Oscillating drop/bubble tensiometry: effect of viscous forces on the measurement of interfacial tension

The oscillating drop/bubble technique is increasingly popular for measuring the interfacial dilatational properties 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 affect 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 at small amplitudes and frequencies ranging between 0.01 and 1 Hz. Due to viscous forces, the measured interfacial tension oscillates sinusoidally with the same frequency as the oscillation of the drop volume. The tension oscillation precedes that of the drop volume, and the amplitude varies linearly with Capillary number, Ca=ΔμωΔV/γa2, where Δμ=μD−μ is the difference between the bulk Newtonian viscosities of the drop and surrounding continuous fluid, ω is the oscillation frequency of the drop, ΔV is the amplitude of volume oscillation, γ is the equilibrium interfacial tension between the PDMS drop and water, and a is the radius of the capillary. A simplified model of a freely suspended spherical oscillating-drop well explains these observations. Viscous forces distort the drop shape at Ca>0.002, although this criterion is apparatus dependent.