Effect of surface tension on the free outflow of a wetting fluid from a horizontal tube

Abstract

The flow structure for which the Karman hypothesis is valid is explored experimentally and theoretically. It is established that there exists not a point but a region of finite size, adjacent to the upper generator of the tube and including the moving line of contact between the phase interface and the wall, in which the fluid is stationary relative to the line of contact, i.e., in which the no-slip condition is not satisfied. The dimensions of the region depend on the surface tension. The action of this stagnant zone on the flow is fully explained by the effect of the surface tension in experiments [1]. It is established that depending on the ratio of the tube diameter to the dimension of the stagnant zone two flow regimes are possible: in sufficiently wide tubes, an inertial regime for which Karman's hypothesis holds and the no-slip condition is not satisfied, and, in sufficiently narrow tubes, a creep regime in which the no-slip condition continues to apply. The values of the determining dimensionless parameter corresponding to the change of regime and the cessation of flow are calculated. They are similar to the experimental values.