Effect of Gas Boundary Layer on the Stability of a Radially Expanding Liquid Sheet

Linear stability analysis is performed for a radially expanding liquid sheet in the presence of a gas medium. Liquid sheet can break up because of aerodynamic effect as well as its thinning. However, study of the aforementioned effects is usually done separately as the formulation becomes complicated. Present work combines both, aerodynamic effect and thinning effect, ignoring the non-linearity in the system. This is done by taking into account the formation of gas boundary layer whilst neglecting viscosity in the liquid phase. Base state analysis results in a Blasius-type system. To study the stability of the liquid sheet, gas-liquid interface is subjected to small perturbations. The linear model derived here can be applied to investigate the instability for sinuous as well as varicose modes, where the former represents displacement in centerline of the sheet and the latter represents modulation in sheet thickness. Temporal instability analysis is performed for sinuous modes, which are significantly more unstable than varicose modes, for a fixed radial distance implying local stability analysis. The growth rates, measured for fixed wavenumbers, predicated by the present model are compared with those obtained by the inviscid Kelvin-Helmholtz instability.