Simulating surfactant spreading: Influence of a physically motivated equation of state

Abstract

In this paper, we present numerical simulations that demonstrate the effect of the particular choice of the equation of state (EoS) relating the surfactant concentration to the surface tension in surfactant-driven thin liquid films. Previous choices of the model EoS have been an ad-hoc decreasing function. Here, we instead propose an empirically motivated EoS; this provides a route to resolve some discrepancies and raises new issues to be pursued in future experiments. In addition, we test the influence of the choice of initial conditions and values for the non-dimensional groups. We demonstrate that the choice of EoS improves the agreement in surfactant distribution morphology between simulations and experiments, and influences the dynamics of the simulations. Because an empirically motivated EoS has regions with distinct gradients, future mathematical models may be improved by considering more than one timescale. We observe that the non-dimensional number controlling the relative importance of gravitational versus capillary forces has a larger influence on the dynamics than the other non-dimensional groups, but is nonetheless not a likely cause of discrepancy between simulations and experiments. Finally, we observe that the experimental approach using a ring to contain the surfactant could affect the surfactant and fluid dynamics if it disrupts the intended initial surfactant distribution. However, the fluid meniscus itself does not significantly affect the dynamics.

An Immersed Boundary Method for Simulating Interfacial Flows with Insoluble Surfactant in Three Dimensions

“…7(c). This result is also qualitatively comparable with the one found in [39]. The relative error of total surfactant mass shown in Fig.…”

“…In our results of this inward spreading dynamics, the evolution of the interface and surfactant distribution are quite qualitatively comparable to that of observed using different equation of state in [39], although we use the linear equation of state (2.5). There is another difference that we solve the Navier-Stokes equations while the authors in [39] solve a modified thin film equation. Further studies in the future are needed for better understanding of this physical phenomenon.…”

Capillary waves with surface viscosity

“…It would therefore be fruitful in a future contribution to investigate this surfactant interference mechanism through a more systematic experimental and theoretical study. In particular, a numerical approach similar to that of Sinclair et al (2018)…”