  We investigate the non-equilibrium dynamics of coupled Coulomb crystals of
different sizes trapped in a double well potential. The dynamics is induced by
an instantaneous quench of the potential barrier separating the two crystals.
Due to the intra- and inter-crystal Coulomb interactions and the asymmetric
population of the potential wells we observe a complex reordering of ions
within the two crystals as well as ion transfer processes from one well to the
other. The study and analysis of the latter processes constitutes the main
focus of this work. In particular we examine the dependence of the observed ion
transfers on the quench amplitude performing an analysis for different
crystalline configurations ranging from one-dimensional ion chains via
two-dimensional zig-zag chains and ring structures to three-dimensional
spherical structures. Such an analysis provides us with the means to extract
the general principles governing the ion transfer dynamics and we gain some
insight on the structural disorder caused by the quench of the barrier height.
