Why won't ketchup come out — until it suddenly floods out?
― Until the force crosses a "threshold," ketchup pretends to be a solid
Turn it upside down: nothing comes out. Shake it: still nothing. Then, the very next instant, there's a mound on your plate. Ketchup isn't being fickle because of how hard you're pushing. It's a substance that responds like a "solid" to any force below a certain strength, and like a "liquid" above it.
You're about to squirt ketchup on your omelette rice, so you tip the bottle upside down. But not a single drop falls from the tip.
You give it a firmer shake. Still nothing. You shake it once more, this time swinging it down hard.
Then a big blob suddenly drops out, turning half the egg red. Water or soy sauce would never do this.
There are only two reasons
Inside ketchup, fine tomato fibers and particles tangle together, forming a loose mesh. Until the pushing force crosses a certain strength (the threshold), this mesh holds its shape, and the ketchup sits there like a soft solid.
When the mesh collapses past the threshold, the ketchup starts to flow. And the faster it flows, the more the mesh unravels, making it flow even more easily. There's almost no middle ground of "coming out a little at a time" — which is why it all rushes out at once.
Water flows a little no matter how weak the force. Ketchup is an "all or nothing" substance. Put these two properties together, and you get that "won't come out → floods out" moment.
What's happening at the mouth of the bottle?
At the opening of an upside-down bottle, the ketchup inside is being pushed downward by its own weight. That force is held back by the inner wall of the opening.
Look at the left side of Figure 1. A tube bottle's opening is narrow — around 4 millimetres across — so the force generated by the ketchup's weight is small. Do the math, and the force at the boundary with the wall comes to only about half the threshold. That's why simply turning the bottle upside down leaves it stuck at the tip.
When you shake the bottle, the swing and sudden stop push the ketchup with a force many times its weight. As shown on the right of Figure 1, the moment the force crosses the dotted threshold line, the flow speed shoots up from zero all at once.
Why is it so hard to get "just the right amount" out?
Once ketchup crosses the threshold, the faster it flows, the thinner it gets. This property is called shear-thinning. Because even a little bit of flow makes it flow more easily, easing off with your hand can't keep pace.
What's more, ketchup left standing rebuilds its mesh, and the threshold creeps back up. This is thought to be why ketchup fresh from the fridge is especially stubborn. Conversely, giving the sealed bottle a good shake loosens the mesh, so it takes less force to get it started.
The trick to getting just the right amount out is applying force "gently but for longer," not "briefly but hard." For a tube bottle, the surest method is to store it standing with the cap down, then press gently and slowly.
Sometimes, right after opening, a watery liquid comes out first that isn't red. While sitting, the mesh shrinks slightly and squeezes water out of the gaps toward the opening. Shaking the bottle a few times while still sealed, before use, tends to prevent this.
Toothpaste holds its shape on the brush but comes right out when you squeeze the tube. That's because it's also a substance with a threshold. This trait — flowing only when you want it to — is deliberately engineered into product design.
Summary
Ketchup sits still like a solid as long as the force stays below the threshold. The instant it's crossed, it starts flowing, and the more it flows, the runnier it gets. That's why there's almost no middle ground between "won't come out" and "floods out."
Ketchup isn't being fickle.
It's responding exactly as designed: "a solid under weak force, a liquid under strong force."
You can read about ground that similarly "changes firmness depending on how force is applied" in our article on quicksand, and about the air moving in and out when liquid leaves a container in our article on why plastic bottles glug.
- Squeeze a little ketchup onto a small plate and tilt the plate gradually. At an angle where water would already be flowing, ketchup stays put for a while.
- While still tilted, tap the edge of the plate lightly with a finger. You'll see the ketchup slide, but only right at the moment you tap it.
- Compare pressing a well-shaken tube against an unshaken one with the same force. The shaken one usually starts out lighter to squeeze.
You can try the same experiment with mayonnaise or mustard. Anything that can hold a mound shape on a plate belongs to the same family of threshold substances.
For those who want to know more ― terms, formulas, and how it connects to textbooksLabels show exactly which level each part belongs to, 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, rheology)
- ResearchNot yet settled "textbook fact" even at university — an active research question
MSTerminology: this phenomenon has a name
- Yield stress: the threshold force per unit area needed for a substance to start flowing (for its shape to start collapsing). For ketchup, this is said to be on the order of tens of pascals.
- Shear-thinning: the property where viscosity (thickness) drops the faster something flows. Seen in ketchup, mayonnaise, paint, and more.
- Thixotropy: a time-dependent property where stirring makes something flow more easily, and leaving it alone lets it firm back up.
MSHSChecking with a formula: the force on ketchup inside the opening
Suppose there's a cylindrical plug of ketchup with radius R inside the mouth of the upside-down bottle. Assume the entire side surface of this cylinder (the boundary with the inner wall of the opening) is holding up its weight. If the force per unit area at the boundary with the wall exceeds the yield stress, the ketchup starts to flow.
| In symbols | τ = ρ × a × R ÷ 2 (flow starts once τ exceeds τy) |
| In words | Force at the wall boundary = density × acceleration involved × radius of the opening ÷ 2 |
| Where it comes from | Balancing the cylinder's weight ρ × a × πR² × L against the force the side surface holds, τ × 2πR × L. Cancel πR × L from both sides and you get this form |
| Symbol | Meaning and units |
| τ | Force per unit area at the wall boundary (pascals) |
| τy | Yield stress = the threshold to start flowing (pascals) |
| ρ | Density of the ketchup (kilograms per cubic metre) |
| a | Acceleration involved. Just turning it upside down means gravitational acceleration g (metres per second squared) |
| R | Inner radius of the opening (metres) |
| Density of ketchup ρ | about 1100 kg/m³ |
| Gravitational acceleration g | 9.8 m/s² |
| Radius R of the tube bottle opening (4mm diameter) | 0.002 m |
| Yield stress τy of ketchup | said to be roughly 15–30 pascals; we'll use 20 pascals |
| Density × gravitational acceleration | 1100 × 9.8 = 10780 |
| × radius of the opening | 10780 × 0.002 ≒ 21.56 |
| ÷ 2 = τ when just turned upside down | 21.56 ÷ 2 ≒ 10.78 pascals |
| How many times the weight-only force is the threshold | 20 ÷ 10.78 ≒ 1.86 times |
| Acceleration needed to start flowing | 9.8 × 1.86 ≒ 18.2 m/s² |
Just turning it upside down gives a wall force of only about 11 pascals, short of the roughly 20-pascal threshold. Apply about 1.9 times the acceleration of gravity, and it finally starts to flow. Swinging the bottle down and stopping it abruptly is said to be enough to reach this level of acceleration by hand. And since viscosity drops the instant flow starts, you can't stop it at "exactly 1.9 times."
HSHS+What if the opening is wider?
HSLooking at the formula, τ is proportional to the opening's radius R. Double the opening's radius, and the wall force from the same weight doubles too. In a wide-mouthed glass jar, weight alone can approach the threshold, sometimes causing it to trickle out very slowly.
HS+For liquids without a threshold, like water, it will always flow out eventually through even the narrowest tube, given enough time. Substances like ketchup, where force and flow aren't proportional, are called non-Newtonian fluids.
Univ.Ketchup through the lens of rheology
The relationship between force and flow in ketchup is often approximated by the Herschel–Bulkley equation, which adds shear-thinning to the idea of a Bingham plastic with yield stress. In this equation, stress is expressed as "yield stress + coefficient × shear rate to a power," and an exponent less than 1 represents the shear-thinning. In real containers, a thin, water-rich layer forms right next to the wall, letting the whole plug slide as a block — called "wall slip" — which further affects how it comes out.
📖 For the derivation of the formula and further reading: Non-Newtonian fluid (Japanese Wikipedia) / Thixotropy (Japanese Wikipedia)
ResearchWhat's still not fully understood
- Does a true threshold even exist? A 1985 paper titled "Is yield stress a myth?" sparked ongoing debate over whether even a very weak force will eventually produce flow, given a long enough time.
- The identity and strength of the mesh. Exactly how fragments of tomato cell walls and components like pectin combine to determine the threshold is being investigated for each processing condition.
- Predicting wall slip. How the container's material and surface treatment change the slipping behaviour is a research topic tied directly to container design.
In other words, this article too describes things "as currently understood." Even the value of the yield stress varies considerably depending on how it's measured.
Connections to textbooks (by level)
| Level | Subject/Unit | Where in this article |
|---|---|---|
| MS | Science — force balance, pressure | Weight force and the wall's holding force |
| HS | Physics Basics — equations of motion, acceleration | How much the force multiplies when shaken |
| HS+ | Advanced physics — viscosity | Non-Newtonian fluids vs. water |
| Univ. | Fluid dynamics, rheology | Herschel–Bulkley equation, wall slip |
| Research | Food rheology | The debate over whether yield stress truly exists |
| ― | Connection to daily life | Shake before use, store cap-down |
- H. A. Barnes, K. Walters, "The yield stress myth?", Rheologica Acta 24 (1985)
- H. A. Barnes, J. F. Hutton, K. Walters, "An Introduction to Rheology", Elsevier (1989)
- The Society of Rheology, Japan (ed.), "Lectures on Rheology" (講座・レオロジー), Kobunshi Kankokai (日本レオロジー学会 編『講座・レオロジー』高分子刊行会)
- Wikipedia, "Non-Newtonian fluid" (非ニュートン流体)
※This article is a general-audience science explainer. The figures given are rough estimates meant to aid understanding of the underlying mechanism. Values such as yield stress vary considerably depending on the product, temperature, and measurement method.