Drops in motion

When liquids are moved on a surface, similar frictional forces arise as those acting on solid bodies

Some knowledge gaps persist for a surprisingly long time. While the friction between a solid body and a surface has been well researched for two centuries, physicists have known very little about the movement of liquids on solid surfaces. Yet the behaviour of droplets plays an important role in technology, for example in the rotary printing process or when raindrops roll off window panes. Researchers at the Max Planck Institute for Polymer Research in Mainz have now measured the frictional forces between drops of various liquids and different surfaces. They were also able to shed light on the question of whether drops roll or glide over a surface.

Probably everyone is familiar with the phenomenon: water drops cling to a pane of glass, if it is tilted out of the horizontal plane. Only when a certain angle is reached they slide off. This raises the question of whether the drops in fact slide or roll over the surface. The Mainz-based researchers have not been able to solve this puzzle yet. But they did find some clues to the answer by mixing tiny particles into the liquid, illuminating a drop and filming the movement of the drop and the particles inside it. “At this relatively low resolution, it looks like the drops are rolling over the surface,” says Rüdiger Berger, Leader of a Research Group at the Max Planck Institute for Polymer Research in Mainz. “However, we were unable to observe the process at the boundary between the drop and the surface. It’s possible that the liquid slides there.”

The fact that drops can slide and roll coincides with everyday experience, according to which liquids tend to bead up and roll on water-repellent surfaces, whereas they appear to slide on hydrophilic materials. How a drop moves across a surface also determines the frictional forces between the fluid and the substrate. “It’s like a car,” Rüdiger Berger explains. “As it travels along, the tyres roll on the road surface and the friction is low. But when it brakes hard, the tyres tend to skid across the road surface − at least if the car has no ABS. Compared to rolling tyres, the friction is then much greater.”

Improved windscreen wipers

The researchers therefore investigated the friction of drops on a surface. Physicists have long known what forces act on a solid object as it is being pulled over a surface. Every student sees this demonstrated in physics lessons: The teacher pulls on a spring scale, one end of which is attached to a block. The teacher pulls harder, as the force indicated on the scale increases. Finally, the block begins to move. As the body is sliding along the horizontal surface, the spring scale again shows a smaller force. Why? Initially, static friction holds the object firmly in place. Only when the pulling force overcomes the static friction the object begins to slide. Now sliding friction, which is much weaker, comes into play. This means that less force is needed to keep the body sliding over the surface.

This is a simple experiment that has been in school syllabuses for decades. “We were surprised that this experiment had not been conducted with liquids,” says Rüdiger Berger. There are good reasons to study the forces required to move drops on surfaces: “for example, to develop windscreens that repel raindrops,” he says. Or to better understand how ink droplets behave as they are transferred from a rotating printing drum to paper or other materials. A better understanding of this could help to optimize the printing process, resulting in sharper printed images or reduced ink consumption.

A friction experiment with liquids

Rüdiger Berger and his colleagues therefore devised an elegant experiment to measure the forces needed to move a drop from rest. They dipped a thin glass tube, called a capillary tube, into a droplet of water resting on a silicon plate. They then pulled on the plate, moving the drop along with it. Because water readily wets the glass capillary tube, the tube holds the drop firmly in place. However, the pulling force causes the glass tube to bend slightly. This is analogous to the classical experiment in which a teacher pulls on a block attached to a spring scale. However, in the drop experiment, the force is not measured with a spring scale but by observing the how far a laser beam reflected by the glass tube is deflected. The more the tube bends, the greater the force the drop is exerting on the capillary tube.

In their experiment, the physicists in Mainz observed a similar pattern as in the experiment with a solid body. At first, the force continues to increase. However, it falls rapidly as soon as the drop starts to move, finally reaching a constant level. In principle, this is true of all the liquids and surfaces the scientists studied in their experiments, including the organic liquid hexadecane, an ionic liquid, on silicon, and water on a surface coated with titanium dioxide nanoparticles.

Transitional range between adhesion and sliding friction

“The friction of a drop is divided into a static and a kinetic range, much like that of a solid,” says Rüdiger Berger. Accordingly, liquids also initially experience static friction that is greater than the sliding friction. A drop initially therefore clings to a tilted surface and only starts sliding when a certain angle is reached. Unlike solids, however, there is a transitional range between static friction and sliding friction in which the friction decreases continuously.

Although the static friction was greater than the sliding friction for all the liquids tested, the forces differed considerably in magnitude. For example, a water droplet only begins to move under a force of around 120 micronewtons, whereas hexadecane starts to move under a force of just 40 micronewtons. A similar range of values was also observed for sliding friction.

Friction experiments with feathers

The researchers complemented these measurements with another experiment based on the current theory of drop behaviour. Using a camera, they first measured the angles that drops form with a substrate. They found that the angle is always more obtuse in the direction of motion, i.e. at the front of the drop, than at its rear. They then used the angle measurements together with the width of the drop to calculate the frictional force during movement of the drop. “The results agree well with the measured values,” Berger says. For some liquids and surfaces, however, there is a significant deviation, for example in the case of water on silicon. This shows that the theory is actually a simplification that can only roughly describe the static and sliding friction of droplets, Rüdiger Berger says.

He and his colleagues therefore plan to use an optical microscope to measure the contact angle of droplets in motion more accurately than is possible with a camera. “We want to see exactly how a liquid behaves on a surface,” Berger explains. In doing so, the team will probably also improve our understanding of exactly how rolling friction and sliding friction interact in the movement of drops. The physicists also want to study more materials, including biological surfaces such as feathers. “A duck needs to shed water as quickly and with as little effort as possible when it takes off from a pond,” Berger explains. Here, too, the friction between water and the plumage is crucial. While the duck may not care much about the outcome of such experiments, materials scientists may be able to glean some ideas for surfaces from which liquids slide off smoothly.


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