When you pull on a drop, how does it pull back?

Original paper: How drops start sliding over solid surfaces 

Physicists like to ignore things. In some cases, we may neglect gravity or assume that the temperature is zero degrees Kelvin — colder than any known substance in the universe. And friction is almost comically absent in most models, despite the fact that a world without it would be utterly uninhabitable (this is nicely illustrated in cartoon form here: https://xkcd.com/669/). 

Sometimes, these simplifications are justified. If you’ve ever seen your hair stand on end after taking off a sweater, you know gravity isn’t always the dominant force. And if you’ve ever slipped on ice or slid a puck across an air hockey table, you know that there are situations where friction doesn’t do much.

But there’s another reason we might leave out something like friction: it’s really complicated. Even today, friction between solid objects remains an active topic of research,

with all sorts of interesting topics arising: friction’s role in earthquakes, for example, or how it can encode a kind of memory.

All this talk of friction between solids led Nan Gao and collaborators to ask whether there might be a friction-like effect for liquid-solid interfaces. 

One of the characteristics of friction between two solid objects is that it decreases once the objects start sliding. You may have noticed this when pushing a heavy box: it’s hard to get the box moving, but once it budges it’s easier to continue pushing. This idea is shown in Figure 1 as a plot of force applied to an object versus the amount of time that force is applied. The force increases linearly before the object begins to move, then drops suddenly to a constant value after the object starts sliding. 

Figure 1. Force applied to an object with respect to the amount of time that force is applied for a typical solid object sitting on a solid surface. The force increases linearly before the object begins to move, then drops suddenly to a constant value after the object starts sliding. (Figure adapted from original article)

In this week’s article, Gao and colleagues devise a clever system for measuring the same type of force for a drop of liquid sitting on a solid surface. 

A drop sits on a platform that can be translated in one direction. Inserted in the top of the drop is a thin rod, called a capillary, which remains stationary even as the platform moves. Just as water will stick to your straw as you pull the straw out of your drink, the drop likes to be in contact with the capillary. So rather than simply moving along with the translating platform, the drop pulls on the capillary, causing it to bend. In turn, the capillary pulls back on the drop until the capillary exerts a force on the drop that overcomes the friction between the drop and the platform; the drop stops moving with the platform and remains stuck to the capillary.

As shown in Figure 2, the researchers tracked the position of a laser reflected off the capillary to measure how much the capillary bent. They were then able to back out the so-called “adhesion force,” which is an indicator of the force needed to make the drop move relative to the surface it’s sitting on. 

Figure 2. Cartoon of the setup used. The force due to friction between the drop and the platform, which points in the direction the platform is moving, is represented with a red arrow and labeled “F”. Here, the capillary’s bend is measured by detecting the reflection of a laser (shown in red) off of the capillary. The orange arrows show the length and width of the drop.

Gao and colleagues found that as the platform moves, the adhesion force increases more or less linearly before dropping back to a roughly constant value (see Figure 3). Sound familiar? Just compare with Figure 1 and you’ll see that this behavior strongly mimics friction between two solid surfaces.

Figure 3. Adhesion force of a drop of water on a moving surface of titanium dioxide as a function of time the surface has been moving. Measured values (from the bending of the capillary) are shown as blue circles and calculated values (from an equation for the adhesion force that depends on the shape of the drop) are shown as red squares. In both cases, the force increases roughly linearly for several seconds, reaching a maximum force of 100 uN before dropping to a constant force around 40 uN. (Figure adapted from original article)

This wasn’t just a lucky choice of liquids and solids — they found a similar effect for several fluids on surfaces ranging from titanium dioxide to silicone nanofilaments to goose feathers. The appearance of this effect in such a wide variety of systems suggests that this may be a general phenomenon.

Moreover, their measured values from the bend of the capillary match fairly well with values calculated independently using geometric parameters of their drops like the drop width, drop length, and angles the drop makes with the surface.

Even in systems as simple as a drop of water sitting on a surface, there is an incredible amount of physical richness, which means lots of science still to be explored. And it’s not just how drops stick — how drops land on a surface and how they evaporate both raise unexpectedly subtle and complex questions (see previous posts here and here). What area of drop-related research might physicists slide into next? 

For an even shorter summary of this article, see  https://phys.org/news/2017-11-droplet-friction-similar-solid.html

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