The fluid mechanics of the soap film meter

Abstract

A free soap film extending across the circular cross section of a tube consists of a thin central lamella surrounded by a meniscus or Plateau border at the wall of the tube; this meniscus is the seat of a suction pressure. Measurements of the pressure drop arising from the motion of single and multiple soap films in the vertical cylindrical tube of a soap film meter for measuring gas flow show that the pressure drop is a linear function of both the film velocity and the number of films flowing simultaneously in the tube. This function consists of a static component and a dynamic component: the static component is the pressure drop when the film velocity tends to zero. This static component arises from the film meniscus as the lamella is shown to be very thin. Two non-linear second-order differential equations are derived which describe the shape of a stationary meniscus. Numerical integration of these equations led to the successful prediction of the static pressure drop component by an evaluation of the weight of liquid in the meniscus. The theory is confirmed by experimental measurements of pressure drop in soap film meters of diameters in the range 6.2–73.4 mm. In each case, the theoretical solution also yielded the value of the suction presurre in the Plateau border. A soap film is inherently unstable, for the continuous drainage of the intralamellar liquid into the meniscus eventually leads to its collapse. A critical tube radius is calculated below which the central lamella does not exist and the film consists of a meniscus where the liquid is under hydrostatic equilibrium. This tube radius corresponds to the critical Bond number for stability of equilibrium interfaces. Experiments confirmed that, in a controlled environment, such static menisci are stable for an indefinite period of time.