Numerical study of the impact of contact line with hysteresis on the Faraday instability

Abstract

We report a numerical study of the contact-line effect on the Faraday instability. A momentum balance model is implemented to simulate the hysteresis of the meniscus. By using this model, a stick–slip-motion of the contact line happens on the lateral wall when a vertical vibration is exerted to the container. The numerical result further supports that the contact-line hysteresis can increase the natural frequency by inference. Besides, it can largely delay the timing of the onset because of an extra dissipation provided by the capillary effect. The growth rate can also be affected by the meniscus but the impact of the hysteresis seems limited. The presence of the meniscus is the reason why Faraday instability occurs without any artificial disturbance. Finally, a linear relation between the contact-angle range and the contact-line position is observed from our computation.