Viscous stress distribution over a wavy gas-liquid interface

Viscous stress contributes to momentum transfer between two phases, which plays an important role in both industrial applications and environmental processes. Near a wavy interface, the flow is modulated and produces a spatially non-uniform normal and tangential viscous stress. This study presents measurements of these stresses at a liquid-gas interface populated with two-dimensional millimeter scale waves performed with multiphase particle image velocimetry. Large datasets enable conditional phase-averaging of the data based on wave steepness, which increases the precision of the results and allows statistical analysis. For the first time at this scale, the spatial distribution of normal and tangential viscous stress is obtained for a large range of wave steepness (ak = 0-1, with a the amplitude and k the wavenumber). As the steepness increases, the mean shear stress over a wavelength decreases in magnitude, while the normal viscous stress increases. These trends are linear for ak < 0.6, and correlations are proposed. At ak > 0.7, flow separation is observed in the gas phase near the troughs and drastically alters the viscous stress distribution.