Study of the accumulation of grains in a two dimensional vibrated U-tube without interstitial fluid

We present an experimental and computational study using Molecular Dynamics simulations of the development of an accumulation of grains in one side of a two dimensional U-tube under vertical vibrations. Studying the evolution of the height difference between the columns of grains in the branches of the tube, we found that it reaches a saturation value after vibrating for some time. We obtain that this saturation value is the same if the simulation or experiment start with the arms leveled or with a large initial height difference. We explore computationally the effect of the width of the tube, the density of the grains and the coefficient of restitution between the grains and the wall on the value of the saturation. We obtain a value of the width of the tube for which the saturation value reaches a maximum, and show that the transport of grains between arms is favored for low grain densities and high grain-wall restitution coefficient.