Effects of dynamic contact angle on liquid withdrawal from capillary tubes: (Semi)-analytical solutions

摘要: The displacement of a gas by liquid in both horizontal and inclined capillary tubes where the tube inlet is connected to reservoir constant pressure can be described Lucas-Washburn theory. One also use theory model reverse flow, that is, withdrawal, even though latter case has received relatively little attention. In this paper, we derive analytical solutions for travel time gas-liquid interface as function velocity. position obtained numerically integrating inverted Therefore refer these (semi)-analytical. We neglect inertial forces. However, account dynamic contact angle nondimensional non-equilibrium Young force depends on number form either power law or series. explore entire parameter space. allow us show five different withdrawal scenarios may occur differ direction flow sign acceleration interface: horizontal, upward, steady-state downward, accelerating decelerating downward flow. last case, withdrawn from completely partially. (semi)-analytical are valid within limit constant.