Surfactant spreading on a deep subphase: Coupling of Marangoni flow and capillary waves

Insights into characteristic motions and negative chemotaxis of the inanimate motor sensitive to sodium chloride

Inanimate motors, driven by the difference in surface tension, provide platforms for studying the physics of characteristic motion and mimicking the complex behaviors of biological systems. However, it is challenging to endow inanimate motors with high autonomy, with an emphasis on simulating the behavior of living organisms in response to external stimuli. Herein, by applying sodium chloride (NaCl) as an external stimulus, we achieve the regulation of motion mode and chemotaxis in a self-propelled camphor system. We present a comprehensive surface/interface understanding of motion bifurcation with the increase of concentration NaCl, i.e., continuous motion to no motion via oscillatory motion. The features of motions (the speed and frequency) and the mechanisms are elucidated depending on the concentrations of NaCl and sodium dodecyl sulfate (SDS). Furthermore, the characteristic motion and chemotaxis to the salt stimulus are correlated to the dynamic breaking/reforming of the surface tension balance and gradient-type distribution phenomenon triggered by dynamic camphor dissolution, surfactant adsorption /diffusion and camphor-surfactant interaction. This work sheds light on the typical motions of inanimate motors and scrutinizes the synergy between dual additives, which will boost the design of advanced self-propelled systems with nonlinear characteristic motion.

Interaction of impinging marangoni fields

HYPOTHESIS

Surface tension gradient driven Marangoni flows originating from multiple sources are important to many industrial and medical applications, but the theoretical literature focuses on single surfactant sources. Understanding how two spreading surfactant sources interact allows insights from single source experiments to be applied to multi-source applications. Two key features of multi-source spreading - source translation and source deformation - can be explained by transport modeling of a two-source system.

MODELING

Numerical simulations of two oleic acid disks placed at varying initial separation distances on a glycerol subphase were performed using COMSOL Multiphysics and compared to spreading of a single surfactant source.

FINDINGS

Interaction of two spreading sources can be split into three regimes: the independent regime - where each source is unaffected by the other, the interaction regime - where the presence of a second source alters one or more features of the spreading dynamics, and the quasi-one disk regime - where the two sources merge together. The translation of the sources, manifested as increasing separation distance between disk centers of mass, is driven by the flow fields within the subphase and the resultant surface deformation, while deformation of the sources occurs only once the surfactant fronts of the two sources meet.

Exact solutions for viscous Marangoni spreading

When surface-active molecules are released at a liquid interface, their spreading dynamics is controlled by Marangoni flows. Though such Marangoni spreading was investigated in different limits, exact solutions remain very few. Here we consider the spreading of an insoluble surfactant along the interface of a deep fluid layer. For two-dimensional Stokes flows, it was recently shown that the nonlinear transport problem can be exactly mapped to a complex Burgers equation [D. Crowdy, SIAM J. Appl. Math. 81, 2526 (2021)]SMJMAP0036-139910.1137/21M1400316. We first present a very simple derivation of this equation. We then provide fully explicit solutions and find that varying the initial surfactant distribution-pulse, hole, or periodic-results in distinct spreading behaviors. By obtaining the fundamental solution, we also discuss the influence of surface diffusion. We identify situations where spreading can be described as an effective diffusion process but observe that this approximation is not generally valid. Finally, the case of a three-dimensional flow with axial symmetry is briefly considered. Our findings should provide reference solutions for Marangoni spreading that may be tested experimentally with fluorescent or photoswitchable surfactants.