article are "an explanation based on what's currently understood." Swimming in the small-scale world, despite how simple it looks, still leaves many open questions.
Links to the curriculum (by level)
| Level | Subject / unit | Where in this article |
|---|---|---|
| MS | Science ― small aquatic organisms / force and motion | The part where the water flea halts on the spot |
| HS | Physics Basics ― the law of inertia | The "pushing force" card |
| HS+ | Physics ― viscous drag and types of flow | The Reynolds number calculation, laminar vs. turbulent flow |
| Univ. | Fluid dynamics / biophysics | Stokes flow, the scallop theorem |
| Research | The physics of microscopic swimmers | The research section |
| ― | Connection to daily life | The feel of stirring honey |
- Purcell, E. M., Life at low Reynolds number, American Journal of Physics 45(1), 3–11, 1977 (a classic lecture on swimming in the small-scale world).
- Lauga, E. & Powers, T. R., The hydrodynamics of swimming microorganisms, Reports on Progress in Physics 72, 096601, 2009 (a review of microorganism swimming).
- Vogel, S., Life in Moving Fluids, Princeton University Press, 1994 (a textbook on the relationship between living things and flow).
- Standard fluid dynamics textbook treatments of the Reynolds number, laminar and turbulent flow, and viscous drag.
※This article is a general-audience science explainer. The figures given are approximate, meant to help convey the underlying mechanism. Actual sizes and swimming speeds vary between individual creatures.