Direct Numerical Simulations for surfactant-laden shear flows on an adhered drop beyond the critical micelle concentration
Keywords: Surfactant-laden, Marangoni, Micelles, Surface-Rheology, Multiphase flows
One of the most complex and insufficiently studied transport phenomena in multiphase flows is the behavior of surface-active agents (surfactants). These molecules can act as beneficial additives or unwanted contaminants, significantly influencing flow dynamics. Surfactant-laden multiphase flows are of particular importance due to their widespread occurrence in both natural systems and industrial processes, yet their mechanisms at high concentrations—beyond the Critical Micelle Concentration (CMC)—remain poorly understood. Despite significant progress in this field (see Figure 1, left), prior research has largely been limited to conditions below the CMC. Beyond this threshold, surfactant molecules aggregate into polymer-like structures known as micelles (see Figure 1, right), introducing additional complexities.
Figure 1: (Left) Different layer of complexity linked to Multiphase Surfactant-laden flows. (Right) Graphical representation of the surfactant dynamics: concentration of surfactants.
In such cases, the flow system is governed by the Navier–Stokes equations for two-phase hydrodynamics, coupled with transport equations that account for multiple surfactant concentrations: monomer surfactant at the interface (Γ), monomer surfactant in the bulk (c), polymerized surfactant in micelles (m), and monomer surfactant on solid substrates (cs). In this talk, we present our latest numerical development, the code BLUE (1; 2), which accurately captures all physical mechanisms induced by the presence of surfactants. This numerical framework is broadly applicable to a wide range of multiphase flow configurations across multiple length and time scales (3; 4; 5; 6; 7; 8; 9; 10; 11). Representative applications include drop impact and spreading, Faraday wave dynamics, bubble bursting at free surfaces, mixing, and microfluidic flows, among many others. By accurately resolving interfacial dynamics and surfactant transport, the framework enables systematic investigation of surfactant-mediated effects in both fundamental studies and industrially relevant processes.
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