Session E02: Focus Session: Surfactants as Hidden Variables

Surfactants and fundamental flow fields at interfaces

Interfacially trapped colloids generate long-ranged flows with signatures that reveal the compressibility and the rheology of interfaces. Surfactants, even in a modest concentration, significantly alter these mechanics. We dissect interfacial flows around Brownian colloids to provide insights essential to understanding these effects in dilute surfactant systems. Flow fields, measured by correlated displacement velocimetry, are decomposed into interfacial hydrodynamic multipoles, including force monopole and dipole flows. Prior work has shown that trace surfactant impurities render the interface incompressible. Here we address a Gibbs monolayer of surfactant undergoing a surface phase transition. The flow structure shows that the interface is incompressible for scant surfactant near the gaseous state, but is compressible in two phase coexistence between the gaseous and liquid-expanded state, and incompressible again in the liquid expanded state.  We also realize a non-trivial consequence of the surfactant concentration on the drag imposed on interfacially trapped colloids pointing towards hidden influences of surfactants on the mechanics of interfaces.   

Stability of surfactant-laden droplets with surface viscosity in shear flow

The theoretical description of surfactant-laden interfaces with surface viscosity is challenging and, despite the importance of surface viscosity on the interface behaviour, the influence of surface viscosity is frequently neglected in theoretical and computational studies. Recent work on the deformation of surfactant-laden droplets in shear flow demonstrates a non-trivial influence of both surface shear and dilatational viscosities on the surfactant distribution and, consequently, the droplet shape [Luo et al., J. Fluid Mech. 858 (2019), 91]. Using a front-tracking method in conjunction with the Boussinesq-Scriven model, we study numerically the stability of drops laden with insoluble surfactants in an incompressible shear flow. Our study focuses on the influence of the constitutive parameters (surface pressure, surface shear viscosity, surface dilatational viscosity) of the Boussinesq-Scriven model on the critical capillary number above which the droplet breaks up and the influence of the surface rheology on the evolution of this instability.   

Numerical investigation of the role of surface viscosity on droplet deformation and breakup in extensional flow

In this work, we perform boundary-integral simulations to explore the role of surface viscosity on droplet deformation and breakup in an axisymmetric extensional flow. The problem is solved under the Stokes flow regime, and the surface rheology of the droplet is modeled using the Boussinesq-Scriven constitutive relationship for a Newtonian interface. We compare the results from our boundary element simulations to the small deformation perturbation theories for surface viscosity. We observe that the surface shear/dilational viscosity increases/decreases the critical capillary number beyond which the droplet becomes unstable and breaks apart by reducing/increasing the droplet deformation at a given capillary number compared to a clean droplet. We also explore the coupled influence of surface viscosity, Marangoni stresses, and the effects of pressure thickening/thinning surfactants on droplet dynamics and present the underlying mechanisms behind the different observations in this talk. We conclude by discussing the relative importance of surface shear and dilational viscosity on droplet stability based on their measured values observed in various experimental studies on surfactants, lipid bilayers, and proteins.    

Role of surface viscous stresses in pinch-off of liquid threads

Surfactants are routinely used in diverse applications involving free surface flows with interface pinch-off such as inkjet printing, crop spraying and atomization coating because of their ability to adsorb onto and lower the surface tension of water-air and water-oil interfaces. In addition to lowering surface tension, surfactants may induce surface tension gradients (Marangoni stresses) and cause surface rheological effects. Although much attention has been paid to date to the influence of solutocapillarity and Marangoni stresses on jet/drop breakup, the effect of surface viscous stresses has been inadequately studied given the difficulty in measuring surface viscosities due to the presence of surfactants. We examine their effect on thread breakup by asymptotic analysis and 1D simulations using the slender-jet approximation. We obtain analytical expressions for thinning rate that explicitly depend on surface rheological parameters, thereby also providing a simple new route for measuring surface viscosity. The results obtained with the 1D algorithm are confirmed by direct comparison against predictions made with a 3D but axisymmetric free surface solver.   

Effect of surface rheology on viscous fingering

Surfactants such as fatty acids, alcohols, proteins, and particles generally stabilize fluid interfaces against rupture and coalescence. However, interfacial instabilities occur even in the presence of surfactants. These instabilities are often undesirable and present challenges in common industrial processes involving multiphase flows. We investigate, for the first time, the impact of interfacial rheology on the Saffman-Taylor or viscous fingering problem and demonstrate the stabilizing role of surface viscosity. We use linear stability analysis to show that surface viscosity slows the growth of unstable protrusions and results in thicker fingers. We quantify the growth of the instability in realistic ranges of fluid and geometric parameters, and use these insights to highlight the quantitative changes that are predicted to occur when a typical surface-viscous surfactant is present in a multiphase fluid displacement problem.   

The impact of viscous stress and Marangoni stress on the micro-scale droplet coalescence

Liquid-liquid droplet emulsions are ubiquitous in systems such as bilgewater, food processing, and water-entrained diesel fuels. The dispersed droplets are usually stabilized by the surfactant molecules absorbed onto the interface, which reduces the interfacial tension (IFT) force, and therefore, inhibits the droplet coalescence. In addition to IFT, other factors can also impact droplet stability. When two droplets approach each other, a thin film forms between the droplets and must drain before they can coalesce. Thus, the emulsion stability is determined by the time scale for the film drainage. Studies have shown that the film drainage time can be influenced by the viscous stress and Marangoni stress at the droplet interface. Based on different liquid-liquid systems, both viscous stress and Marangoni stress will inhibit the film drainage to a certain extent. In this work, systematic droplet coalescence experiments will be presented. Systems with different viscosity ratios are investigated to understand the impact of viscous stress. In addition, the film drainage time is also measured for surfactants with different concentrations. Scaling analysis based on the Marangoni number will be performed to understand the effect of the Marangoni stress on the droplet coalescence.   

Effect of surfactant on flow fields in droplets generated in microfluidics devices

We study the effect of surfactants on flow patterns inside a drop moving inside a rectangular microchannel both experimentally and numerically. In our experiments, we use Ghost Particle velocimetry to visualize flows. The numerical simulations are based on solving the full three-dimensional Navier-Stokes equations, coupled with two transports equations for surfactants in the aqueous bulk phase and on the interface.  The results of this work demonstrate that surfactant dynamics has a crucial effect on flow patterns inside the drop. If surfactant equilibration rate is faster than the interface deformation rate then surfactant addition results in suppression of corner flow effect and can be described by change in the capillary number. In the opposite case, Marangoni stresses result in faster surface motion at corners and flow reversal in the central part of drop.   

Predicting slip degradation due to traces of surfactant in laminar flows over superhydrophobic surfaces

In recent years, surfactants have been identified as one of the most influential factors affecting the performance of drag-reducing superhydrophobic surfaces (SHS). Trace amounts of these substances, virtually unavoidable in practical applications and even in nominally clean experiments, induce Marangoni forces that can completely negate slip (Peaudecerf et al. PNAS 2017; Song et al. PRF 2018). Models inclusive of surfactant initially considered flows over transverse SHS gratings (Landel et al. JFM 2020), since this is the simplest 2D flow that allows for the streamwise accumulation of surfactant ultimately responsible for the loss of performance. Here, we present a theory for longitudinal gratings, the most widely used configuration, which necessarily requires considering a 3D flow field (Temprano-Coleto et al. arXiv 2021). Predictions of the slip as a function of the SHS geometry are in good agreement with our simulations and experimental measurements, which we perform using confocal microscopy and micro-PIV in microfluidic channels. In addition, we show how our model can be used to estimate the concentration and physicochemical properties of the unknown surfactants naturally present in experimental setups, which are otherwise extremely challenging to measure directly.   

Modelling turbulent drag reduction for superhydrophobic surfaces with surfactant

Superhydrophobic surfaces (SHS) can reduce the friction experienced at a boundary in turbulent fluid flows. In the laminar regime, it has been demonstrated that naturally-occurring surfactants can negate drag reduction, at times even rendering SHS no better than solid walls. However, extending these findings to turbulent flow remains challenging, as the full numerical solution to the equations which govern the fluid and surfactant are expensive. To address this challenge, we present a theory for both internal or external turbulent flows, over a periodic array of longitudinal or transverse ridges, in the presence of a small concentration of soluble surfactant. To deduce an expression for the turbulent drag reduction, we adopt a technique based upon the shifted log-law, whereas we obtain the slip lengths from local solutions due to laminar theory in the presence of surfactant. We are thereby able to examine how the slip and drag depend on the parameters that characterise surfactant transport and the SHS geometry. This allows one to predict the optimal configurations for turbulent drag reduction in the presence of surfactant. Finally, we summarise several key numerical and experimental works within the literature, which we use to evaluate the effectiveness of our model.