There’s a fraction too much friction –
Simple model describes the transition from static to dynamic friction.
That said, there are a few strong-stomached physicists who are trying to understand friction. One of the problems they face is that is friction is so … individual. Every experiment is different. Even copies of the same experiment are slightly different. Despite that, one group has now managed to come up with a general model that replicates many of the main features of friction.
Friction, how I stab at thee
Actually, part of that last sentence is a lie. The model focuses on the transition between two different types of friction. I’ll get to that in a moment.
When we look at friction in detail, the reasons we find describing it difficult become clear. Imagine two plates being slid across each other. At one level, we can say that friction comes from the force of attraction between the two plates due to local imbalances in electron density. In other words, the positively charged bits of one plate are attracted to the negatively charged bits of the other plate. So far, so mind-numbing.
But the strength of the attraction between the plates depends on all sorts of details about the two surfaces: the materials, the roughness of the surface, the conductivity of the surface, the separation between the surfaces, and many more things. To model this in detail digs a big painful hole of code and buries the physics at the bottom of it.
Experimentally, it is even worse. If we were to repeat the experiment twice using the same plates, we are likely to get a different result. Why? Because the first experiment would have modified the surface, so the second experiment is conducted under different conditions. It is enough to make you despair.
Friction is dynamic
Now, let’s make friction even trickier by starting our experiment from rest. The plates aren’t moving, and we apply a force … and more force … and more force. Suddenly, the plates break free and start to slide. The initial friction is much larger than the friction while the plate is moving. These two frictions are called static and dynamic friction, and the transition between the two is rather more complex than I have just described. You would think that any model that seeks to replicate even the most basic features would be complicated. And you would be wrong.
To understand the transition between static and dynamic friction, a group of researchers created a breathtakingly simple model. One surface is perfectly flat. A series of wheels is placed on the surface so that all the wheels are in contact with each other. The wheels can slide due to an applied force, and they can rotate due to a torque. If one wheel does anything, it is contact with the next, so the forces and torques travel down the chain.
The wheels are held to the surface by a force that is perpendicular to the surface. Friction is described by a single number. No complicated physics for us, thank you very much. The game the researchers play is to push on one of the wheels and apply Newton’s laws repeatedly until the wheels’ motion stabilizes. Then they do it again for a different force … and again.
Setting the wheels in motion
As with reality, the researchers observe a change from static (high) friction to dynamic friction once the force gets above a certain threshold . Examining the dynamics of the wheels more closely, they show that the transition to dynamic friction occurs because the applied force creates a wave that propagates stably along the wheels. That wave allows motion along the surface with far less force than if there is no wave.
The appearance of the wave is presaged by behavior observed for forces below the threshold. For smaller forces, similar waves are generated, but they quickly die out as they propagate, preventing the transition to easy motion. The researchers show all this with a beautiful numerical analysis of the dynamical system.
The model does a remarkably good job of showing the generally observed characteristics of the transition from static to dynamic friction. The model has, as the authors point out, the advantage that you can dig right into the workings and see exactly what is going on. That’s because the model is not something that you can use to calculate real frictional forces for realistic situations; Instead, it is a tool for discovery.
Physical Review Journals, , DOI: 33 / PhysRevLett. 01575879 (
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