## 2016-10-03

### First Paper: "Nonadditivity of van der Waals forces on liquid surfaces"

My first paper has been published! It is in volume 94, issue 3 of Physical Review E, and an older preprint of it is available too for those who don't have access to academic journals (it has all of the same figures and ideas, though it is missing a few sentences of further explanation as well as a couple of new citations that were inserted for the final publication). In the interest of explaining these ideas in a way that is easy to understand, I am using the ten hundred most used words in English (except for the two lines that came before this one), as put together from the XKCD Simple Writer and the Wiktionary list of the 1000 most used words. I will use numbers sometimes without completely writing them out, use words for certain names of things without explaining further, and explain less used words when they come up. Keep reading to see what comes next.

Geckos are small animals with hard skin that your finger can slip over easily. They have feet with special hairs that allow them to stick to almost any hard surface, no matter what the surface is made of. The force that allows them to do that is called the van der Waals (called "vdW" for short) force, and it is a force that happens in nature in many situations other than just geckos sticking to surfaces. One such situation is when a liquid (something wet like water) forms a thin layer on top of a hard surface. If the hard surface is flat, then knowing the vdW force will help with understanding how thick the wet layer is. If the hard surface has an interesting shape, though, then knowing the vdW force along with the shape of the hard surface allows you to know the interesting surface shape of the wet layer too, though this has usually been hard to do. Usually, people have said that the vdW force between two larger things is just the force between each pair of atoms or molecules (smaller things that make up those larger things) all added together. That said, people have known for a long time too that this way of explaining the force is too easy and leaves out a lot of other things. One way to see this is to think of the force among three atoms or molecules: it isn't just the forces between each pair added together, because the third atom or molecule being there will change the force between each pair too. Larger things are made of a huge number of atoms or molecules, so if we were to consider all of those atoms or molecules one by one and count the forces among sets of two, three, four, and so on, we would never get anywhere.

Instead, we consider larger things as if we can't see the smaller atoms or molecules that they are made of (so we pretend that any large thing can be cut into smaller things forever), yet at the same time, we now have ways on the computer to consider the forces among many different atoms or molecules at once that are made easier by pretending we can't see those atoms and molecules than they would have been by actually considering all of those different atoms and molecules. This is how we consider vdW forces in wet layers, which often bend the surface of the wet layer. These wet layers also have surface tension, which is the force that tries to pull back on the surface of a wet layer when it bends away from being flat. The final shape of the surface of the wet layer is what comes out of these two forces being the same. Instead of worrying about real liquids like water, we used a simple system that shows the bigger ideas of how surface shapes matter the most for vdW forces, and we considered both our hard way of considering vdW forces as well as the easy way that other people have done for many years. We found that the wet layer surface shapes that come out are very different when we consider the hard or easy ways. We also found that if the wet layer surface goes toward the hard surface and if the surface tension is small enough, the surface of the wet layer could break up; the surface tension where that happens is very different when considering the hard or easy ways of considering the vdW force.