Complex Patterns and Elementary Structures of Solutal Marangoni Convection: Experimental and Numerical Studies

Abstract

The transfer of a solute between two liquid layers is susceptible to convective instabilities of the time-dependent diffusive concentration profile that may be caused by the Marangoni effect or buoyancy. Marangoni instabilities depend on the change of interfacial tension and Rayleigh instabilities on the change of liquid densities with solute concentration. Such flows develop increasingly complex cellular or wavy patterns with very fine structures in the concentration field due to the low solute diffusivity. They are important in several applications such as extraction or coating processes. A detailed understanding of the patterns is lacking although a general phenomenological classification has been developed based on previous experiments. We use both highly resolved numerical simulations and controlled experiments to examine two exemplary systems. In the first case, a stationary Marangoni instability is counteracted by a stable density stratification producing a hierarchical cellular pattern. In the second case, Rayleigh instability is opposed by the Marangoni effect causing solutal plumes and eruptive events with short-lived Marangoni cells on the interface. A good qualitative and acceptable quantitative agreement between the experimental visualizations and measurements and the corresponding numerical results is achieved in simulations with a planar interface, and a simple linear model for the interface properties, i.e. no highly specific properties of the interface are required for the complex patterns. Simulation results are also used to characterize the mechanisms involved in the pattern formation.