Effect of Viscous Forces on the Measurement of Surface Dilatational Moduli with Oscillating Drops or Bubbles
Erik Freer, Lam Research Corporation, Fremont, CA 94538, Harris Wong, Mechanical Engineering Department, Louisiana State University, Baton Rouge, LA 70803-6413, and Clayton J. Radke, Chemical Engineering, University of California at Berkeley, 275 Tan Hall, Berkeley, CA 94720.
The oscillating drop/bubble technique is increasingly popular to measure the interfacial dilatational moduli of surfactant/polymer-laden fluid/fluid interfaces. A caveat of this technique, however, is that viscous forces are important at higher oscillation frequencies or fluid viscosities; these can infect determination of the interfacial tension. Here, we experimentally quantify the effect of viscous forces on the interfacial-tension measurement by oscillating 100 and 200 cSt poly(dimethylsiloxane) (PDMS) droplets in water for small amplitudes frequencies ranging between 0.01 and 1 Hz. Due to viscous forces, the measured interfacial tension oscillates sinusiodally with the same frequency as the oscillation of the drop volume. The phase angle of the tension oscillation precedes that of the drop volume, and the amplitude varies linearly with a Capillary number in which the characteristic viscosity is that of the difference between the drop and continuous phases. A simplified model of a freely suspended spherical oscillating-drop well explains the experimental observations. We find that viscous forces distort the drop shape at Ca > 0.002, although this criterion is apparatus dependent. We provide a quantitative criterion to establish whether or not the shapes of oscillating drops (bubbles) are infected by viscous forces.