Effects of solute mass transfer on the stability of capillary jets

Abstract

The effects of mass transfer (e.g. via evaporation) of surface-active solutes on the hydrodynamic stability of capillary liquid jets are studied. A linear temporal stability analysis is carried out yielding evolution equations for systems satisfying general non- linear kinetic adsorption relations and accompanying surface constitutive equations. The discussion of the instability mechanism associated with the Marangoni effect clarifies that solute transfer into the jet is destabilizing whereas transfer in the opposite direction reduces instability. The general analysis is illustrated by a system satisfying Langmuir-type kinetic relations. Contrary to a clean system (i.e. in the absence of surfactants), reduced jet viscosity may lead to a substantial reduction in perturbation growth. Furthermore, the Marangoni effect gives rise to an overstability mechanism whereby perturbations whose dimensionless wavenumbers exceed unity grow with time through oscillations of increasing amplitude. The common diffusion-control approximation constitutes an upper bound which substantially overestimates the actual growth of perturbations. Considering solutes belonging to the homologous series of normal alcohols in water–air systems, the intermediate cases (e.g. hexanol–water–air which is ‘mixed-control’) are the most susceptible to Marangoni instability.