Interface Behavior between Two Fluids Vertically Oscillated in a Circular Cylinder under Nonlinear Contact Line Condition

Abstract

The development of waves on a fluid-fluid interface, excited by a vertical, relative motion of a solid wall enclosing the fluids, is affected significantly by the mobility of the interface on the wall. The effective, cycle-averaged mobility depends on the amplitudes of excitation and waves, because of a non-linear dependence of the velocity of the fluid-fluid-wall contact line on the angle of the interface hitting the wall. At higher amplitudes of excitation and waves, moreover, the interface motion is tied to the low mobility of the contact line only for a limited fraction of each cycle; for the rest of the cycle the interface is virtually untied from the wall, being connected to the contact line only through the surface of a thin, flat liquid film left on the wall. An analytical model is developed on the wall surface boundary conditions for the interface profile, in terms of non-linear relationship between the interface velocity along the wall and the near-wall inclination angle of interface. The model is based on optical data taken in a quasi-static experiment where measurements of near-wall interface configuration were essentially unaffected by wave generation on the interface. Numerical simulation with this model reproduces successfully the changes in the near-wall configuration of the interface in the experiment, including development and depletion of a liquid film on the wall associated with relative motion between the contact line and the interface elevation away from the wall.

Keywords

• two-layer fluid
• numerical analysis
• wave
• contact line
• contact angle
• hysteresis
• liquid film