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

Abstract

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.

Surface deformation and film corrugation during drying of polymer solutions induced by Marangoni phenomena

“…These secondary structures become constantly consumed by the already established large permanent formations. The process is similar to what is seen in 3D simulations [42][43]. Up to M = 20,000 the number of the final cells remains the same, whereas at M = 40,000 their number increases.…”

Relaxation oscillations of solutal Marangoni convection at curved interfaces

“…Simultaneously, small structures appear at the interface in the form of high-frequency modulations of gray value. This hierarchy of large-scale convection with an embedded substructure is a common feature of solutal Marangoni instability and was analyzed in-depth in [15]. The ensuing relaxation phase in Fig.…”

“…The combination of experimental flow visualization and numerical analysis has recently improved understanding of the mechanisms underlying the evolution of patterns in Marangoni convection [13][14][15]. According to [15], a typical feature is the coarsening of structures, i.e. a steady increase in the size of the Marangoni cells, which compensates for the equilibrated mixing zone inside the cells by entraining fresh fluid.…”

“…the overview given in [12]. The combination of experimental flow visualization and numerical analysis has recently improved understanding of the mechanisms underlying the evolution of patterns in Marangoni convection [13][14][15]. According to [15], a typical feature is the coarsening of structures, i.e.…”

Three-Dimensional Numerical Simulation of Pure Solutocapillary Flow in a Shallow Annular Pool for Mixture Fluid with High Schmidt Number

“…It propagates in the azimuthal direction, which is the same as the hydrothermal wave. Schwarzenberger et al (2014) and Köllner et al (2013) studied the flow pattern formation in stationary solutal Marangoni convection and the characteristics of interfacial mass transfer in the liquid-liquid system. They reported several complex hierarchical cellular structures and the transition processes.…”