Why Does a Drop of Coffee Leave a Ring When It Dries?
― The Tiny River Made by Evaporation
Sometimes a coffee spill dries into a ring-shaped mark: pale in the middle, with a sharp, dark edge. You might expect the color to thin out evenly. So why does the dark material gather only at the edge?
Have you ever spilled coffee or tea and left it to dry? When you look again later, the middle of the stain is pale, and only the outer edge of the ring is sharp and dark. This is called the "coffee ring effect". It is said to be common whenever a colored liquid is spilled and dries, not just with coffee.
If a drop dried evenly, you would expect its color to fade evenly too. So why does the material pile up only at the edge?
The edge of a drop is thin, and has a wide surface open to the air. That is why evaporation is said to run especially fast there.
To make up for the water that evaporates at the edge, a small flow is thought to arise, running from the center of the drop out to the edge.
Let's look step by step at how this flow arises from faster evaporation at the edge.
Why does the edge of a drop evaporate faster?
Seen from the side, a drop is plump in the middle and gets thinner toward the edge. In this thin edge region, a large share of the water is right at the surface, open to the air. That is why evaporation is said to run faster there than at the center.
The flow from the center that replaces water lost at the edge
The key point is that the edge of the drop (the contact line) stays fixed where the liquid was spilled and does not easily move. For a drop of coffee on a tabletop, the edge tends to stay in the shape it had when first spilled. Even as water evaporates at the edge, the edge itself does not move. So a flow from the center of the drop to the edge is thought to arise, replacing the lost water.
It is the trace of a "river" that kept flowing inside the drop while it dried.
Particles are carried to the edge by the flow
Tiny particles that remain undissolved in the coffee (the coffee material) are caught up in this center-to-edge flow and carried along with it. By the time the drop has dried completely, almost all the particles have gathered at the edge. What is left is a ring-shaped stain, dark only at the edge and pale in the middle.
Not every liquid leaves a ring. Research has shown that the shape of the particles, or certain substances in the liquid (such as ones that change surface properties), can make the ring harder to form. By tuning the liquid and the particles, this is also used in techniques for drying things evenly.
Try it yourself
- Put one drop of diluted coffee or tea on a white sheet of paper or a plate
- In the same spot, put one drop of plain water with nothing dissolved in it for comparison
- Let both dry naturally
- Once dry, compare the shape and darkness of the stains
You can see that a liquid with something dissolved in it tends to leave a ring-shaped stain, while plain water tends to leave no noticeable mark.
Summary
A coffee ring forms because evaporation runs fast at the edge of the drop, and a flow from the center to the edge arises to replace the lost water. This flow carries the coffee particles out to the edge and piles them up there. Once the drop is dry, a ring-shaped stain is left, dark only at the edge.
A coffee ring is the memory of a "small river" that really did keep flowing inside the drop for the few minutes to few tens of minutes it took to dry.
For the opposite case, where drops "burst and fly off", see Why does rain have a distinctive smell when it starts to fall? It explains how bubbles made when raindrops hit the ground burst and throw droplets too fine to see up into the air.
For those who want to know more ― terms, numbers, and links to textbooksEach part is labeled with its level, from middle-school science to active research
- Middle schoolCovered in middle-school science
- High schoolCovered in high-school basic physics
- High school+Advanced or sidebar material in high-school textbooks
- UniversityUniversity-level content (fluid mechanics) not taught in high school
- ResearchTopics researchers are still investigating, not taught even at university as settled fact
Middle schoolTerms: words around the coffee ring effect
- Evaporation: the change of a liquid into gas, bit by bit, from its surface.
- Contact line: the ring-shaped boundary where a drop touches a solid surface.
- Coffee ring effect: the way material gathers at the edge of a drying drop and leaves a ring-shaped stain.
High schoolChecking with a formula: a simplified estimate of how long a drop takes to dry
Here we use a simplified model to work out how long a drop takes to dry, from its evaporation rate and its original amount.
| In symbols | v ＝ V ÷ ( L × h × t ) |
| In words | Speed of the flow toward the edge ＝ volume of the drop ÷ (length of the edge × thickness of the liquid × time to dry) |
| Where it comes from | Conservation of volume. Since the edge does not move, the water lost to evaporation must be replaced by flow from the inside. That flow carries the particles |
| v | Speed of the flow toward the edge. Unit: millimeters per second (mm/s) |
| V | Volume of the drop. Unit: cubic millimeters (mm³) |
| L | Length of the edge (its circumference). Unit: millimeters |
| h | Thickness of the liquid near the edge. Unit: millimeters |
| t | Time to dry. Unit: seconds |
Original amount of the drop (mL) ＝ evaporation rate (mL/min) × time to dry (min)
| Evaporation rate | A rough measure of how much water is lost per minute |
| Time to dry | The time the drop takes to dry completely |
| Original amount of the drop (mL) | 0.02 × 25 ＝ 0.5 |
| Result | A drop of about 0.5 mL takes 25 minutes to dry |
| Original amount of the drop (mL) | 0.02 × 50 ＝ 1 |
| Convert minutes to hours | 50 ÷ 60 ≒ 0.83 |
| Result | A drop of about 1 mL takes 50 minutes (about 0.83 hours) to dry |
Throughout these tens of minutes before the drop dries completely, the center-to-edge flow keeps working, carrying particles little by little to the edge. The bigger the drop, the longer it takes to dry, and the longer the flow keeps working.
* The numbers here are simplified rough values, chosen to help you grasp the mechanism. Real evaporation rates are said to vary a great deal with temperature, humidity and drop size.
Put numbers into the formula in ⓪ to find the speed of the flow toward the edge. Take a drop 10 mm across, with a volume of 20 mm³, that dries in 25 minutes (1500 seconds).
| Find the length of the edge | 31.4 × 0.2 ＝ 6.28 |
| Multiply by the time | 6.28 × 1500 ＝ 9420 |
| Divide the volume by that to get the flow speed | 20 ÷ 9420 ≒ 0.0021 |
| Distance a particle travels before drying | 0.0021 × 1500 ≒ 3.2 |
The flow speed is only about 0.002 mm per second. Even after an hour it would barely cover 8 mm, far too slow for the eye to see. But the drop's radius is 5 mm. Over the 25 minutes it takes to dry, a particle is carried a little over 3 mm. Even particles that started near the center reach the edge by the time the drop has dried. The ring forms because this slow flow can use the entire drying time.
* The edge length of 31.4 mm comes from a circle of radius 5 mm, and the thickness of 0.2 mm is taken as an average near the edge. Both are rough values to help you grasp the mechanism.
High school+The idea of the "pinned contact line"
The edge of a drop staying fixed in place is technically called "contact line pinning". Tiny bumps on the surface, and the particles that are drying out themselves, are thought to act to stop the edge from moving. Because the edge does not move, the flow that replenishes it from the center keeps going without a break.
UniversityThe theoretical explanation of the coffee ring effect
In fluid mechanics, research in the 1990s used mathematics to explain the relationship between evaporation at the edge of a drop and the internal flow that replaces it. The phenomenon is called the coffee ring effect, and the condition of a stationary edge is known as contact line pinning. Also, when surface tension differs from place to place on a liquid's surface, that alone creates another flow. This is called Marangoni convection, and it is thought sometimes to work in the direction of weakening the ring.
📖 Derivations and further reading: Marangoni convection (Japanese Wikipedia, "Convection")
ResearchWhat is still unclear
- Under what conditions the ring becomes harder to form (the effect of particle shape and liquid composition) is a topic still under detailed study in fluid mechanics.
- Research is also under way on applications to inkjet printing and coating technology, either suppressing the coffee ring effect on purpose or putting it to use.
- Differences in drying patterns on different substrate materials, and in environments where gravity has little effect, are also still being investigated.
Even a single spilled-coffee stain hides a rich topic, where fluid mechanics meets surface science and research continues today.
Links to textbooks (by level)
| Level | Subject and unit | Where in this article |
|---|---|---|
| Middle school | Science: changes of state | Basic terms: evaporation, contact line, coffee ring effect |
| High school | Basic physics: evaporation and time | The simplified calculation of how long a drop takes to dry |
| High school+ | Physics: surface phenomena (advanced) | The idea of contact line pinning |
| University | Fluid mechanics | The theoretical explanation of the coffee ring effect |
| Research | Fluid mechanics and surface science (active research) | Conditions that suppress ring formation, industrial applications |
- Explanations of droplet evaporation and internal flow in fluid mechanics textbooks and materials.
- Research reviews on the theoretical explanation of the coffee ring effect in physics.
- Research reviews on suppressing ring formation through particle shape and liquid composition in surface science.
- Explanations of applied research on inkjet printing and coating technology in applied engineering.
- Explanations of the contact line pinning phenomenon in physics materials.
* Evaporation rates and drying times are simplified rough values. They are said to vary a great deal with actual conditions (temperature, humidity, type of liquid).
* This article is a science explainer for a general audience. If you spill a drink, please wipe it up promptly and take care around nearby furniture and electronics.