A new model to determine dynamic surface tension and elongational viscosity using oscillating jet measurements

Abstract

We present an integro-differential equation model which, combined with experimental measurements of an oscillating free surface jet, calculates dynamic surface tension and elongational viscosity of a fluid. Our model builds upon previous models due to Rayleigh and Bohr in that it self-consistently incorporates the effects of viscosity and gravity. Further, surface tension and viscosity are allowed to be non-constant. The principal result of this paper is a technique for the measurement of surface tension of newly forming surfaces on the millisecond timescale relevant for agricultural spray mixtures. Coincidentally, our model independently yields the elongational viscosity of the fluid, although our present experimental apparatus limits the accuracy of measurement of this material property.In this paper we take measurements from physical jet experiments and implement our inverse model to deduce these material properties. The model is first benchmarked against standard techniques on a well-characterized fluid with constant surface tension and Newtonian viscosity. We then apply our method to an agricultural spray mixture, with non-constant surface tension and non-Newtonian rheology. We measure (i) the rapid decay of surface tension from the newly formed surface (aged less than a millisecond) to the much lower equilibrium value, and (ii) the rate dependence of elongational viscosity.