Evolution of Liquid Meniscus Shape in a Capillary Tube

Abstract

There are still many unanswered questions related to the problem of a capillary surface rising in a tube. One of the major questions is the evolution of the liquid meniscus shape. In this paper, a simple geometry method is proposed to solve the force balance equation on the liquid meniscus. Based on a proper model for the macroscopic dynamic contact angle, the evolution of the liquid meniscus, including the moving speed and the shape, is obtained. The wall condition of zero dynamic contact angle is allowed. The resulting slipping velocity at the contact line resolves the stress singularity successfully. Performance of the present method is examined through six well-documented capillary-rise examples. Good agreements between the predictions and the measurements are observable if a reliable model for the dynamic contact angle is available. Although only the capillary-rise problem is demonstrated in this paper, the concept of this method is equally applicable to free surface flow in the vicinity of a contact line where the capillary force dominates the flow.

Capillary rise of a meniscus with phase change

“…developing flow and energy dissipation at the capillary entrance, as well as contact line dynamics, e.g. contact angle hysteresis, friction and meniscus evolution [5][6][7][8][9]. Another extension considered an additional viscous drag due to the displaced gas in the capillary [7].…”

Dimensionless scaling methods for capillary rise

“…There also exist studies involving gravity, thus leading to different scaling approaches e.g. by Quéré et al [13,14], Marmur and Cohen [15], Zhmud et al [16], Lee and Lee [17] or Fries and Dreyer [18,19]. McKinley [20] investigates dimensionless groups for free surface flows with a focus on complex fluids.…”

Influence of wettability variations on dynamic effects in capillary pressure

“…is typically applied using a constant contact angle, taken to be the static contact angle [ Washburn , 1921; Blake and De Coninck , 2004; Dahle et al , 2005; Ralston et al , 2008]. However, can also be applied using the dynamic contact angle [ Martic et al , 2003; Blake and De Coninck , 2004; Lee and Lee , 2007]. Several relationships have been proposed for θ d = f (d l /d t ,θ), based on hydrodynamic and molecular‐kinetic approaches [e.g., Blake and Haynes , 1969; Hoffman , 1975; Voinov , 1976; Cox , 1986; Zhou and Sheng , 1990; Brochard‐Wyart and de Gennes , 1992].…”