A Novel Method of Measuring Dynamic Surface Tension from the Profile of Capillary Jet : 1st Report, Theoretical Analysis of Jet Profile(Fluids Engineering)

Abstract

A theoretical and experimental consideration is conducted to propose a novel method to measure the dynamic surface tension of surfactant solution. The trajectory of laminar jet injected from a horizontal capillary tube is considered from an approximate theory. The momentum balance is discussed between surface tension, gravitational force, pressure and viscous force. Since the effect of gravitational force is relatively small compared with the surface tension, the cross section of jet is assumed as a circle and the pressure inside the jet is approximately obtained from the Laplace equation. The ordinary differential equation of motion is solved numerically by the simple Runge Kutta's method to obtain the profile of jet trajectory. The trajectory profiles are measured experimentally for water and two kinds of ethanol solutions with smaller surface tension than that of water. The theoretical profiles agree well with experimental ones for each condition and the trajectories are strongly dependent on the surface tension. It is demonstrated that the change of surface tension of surfactant solution could be measured by the method proposed in this study.