Capillary Phenomena on a Liquid Surface

Contraction of a liquid sheet of an incompressible Newtonian fluid in a passive ambient fluid is studied computationally to provide insights into the dynamics of capillary wave created during contraction. The problem composed of the Navier-Stokes system is associated with initial and boundary conditions that govern the time evolution of the capillary wave and the pressure and velocity fields within it. The correctness of the algorithm is verified with the data of experiment. It can be found that the prediction of the computation agrees well with the experiment. The algorithm is capable of capturing the capillary wave and therefore it is used to study the characteristic phenomena of that wave created on the surface of the liquid. Results show that the capillary wave is radiated from the tip of the liquid sheet caused by surface tension. The amplitude of the tip wave is much larger than any other waves and the asymptotic approach of the wave peaks can be observed during the propagation of waves. The tip wave contains the highest pressure and gradually the peak values of both high and low pressures decrease with the propagation of waves. Fluid velocity is motivated by both pressure due to surface tension and recirculation in peak and trough of the wave. During the contraction of the liquid sheet, the tip velocity is not uniform. Initially the length of the sheet increases a little and very soon the contraction occurs and continues. After long time, the gradient of tip velocity becomes very small.