Influence of interface pollution on the linear stability of a rotating flow

The boundary conditions at a liquid-gas interface can be modified by the presence of pollutants. This can in turn affect the stability of the associated flow. We consider this issue in the case of a simple open cylindrical cavity flow where a liquid is set in motion by the rotation of the bottom. The problem is addressed using an experimental set-up, a linear stability code and direct numerical simulation. A robust mismatch between numerical and experimental predictions of the onset of instability is found. We model the possible effect of unidentified pollutants at the interface using an advection-diffusion equation and a closure equation linking the surface tension to the superficial pollutant concentration. The chosen closure is inspired by studies of free-surface flows with surfactants. Numerical stability analysis reveals that the base flow and its linear stability threshold are strongly affected by the addition of pollutants. Pollutants tend to decrease the critical Reynolds number; however, the nonlinear dynamics is less rich than without pollutants. For sufficiently high pollution levels, the most unstable mode belongs to a different family, in agreement with experimental findings.