Why does liquid stay in a horizontally turned straw, but not in a glass?

A new paper, co-authored by Oxford University’s Prof Dirk Aarts, presents a precise mathematical criterion determining whether the liquid in a capillary of arbitrary cross-section will remain in it, or will flow out, when the capillary is at a horizontal position.

Have you ever noticed that liquid stays inside a straw when it’s held horizontally? Or that the same thing doesn’t happen when you turn a glass on its side?

A team of researchers including Professor Dirk Aarts from Oxford University’s Department of Chemistry has been investigating this phenomenon – one that’s ‘surprisingly difficult’ to explain from a scientific point of view.

Professor Aarts worked with colleagues Carlos Rascón from Universidad Carlos III de Madrid in Spain and Andrew Parry from Imperial College London for the study, which is published in the journal PNAS. Professor Aarts said: ‘We considered the following seemingly simple question: why does the liquid spill out when I hold a glass – say, of beer – horizontally, but stays in a straw when I do the same thing?

‘This question is actually surprisingly difficult, especially when considering non-circular cross-sections of the capillaries, or tubes.

‘For a liquid trapped between two parallel walls, and for a liquid trapped in a circular capillary like a straw, the answer is one that we would intuitively expect: the liquid wants to flow out because of gravity, but is trapped due to the surface tension.’

The ‘capillary action’ described here is the ability of a liquid to flow in narrow spaces, often in opposition to external forces such as gravity. For example, if you zoom in on the surface of water in a glass, you’ll see that it curves upwards by a couple of millimetres at the wall. This curve is known as the meniscus.

Professor Aarts said: ‘The competition between gravity and surface tension leads us to the capillary length, which sets the height to which a meniscus will climb at a wall. Indeed, if the separation between the two walls is less than roughly the capillary length, or if a circular capillary has a diameter less than roughly the capillary length, the liquids will stay put. If not, the liquids will flow out.

‘However, if you change the cross-sectional shape of the capillary – for example, making it a triangle – the situation may change completely, and for certain geometries the liquid may spill out at any length scale, well below the capillary length.

‘We figured out how to calculate this behaviour for general cross-sectional shapes, although the actual numerical calculations, carried out by Carlos Rascón, took almost seven years to complete. One of the reasons for this was that the spilling out may occur via different pathways, and the crossovers between those pathways were hard to understand.’

The researchers were able to solve the problem by reducing it down to an equivalent two-dimensional problem, which is numerically more accessible. The paper shows how ’emptying diagrams’ can be created by calculating the energy of the problem in 2D. As soon as the energy became smaller than zero, no 3D solution for the meniscus exists, and the liquid empties.
Professor Aarts added: ‘The surprising result here is that a capillary may empty even at lengths much smaller than the capillary length. This has implications for any technologies where liquids are used or are present on small scales, such as microfluidics, biomedical diagnostics, oil recovery, inkjet printing and so on.’

This article was written by Stuart Gillespie and originally appeared in the Oxford Science Blog.

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