A statistical analysis of the dynamic behaviour of a bed of particles on the wall of a fluid flow is presented. By applying the different forces acting on each particle, i.e. fluid forces, adhesion to the wall and autohesion forces, conditions needed to obtain possible motions are determined and motions of the last downstream particle are described. It is shown that, above a critical value, increasing flow rate will promote the re-entrainment process along the wall, whereas increasing adhesion and autohesion forces will maintain the line bed stationary. Moreover, in some circumstances, starting particles execute some small jumps before rolling and/or sliding along the wall, which reduces the residence time of the particle on the wall. These results confirms some published hypotheses.