Relaxation oscillations of Marangoni convection at curved interfaces and drops

Mass transfer of surface-active substances across fluidic interfaces is frequently accompanied by Marangoni instability [1]. Marangoni convection can show a temporal periodicity in the form of relaxation oscillations due to subsequent consumption and regeneration of its driving force. Contrary to the complex behavior of strong surfactants or reactive mass transfer, a simple two-phase-system consisting of paraffin oil and water is employed in our study. Due to mass transfer of isopropanol as a weak surfactant, concentration gradients and, by implication, density gradients are produced in-situ.
We have first studied single small droplets, placed in the concentration gradient, by means of a combination of experiments and simulations. The experiments are conducted in a Hele-Shaw experiment in which the droplets are visualized by shadowgraphy [2]. The 2D numerical simulations are based on a diffusiveinterface approach and assume a linear concentration and density gradient. We show that the single droplets perform about hundred periods of regular ROs over almost one hour. By analyzing their characteristics, the underlying mechanism can be attributed to the interaction between the mixing by Marangoni convection and the restoring effects of diffusion and buoyant convection on the driving concentration gradients. In the next step, ensembles of droplet comprising droplet pairs as well as linear or circular chains of droplets are investigated. If the spatial distance between the droplets in within the propagation depth of the relaxation oscillations, we observe an excitation of the relaxation oscillation from one droplet to its neighbor [3]. As a result, neighboring droplets are forced to oscillate with the same frequency. On arranging the droplets in chains, an efficient transmission of the relaxation oscillation can be achieved.
References
[1] K. Eckert, T. K¨ollner, K. Schwarzenberger, T. Boeck, Transport Processes at Fluidic Interfaces, Eds: D. Bothe, A. Reusken, Springer (2017).
[2] Schwarzenberger, S Aland, H Domnick, S Odenbach, K Eckert, Colloids and Surfaces A: Physicochemical and Engineering Aspects 481, 633-643 (2015).
[3] M. Mokbel, K. Schwarzenberger, K. Eckert, S. Aland (2017), in preparation.