Soluble surfactant spreading: How the amphiphilicity sets the Marangoni hydrodynamics

Abstract

Amphiphiles are molecules combining hydrophilic and hydrophobic parts. The way they arrange in bulk and at interfaces is related to the balance between these two parts, and can be quantified by introducing the critical micellar concentration (cmc). Amphiphiles (also named "surfactants") are also at the origin of dynamical effects: local gradients of interfacial concentrations create the so-called Marangoni flows. Here we study the coupling between the molecule amphiphilicity and these Marangoni flows. We investigate in detail a spreading configuration, where a local excess of surfactants is locally sustained, and follow how these surfactants spread at the interface and diffuse in bulk. We have measured the features of this flow (maximal distance and maximal speed), for different types of surfactant, and as a function of all experimentally available parameters, as well as for two different configurations. In parallel, we propose a detailed hydrodynamical model. For all the measured quantities, we have found a good agreement between the data and the model, evidencing that we have captured the key mechanisms under these spreading experiments. In particular, the cmc turns out to be-as for the static picture of a surfactant-a key element even under dynamical conditions, allowing us to connect the molecule amphiphilicity to its ability to create Marangoni flows.

Hydrodynamic response of a surfactant-laden interface to a radial flow

“…Emphasis was put on the dilute regime of surfactants. This study is thus complementary to the wealth of experimental and theoretical works that have been performed recently at high concentration in a similar geometry [38][39][40][41]. Here, we have shown that the presence of a minute amount of insoluble surfactants possesses a clear hydrodynamic signature.…”

Axisymmetric spreading of surfactant from a point source

“…The agreement between the experimental measurements and our theory suggests that the more general surfactant dynamics may under certain circumstances be reduced to simple models akin to Marangoni and Gibbs elasticity of surfactant-laden liquid interfaces. The solutions developed here could also provide insight into the surfactant dynamics based on flow velocimetry in experimental systems, such as by Roché et al (2014) and Le Roux et al (2016). The precise criteria under which simplification is possible and conditions for transition are left to be undertaken in the future.…”

“…) or thermo-soluto-capillary convection (Bratukhin & Maurin 1968), with the notable exception of Jensen (1995) who analyzed transient dynamics from localized release of adsorbed surfactant. Interest has recently increased in the study of steady flow set by release of soluble amphiphiles at a constant rate (Roché, Li, Griffiths, Le Roux, Cantat, Saint-Jalmes & Stone 2014;Le Roux, Roché, Cantat & Saint-Jalmes 2016). In this case, the surfactant is removed from the vicinity of the interface as it dissolves in fluid bath, establishing a state that changes very slowly with the surfactant concentration in the bath.…”

Effective diffusion coefficient including the Marangoni effect

“…Recently, several experiments have been performed to clarify the generic aspect of this system. [24][25][26][27] Specifically, it was found that for the large Péclet number and the finite Reynolds number, the velocity field maintains self-similar profiles. We consider in this this study a different situation where the velocity generated by the Marangoni flow is sufficiently slow, i.e., the Reynolds number is small (see Sec.VI).…”