title: Transient Surface Tension of an Expanding Liquid Sheet.
abstract: We address the problem of dynamic surface tension using measurements of sheet diameters that results from the impact of a liquid jet of diameter d(0) on a small disk of diameter d(i) (d(i)/d(0) approximately 4). At low velocities, the sheet diameter D is related to d(0) by the Weber number We, constructed with the liquid density rho, the jet velocity u(0), and the surface tension sigma at the rim: D/d(0)=18 We=18 [rho u(0)(2)/(sigma/d(0))]. This relation expresses the equilibrium between inertial forces and surface tension forces at the sheet rim. When a surfactant has been dissolved in the bulk of the liquid prior to the formation of the initial jet, the rim surface tension, and therefore the sheet diameter, depends on the amount of surfactant adsorbed at the rim. This amount is fixed by a competition between surface formation induced by radial extension and repopulation of the liquid interface in surfactant. The experimental setup proposed here provides a method to measure dynamic surface tension from sheet diameter measurements and symmetrically to monitor the adsorption of a surfactant on a liquid surface. The available adsorption time ranges from 10 to 100 ms. Experimental data obtained with two surfactants are in agreement with a model of a diffusion-controlled adsorption at the interface. Copyright 2000 Academic Press.
authors.affiliation: LEGI-CNRS, Institut de Mécanique de Grenoble, Grenoble Cedex, 38041, France
authors.initials: P
authors.lastname: Marmottant
authors.initials: E
authors.lastname: Villermaux
authors.initials: C
authors.lastname: Clanet