Karin Schwarzenberger

Pattern formation and mass transfer under stationary solutal Marangoni instability

According to the seminal theory by Sternling and Scriven, solutal Marangoni convection during mass transfer of surface-active solutes may occur as either oscillatory or stationary instability. With strong support of Manuel G. Velarde, a combined initiative of experimental works, in particular to mention those of Linde, Wierschem and coworkers, and theory has enabled a classification of dominant wave types of the oscillatory mode and their interactions. In this way a rather comprehensive understanding of the nonlinear evolution of the oscillatory instability could be achieved. A comparably advanced state-of-the-art with respect to the stationary counterpart seemed to be out of reach a short time ago. Recent developments on both the numerical and experimental side, in combination with assessing an extensive number of older experiments, now allow one to draw a more unified picture. By reviewing these works, we show that three main building blocks exist during the nonlinear evolution: roll cells, relaxation oscillations and relaxation oscillations waves. What is frequently called interfacial turbulence results from the interaction between these partly coexisting basic patterns which may additionally occur in different hierarchy levels. The second focus of this review lies on the practical importance of such convection patterns concerning their influence on mass transfer characteristics. Particular attention is paid here to the interaction between Marangoni and buoyancy effects which frequently complicates the pattern formation even more. To shed more light on these dependencies, new simulations regarding the limiting case of stabilizing density stratification and vanishing buoyancy are incorporated.

Multiscale structures in solutal Marangoni convection: Three-dimensional simulations and supporting experiments

Transient solutal Marangoni convection in a closed two-layer system is studied by a combination of numerical simulations and supplementary validation experiments. The initially quiescent, equally sized liquid layers are the phases of a cyclohexanol/water mixture. Butanol is additionally dissolved in the upper organic layer. Its diffusion across the interface is sensitive to the Marangoni instability. Complex convective patterns emerge that develop a hierarchical cellular structure in the course of the mass transfer. Our highly resolved simulations based on a pseudospectral method are the first to successfully reproduce the multiscale flow observed in the experiments. We solve the three-dimensional Navier-Stokes-Boussinesq equations with an undeformable interface, which is modeled using the linear Henry relation for the partition of the weakly surface-active butanol. Length scales in the concentration and velocity fields associated with the small and large-scale cells agree well with our experimental data from shadowgraph images. Moreover, the simulations provide detailed information on the local properties of the flow by which the evolution of the patterns and their vertical structure are analyzed. Apart from relatively weak influences due to buoyancy, the evolution of the convective structures is self-similar between different initial butanol concentrations when length and time are appropriately rescaled.

Pattern Formation Emerging from Stationary Solutal Marangoni Instability: A Roadmap Through the Underlying Hierarchic Structures

The complexity of interfacial convection has long exerted a pull and, at the same time, is the reason why this type of flow still belongs to the class of problems in chemical engineering and non-linear physics which are not fully resolved. This flow arises from the Marangoni instability which typically occurs when surface-active solutes, or heat, undergo a mass or heat transfer across an interface. During these processes various types of both quasi-steady and time-dependent flow structures have been observed [1–12].

Self-Pinning on a Liquid Surface

We report on the first experimental evidence of a self-pinning liquid drop on a liquid surface. This particular regime is observed for a miscible heavier oil drop (dichloromethane) deposited on an aqueous solution laden by an ionic surfactant (hexadecyltrimethylammonium bromide). Experimental characterization of the drop shape evolution coupled to particle image velocimetry points to the correlation between the drop profile and the accompanying flow field. A simple model shows that the observed pinned stage is the result of a subtle competition between oil dissolution and surfactant adsorption.

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

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.