(461f) Flow and Particle Dynamics on Interfaces with Non-Trivial Surface Rheology

Fluid interfaces appear throughout science, technology, industry and biology. Almost without exception, ‘surface-active’ molecules and/or particles exert a controlling influence on the dynamics of multiphase materials. Surfactants reduce the energetic cost of creating interfacial area, and it is widely known that surfactant gradients exert Marangoni stresses on interfaces. Additionally, surfactants may relax surface stresses by adsorption/desorption from/to the bulk fluid, via 2D phase transitions, through surface rheology that resists flow and deformation within the plane of the interface, or some combination of these processes. One striking display of the complexity of these materials arises due to non-trivial surface rheology. Specifically, the surface shear viscosity often depends strongly on the surface pressure (or concentration) of that surfactant. This has dramatic consequences, which we theoretically illustrate using experimentally accessible examples. We reveal qualitatively new features such as self-limiting surfactant fluxes and a maximum velocity of surface-attached probes. Further, relative motion of surface-attached particles breaks fore-aft symmetry of low-Reynolds-number flows, leading to non-intuitive trajectories. Finally, we analyze 2D suspension dynamics in this context and show that particle pairs end up being well-separated or aggregated depending on whether the surface rheology of the monolayer thickens or thins as a function of surface pressure. Ultimately, these problems provide the mathematical framework and the intuitive understanding required for the conceptual design and analysis of complex 2D interfacial materials.