New model predicts how sand and other granular materials flow

Sand in an hourglass might seem simple and straightforward, but such granular materials are actually tricky to model. From far away, flowing sand resembles a liquid, streaming down the centre of an hourglass like water from a faucet. But up close, one can make out individual grains that slide against each other, forming a mound at the base that holds its shape, much like a solid. 

Sand's curious behaviour - part fluid, part solid - has made it difficult for researchers to predict how it and other granular materials flow under various conditions. A precise model for granular flow would be particularly useful in optimising processes such as pharmaceutical manufacturing and grain production, where tiny pills and grains pour through industrial chutes and silos in mass quantities. When they aren't well-controlled, such large-scale flows can cause blockages that are costly and sometimes dangerous to clear.

Now Ken Kamrin of MIT's Department of Mechanical Engineering has come up with a model that predicts the flow of granular materials under a variety of conditions. The model improves on existing models by taking into account one important factor: how the size of a grain affects the entire flow.

 Kamrin and Georg Koval, assistant professor of civil engineering at the National Institute of Applied Sciences in Strasbourg, France, used the new model to predict sand flow in several configurations - including a chute and a circular trough - and found that the model's predictions were a near-perfect match with actual results. A paper detailing the new model will appear in the journal Physical Review Letters.

''The basic equations governing water flow have been known for over a century,'' says Kamrin, the Class of '56 Career Development Assistant Professor of Mechanical Engineering. ''There hasn't been something similar for sand, where I can give you a cupful of sand, and tell you which equations will be necessary to predict how it will squish around if I squeeze the cup.''

Kamrin explains that developing a flow model - also known as a continuum model - essentially means ''blurring out'' individual grains or molecules. While a computer may be programmed to predict the behaviour of every single molecule in, say, a cup of flowing water, Kamrin says this exercise would take years. Instead, researchers have developed continuum models.