Role of axisymmetric axial velocity gradients in nonlinear disintegration of liquid sheets

The nonlinear growth of sinuous and dilatational disturbances on thin inviscid liquid sheets with a velocity profile across the thickness is determined. Variations of the velocity profile in the liquid sheet, with maximum velocity at the centre linearly decreasing to a minimum at the interfaces, show an optimum value of the velocity gradient, below which disintegration of the liquid sheet is accelerated. The ligaments are formed in local dilatational and global dilatational modes and are asymmetric, unlike the symmetric ligaments formed with a liquid sheet issuing at constant velocity. The presence of velocity gradients is seen to yield smaller ligaments when breakup occurs in the local dilatational mode. © 2010 The Japan Society of Fluid Mechanics and IOP Publishing Ltd.