Surface shear viscosity of Gibbs and Langmuir monolayers

Abstract

In this paper, we present a new two-dimensional viscometer, and the hydrodynamic calculations used to obtain the surface viscosities from the measurements. In order to interpret the experiments, performed with solutions of sodium dodecyl sulfate (SDS) and also with monolayers of insoluble surfactants, we develop various hydrodynamic models of soluble Gibbs monolayers and of incompressible Langmuir monolayers, that describe well the experimental results. In the case of SDS solutions, the calculations allow the determination of the surface shear viscosity, and its value is in good agreement with previous studies.

Surface viscosity and Marangoni stresses at surfactant laden interfaces

“…The limit Bo 1 → ∞ is singular as neglecting the motion in the bulk fluid leads to the well-known Stokes paradox for the interface flow problem. Conversely, the limit of vanishing surface rheology must be taken with care, as discussed by Barentin et al (1999), as the limit is singular within the lubrication approximation. Specifically, the lubrication approximation breaks down at probe boundaries, where the interface is closer to the boundary than the film thickness H. Surface rheology introduces an in-plane stress that persists even within the lubrication approximation, allowing a no-slip condition to be imposed at the probe boundary while remaining consistent with the lubrication approximation.…”

“…First, as a point of comparison, we briefly review the probe drag in an incompressible monolayer of an insoluble surfactant (β → 0, → ∞), which was previously studied by Barentin et al (1999). We then focus on a soluble surfactant about two distinct slow probe limits: diffusion-dominated (Pe s 1, {β, } = O(1)) and adsorption/desorption-dominated ( 1, {β, Pe s } = O(1)).…”

“…Others have considered the consequence of a viscous compressible interface (Danov et al 1995;Barentin et al 1999;Dimova et al 2000), but no work yet considers a probe at a viscous, compressible interface that generates Marangoni flows. Our work extends the analysis of Barentin et al (1999), who considered a compressible Gibbs monolayer that equilibrates instantaneously with the subphase The subphase has viscosity η and depth H, and the interface has surface shear and dilatational viscosities η s and κ s , respectively. The disk base is denoted D while the perimeter is ∂D.…”

“…Dimova et al (2000) also considered concentration variations, but did not couple the interface to a bulk fluid and did not determine the Marangoni flow, but only the leading-order change in the surface tension. For analytical ease, as in Barentin et al (1999), we assume a flat (two-dimensional) disk at the interface and solve the hydrodynamic equations explicitly assuming that the subphase is shallow compared to the radius of the disk. In this case, the bulk phase flow problem is reduced to the thin-film/lubrication limit and is effectively slaved to the interfacial dynamics.…”

“Bottleneck Effect” in Two-Dimensional Microfluidics

“…At t 0, the barrier is abruptly set to motion with fixed velocity v b . We assume a planar, essentially unidirectional flow of the monolayer at the compression chamber, described by [23] where subindex s refers to the shear viscosity and flow velocity of the subphase (strongly coupled to the monolayer flow, as shown above). The quantities without subindex apply to the monolayer, z 0 corresponds to the monolayer level of the subphase flow, and x denotes the longitudinal (streamwise) direction with x 0 the initial barrier position.…”