Motion of grains in a vibrated U-tube

We investigate experimentally the behavior of the rate of growth of a column of grains, in a partially filled vertically shaken U-tube. For the set of frequencies used we identify three qualitatively different behaviors for the growth rate $\gamma$ as a function of the dimensionless acceleration $\Gamma$: 1) an interval of zero growth for low $\Gamma$ with a smooth change to nonzero growth, analogous to a continuous phase transition; 2) a sigmoidal region for $\gamma$ at intermediate values of the dimensionless acceleration $\Gamma$; and 3) an abrupt change from high values of $\gamma$ to zero growth at high values of $\Gamma$, similar to a first order phase transition. We obtain that our data is well described by a simple differential equation for the change of the growth rate with the dimensionless acceleration of the vertical vibrations.