Hydrodynamic stability of liquid films adjacent to imcompressible gas streams including effects of interface mass transfer

A theoretical study of linear stability of a gas/liquid interface with and without evaporation at the interface is presented. The zero mass transfer problem is solved for linear mean velocity profiles in both gas and liquid. The mass transfer problem is solved for small rates of evaporation, which allows the reduction of exponential mean profiles to linear profiles. This makes the governing Orr-Sommerfeld, temperature and concentration perturbation equations amenable to closed form analytical solutions and therefore enables one to isolate the effects of mass transfer. The present analysis considers instabilities in both gas and liquid motions and thus departs from the customary assumption of gas motion over a rigid wavy wall. The system of governing equations yields an eigenvalue problem upon employing the methods of stability theory.

It is found that several eigenvalues or modes exist in the case of the zero mass transfer problem. A small perturbation approach for long wavelength disturbances leads to one of these eigenvalues. This eigenvalue depends only on the ratio of boundary layer to liquid layer thickness and the ratio of viscosities and it is independent of the Reynolds, Weber and Froude numbers of the problem. Also, this mode is observed to be stable for all values of wave numbers and it is therefore associated with the Tollmien-Schlichting type of stability. Several other eigenvalues are obtained numerically using a Newton-Raphson technique. One of these modes has nearly the same speed of propagation as a Kelvin-Helmholtz wave for small wave numbers and hence it was called the modified Kelvin-Helmholtz mode.

The variation with respect to the disturbance wave number, of the first five slow moving modes and a representative fast moving mode, is investigated. One of these modes is found to be always unstable and all other slow moving modes (with the exception of the modified Kelvin-Helmholtz mode) are stable. The fast moving disturbance oscillates between stable and unstable regions as the wave number increases. The modified Kelvin-Helmholtz mode, on the other hand, is stable for small values of wave number and then remains unstable after passing through the neutrally stable wave number.

The present results show that neglecting instabilities in the gas motion would predict a stable interface at moderate values of wave number when it is actually unstable. Mass transfer investigations are restricted to the modified Kelvin-Helmholtz mode and computations indicate that interface evaporation has a destabilizing effect at moderate wave numbers.