Differential roles of interfacial dilatational and shear viscosities in liquid-thread breakup

Surfactants are widely used to tailor fluid rheology, and interfacial viscoelasticity has received increasing attention in recent years. Previous studies on the effect of interfacial viscosity on liquid-thread breakup have often treated interfacial viscosity as a combined effect or assumed that the interfacial dilatational viscosity is equal to the interfacial shear viscosity. However, the one-dimensional model derived in the present work shows that this assumption masks the independent contribution of dilatational viscosity. Moreover, how interfacial dilatational and shear viscosities differ in their mechanisms and in the magnitude of their effects remains unclear. To address this issue, we develop a one-dimensional model for a surfactant–laden liquid thread, with particular emphasis on separating the effects of the two interfacial viscosities, and investigate the dynamics using linear stability analysis and numerical simulations. The results show that, in the dispersion relation corresponding to the linear stage, the coefficient associated with interfacial shear viscosity is nine times that associated with dilatational viscosity. In suppressing satellite droplets, the overall effect of interfacial shear viscosity is comparable to that of a 12-times larger dilatational viscosity. Moreover, the mechanisms by which the two viscosities suppress satellite-droplet formation are distinct: dilatational viscosity reduces the satellite volume by flattening the satellite droplet, whereas shear viscosity tends to keep the pinch-off location near the midplane, thereby inhibiting satellite-droplet formation. These results show that interfacial dilatational and shear viscosities are not interchangeable in liquid-thread breakup, even within the same interfacial rheological framework.