Tag Archives: Science

Everyday things vaguely to do with physics: 3 — sun on a field

On holiday in France, me and my family were walking along a road through a field of smooth mud/dirt. The sun was coming from the right hand side. Looking to the left hand side, the field looked a sort of clay-y orangey tan. Looking to the right, it looked dark brown. When we came to another road that was parallel to the original one, the field that had been on our right and looked dark brown was now on our left, looking orangey tan instead.

An observer in the middle of a field whose surface is slightly rough

This seemed a bit weird, because the field was very smooth and there weren’t any trees or buildings casting shadows. What (I think) explains it is that the surface of the field, although smooth-looking, was slightly rough, being made of dirt. So, on a scale of a few inches, the field’s surface had little peaks and troughs, as shown in the diagram. When the observer is looking in the direction that the sun comes from, this means that lots of tiny bits of the field are in shadow, caused by raised and depressed bits of dirt, as shown in the inset.

Because it had been made quite smooth, we couldn’t really see the actual texture of the field, but the overall reduction in the amount of sunlight reaching us from it made it look dark when viewed in this way, even though the whole field was ‘really’ the same colour. The field, viewed from the right direction, is ‘in shadow’, but on a very small length scale. The relative difference in perceived colour or brightness when you look in each direction must be related somehow to the density and characteristic size of the peaks and troughs in the field’s surface. Fun bit of maths to do?

Research paper: Spinodal fractionation in a polydisperse square well fluid

EDITED: August 2012

The paper has been published in final form by Physical Review E — the final arXiv update is available here.

Here my first publication co-authored with Mike Evans. As well as being published in Physical Review E, it’s available on arXiv, which is freely accessible and contains copies of most of the papers published in recent years in a variety of physics and other fields. In fact, the conditions of my PhD funding explicitly require that my work has to be freely available — isn’t science good?

Most substances in soft matter (colloids, polymers, biological stuff and so on) are ‘polydisperse’ which, as explained here, means that all the constituent particles of a big container of the stuff are different in terms of e.g. their size or charge. This is in contrast to simple molecular fluids like water, in which every molecule of H2O is identical. Statistical mechanics and thermodynamics were originally designed for these simple fluids, so while they have been applied in soft matter with some success, traditional theories fail to capture some important and interesting phenomena in polydisperse materials.

For example, during phase separation, particles with different properties can end up being partitioned, or fractionated, into the different phases. In a simple example, a crystal growing from an initially disordered fluid of size-polydisperse particles might end up incorporating predominantly larger than average particles. This might not matter too much, but if you’re trying to create a precisely-characterised photonic crystal with a certain lattice parameter, it could matter quite a lot. Or, you might want the particles to fractionate between the phases, in order to then scoop out some of one phase and end up with a purer substance than you had before. In any case, it’s important to know how fractionation happens in polydisperse systems.

In the paper, we’ve simulated gas-liquid phase separation in a polydisperse fluid, and observed fractionation of particles between the two phases on a surprisingly short timescale. Even while the system is very quickly changing and coarsening its spinodal texture, particles of different sizes end up finding their way preferentially into one or the other phase. There’s also a striking dependence on a very trivial-seeming detail of the particle interaction, which ends up completely altering the observed ‘direction’ of the fractionation.

Fractionation has been measured in experiments, but the early stages of phase separation are very difficult to access because of how quickly the system is evolving. So, our simulations give a nice insight into how the final states observed in experiments are actually enacted through the course of the phase separation, and as far as we know constitute the first such measurements on a truly polydisperse model colloidal fluid. There are some nice pictures too.