On the droplet entrainment from gas-sheared liquid film

We formulate the droplet entrainment detached from a thin liquid film sheared by a turbulent gas in a circular pipe. In a time-averaged sense, the film has a Couette flow with a mean velocity of um. Then, a roll wave of wavelength λ and phase velocity uc is formed destabilized through Kelvin-Helmholtz instability, followed by a ripple wave of wavelength λp due to Rayleigh-Taylor instability, wherein the vorticity thickness of the gas stream is consistently a characteristic length scale. Superposing the two types of waves in axial and transverse directions produces conical cusps as the root of ligaments, from which droplets are torn off. The droplet entrainment rate is derived as λpλucum, validated by recent experimental results.