Multiphase Radial Reaction Fronts

Multiphase radial reaction fronts form when one reactant is injected from a central point into the other one and a radially spreading product phase forms, e.g. by precipitation or phase separation. The underlying phenomena are strongly affected by buoyancy/gravity.

Motivation

Reaction-Diffusion-Advection (RDA) fronts are present in a wide variety of disciplines; ranging from nanotechnology and catalyst particle synthesis to CO2 sequestration. In spite of this, the complete mechanism and dynamics of such systems are yet to be understood. To unravel the underlying mechanisms, gravity-driven effects like buoyancy convection or particle sedimentation need to be separated from the RDA dynamics. In order to achieve this, experiments are conducted in the microscale and different experimental micro-gravity platforms are utilized.

Goals

• Investigation of flow patterns and instabilities in reaction-diffusion-advection fronts
• Compare results with existing theory and support the development of new models
• Transfer knowledge to industrial applications (soil reparation, art restoration, re-calcification)

Techniques

• Flow visualization techniques (i.e. optical microscopy, shadowgraphy, μ-PIV, stereo-PIV)
• Custom-made experimental microscale devices (such as Hele-Shaw cells and ultra-thin capillaries)
• Laser diffraction for particle sizing
• Utilization of micro-gravity platforms (sounding rocket mission, parabolic flight)

Results

A central finding is the impact of gravity modulation on the dynamics of reaction fronts in radial Hele-Shaw cells. These cells are horizontal reactors with a disk-like flow gap, where one reactant solution is injected into the other one from a central inlet. They are typically described by a simplified model due to the small vertical length scale. However, the product formation in reaction fronts exposed to a modulated gravity environment shows the need to consider varying buoyancy effects despite of the small vertical length scale to correctly describe the yield of chemical processes for corresponding terrestrial and space-based applications.

The high-quality and long-duration microgravity conditions of a sounding rocket flight allow to differentiate Taylor dispersion from buoyancy-driven effects on the front dynamics. Both the results from the parabolic flight gravity modulations and the comparison between the sounding rocket and on-ground experiments show that this can only be achieved by pure microgravity conditions. On Earth, this is not possible for larger Hele-Shaw gap heights due to the slight density differences between the reactant and product solutions which cannot be avoided even with a most careful choice of reaction type and conditions. The microgravity experiments further point out the limits of existing one-dimensional (1D) models that are applicable only for very small gap heights and low flow velocities. Most importantly, they validate the extended two-dimensional (2D) model, which must be employed for Taylor dispersion-dominated systems to describe the behavior at larger gap heights.

For precipitation reactions, three characteristic regimes could be identified: advection of separated particles, flow path clogging by agglomerated particles, and the formation of gel-like reaction fronts. The analysis shows that the transition between these regimes is influenced by both hydrodynamic (e.g., flow velocity, gap height) and chemical (e.g., reactant concentration) parameters. Experiments in rectangular capillaries reveal surprising similarities with the regimes observed in radial geometries, although the driving flow field is basically different. These findings are highly valuable for precipitation reactions in confined spaces like geological pores or reactor flow channels.

The formation of a gel-like front in a coacervation multiphase reaction can trigger distinct types of pattern formation in an otherwise stable system. The pattern type can be controlled by the flow parameters, providing e.g. compact coacervate barrier layers, or a widespread product distribution by viscous fingering effects. These results open the possibility to achieve a desired product distribution just by tuning the injection rate of the reactant solution.

Publications

Stergiou, Y., Perrakis, A., De Wit, A., & Schwarzenberger, K. (2025). Flow-driven pattern formation during coacervation of xanthan gum with a cationic surfactant. Physical Chemistry Chemical Physics.

Keshavarzi, B., Reising, G., Mahmoudvand, M., Koynov, K., Butt, H. J., Javadi, A., ... & Eckert, K. (2024). Pressure Changes Across a Membrane Formed by Coacervation of Oppositely Charged Polymer–Surfactant Systems. Langmuir, 40(19), 9934-9944.

Stergiou, Y., Escala, D. M., Papp, P., Horváth, D., Hauser, M. J., Brau, F., ... & Schwarzenberger, K. (2024). Unraveling dispersion and buoyancy dynamics around radial A+ B→ C reaction fronts: microgravity experiments and numerical simulations. npj Microgravity, 10(1), 53.

Stergiou, Y., Hauser, M. J., Comolli, A., Brau, F., De Wit, A., Schuszter, G., ... & Schwarzenberger, K. (2022). Effects of gravity modulation on the dynamics of a radial A+ B→ C reaction front. Chemical Engineering Science, 257, 117703.

Stergiou, Y., Hauser, M. J., De Wit, A., Schuszter, G., Horváth, D., Eckert, K., & Schwarzenberger, K. (2022). Chemical flowers: Buoyancy-driven instabilities under modulated gravity during a parabolic flight. Physical Review Fluids, 7(11), 110503.

Keshavarzi, B., Schwarzenberger, K., Huang, M., Javadi, A., & Eckert, K. (2019). Formation of Structured Membranes by Coacervation of Xanthan Gum with C n TAB Surfactants. Langmuir, 35(42), 13624-13635.