Global stability analysis of hydrodynamic focusing in the presence of a soluble surfactant

• Published in: Journal of fluid mechanics 2024-10, Vol.997, Article A23
• Main Authors: Rubio, M., Cabezas, M.G., Montanero, J.M., Herrada, M.A.
• Format: Article
• Language: English
• Subjects: Base flow; Capillarity; Capillary flow; Diffusion rate; Flow rates; Flow velocity; Hydrodynamics; Interface stability; JFM Papers; Liquid flow; Minimum flow; Perturbation; Stability; Stability analysis; Stream discharge; Stream flow; Stream flow rate; Streaming; Surface stability; Surface tension; Surfactants
• ISSN: 0022-1120; 1469-7645
• DOI: 10.1017/jfm.2024.804

We numerically study the influence of a soluble surfactant on the microjetting mode of the liquid–liquid flow focusing configuration. The surfactant adsorbs on the interface next to the feeding capillary and accumulates in front of the emitted jet, significantly lowering the surface tension there. The resulting Marangoni stress substantially alters the balance of the tangential stresses at the interface but does not modify the interface velocity. The global stability analysis at the minimum flow rate stability limit shows that the Marangoni stress collaborates with soluto-capillarity to stabilize the microjetting mode. Our analysis unveils the noticeable effect of the Marangoni stress associated with the surface tension perturbation. Surfactant diffusion and desorption hardly affect the stability limit. Transient numerical simulations show how subcritical and supercritical base flows respond to a spatially localized initial perturbation. Our parametric study indicates that the minimum flow rate ratio depends on the adsorption constant and the surfactant concentration through the product of these two variables. The surfactant stabilizing effect increases with the outer stream flow rate. We show that surfactants not only stabilize the microemulsion resulting from the jet breakup in hydrodynamic focusing, but also allow for the reduction of droplet size. Our findings advance the fundamental understanding of the complex role of surfactants in tip streaming via hydrodynamic focusing. In particular, our results contradict the common assumption that adding surfactant favours tip streaming simply because it reduces the meniscus tip surface tension.