PHILADELPHIA -- Sand.  A single grain is tiny, but solid, and shares the physical properties of other solid matter.  But pack or transport millions of grains together - as modern society does with coffee grounds, flour and industrial chemicals - and granular materials act differently, baffling engineers.  They take the shape of their containers and flow freely, like liquids.  In certain circumstances, they exert pressure like a gas.  The basic lack of behavioral knowledge contributes to wasted resources and energy, as well as erosion and other natural phenomena.  

Now, researchers at the University of Pennsylvania have devised, for the first time, a mathematical formula to measure the impact force of objects dropped into granular matter, clarifying its physical behavior not as solid-, liquid- or gas-like but with its own distinct and verifiable physical properties.

Penn researchers dropped a 1-inch-diameter steel sphere from a range of heights into non-cohesive glass beads.  The study helped resolve a controversy among physics researchers who had proposed past force laws that often conflicted with one other.  With more precise data, and a wider range of impact speeds, Penn physicists demonstrated that the interaction between the steel sphere and the granular medium can be explained by the sum of velocity-dependent inertial drag plus depth-dependent friction:

Total force = gravity + friction + inertial drag

(F = (mg + k(z( ( mv2/d1

Working with this formula, researchers are able to explain some interesting phenomena, such as why high force impacts (like a golf ball crashing into a sand trap) come to rest faster in granular matter than low-force impacts (a golf ball gently placed into sand).  This behavior is not shared by solids or liquids.

"Experiments on the low-speed impact of solid objects into granular  media have been used both to mimic geophysical events and to probe  the unusual nature of the granular state of matter," said Douglas Durian, professor of physics and astronomy in Penn's School of Arts and Sciences.  "Our understanding is important not just to industry but to other sciences where the very nature of matter is explored."

Granular material interests physicists who study the formation of cells.  Geologists study tectonic plates, formed by granular matter.  In nature, granular materials combine to form the planets and stars of the universe.  On a smaller scale, they form the soil and sediment of the earth.  A better understanding of their behavior may help populations affected by landslides and erosion.

The study was conducted by Durian, as well as Hiroaki Katsuragi, also of Penn's Department of Physics and Astronomy.

The research was supported by the National Science Foundation and the Japan Society for the Promotion of Science Postdoctoral Fellowships for Research Abroad.