Lost Marbles

Not the angle of repose I was looking for

I lost several hours this morning when I fell down a rabbit hole of interesting facts. I was looking for something specific about what is called an ‘angle of repose.’ No it isn’t the angle of my lawn chair - although I did stumble upon a blog called ‘My Angle of Repose’ and a 1971 novel titled ‘Angle of Repose’.

The angle of repose I’m interested in is the maximum angle a pile of something (i.e. a granular material) could reach before tumbling down. A google scholar search found scientists piling a plethora of items from mustard seeds to firewood.

Not surprisingly, the shape of what you are piling matters. In a 1966 paper, piles of tiny spheres and angular crushed quartzite were examined. For diameters of 0.5 mm, the angle of repose for the spheres was 38 degrees while for the quartzite it was a steeper 57 degrees. Meaning flatish, irregular things pile better than round things.

But, diameters of 0.5 mm are tiny, what about something bigger? For bigger things, the angle of repose decreases. The tiny spheres above would form a pile while attempting to pile marbles would only lead to escaped marbles - and an excuse to say: “help, I’ve lost my marbles.”

Adding water changes things - and this is where I really got sucked in. A 1997 paper titled ‘What keeps sandcastles standing’ was irresistible to me and completely unrelated to what I was looking for, so I read it.

If you are going to build a fancy sandcastle, you’ll quickly discover that dry sand won’t work, only wet sand will do. That’s because the properties of wet and dry sand are different. They did a lab experiment to prove it by modeling wet sand with spherical polystyrene beads ‘wetted’ with corn and vacuum-pump oil.

As a tangent - a completely different study used rice piles to model avalanches. What you use likely comes down to what you can get to work in the lab. My experience with lab experiments I designed myself clearly demonstrated that it isn’t easy to come up with something that works.

They found that by only slightly coating the beads (coating of less than 50 nm) dramatically increases the angle of repose. This means that by adding water to sand, the liquid introduces attractive forces that act to bind the particles. At first clumps form, which grow as more liquid is added until what you are working with (sand, polystyrene beads, etc) holds together.

The angle of repose is an important factor when studying slope stability and landslide prediction. How gravity influences the angle has also been studied, so what we know here can be transferred to exotic locals such as Mars. A point to ponder if you have to trek across scree in your local mountains or on Mars.