Measurement of grain-wall contact forces in a granular bed using frequency-scanning interferometry

Micro-mechanical theories have recently been developed to model the propagation of force through a granular material based on single grain interactions. We describe here an experimental technique, developed to validate such theories, that is able to measure the individual contact forces between the grains and the wall of the containing vessel, thereby avoiding the spatial averaging effect of conventional pressure transducers. The method involves measuring interferometrically the deflection of an interface within a triple-layer elastic substrate consisting of epoxy, silicone rubber, and glass. A thin coating of gold between the epoxy and rubber acts as a reflective film, with the reference wave provided by the glass/air interface. Phase shifting is carried out by means of a tunable laser. Phase difference maps are calculated using a 15-frame phase-shifting formula based on a Hanning window. The resulting displacement resolution of order 1 nm allows the wall stiffness to be increased by some two orders of magnitude compared to previously described methods in the literature.