Finite element approximation of soluble surfactant spreading on a thin film

Published versio

Thermodynamically consistent description of the hydrodynamics of free surfaces covered by insoluble surfactants of high concentration

In this paper we propose several models that describe the dynamics of liquid films which are covered by a high concentration layer of insoluble surfactant. First, we briefly review the 'classical' hydrodynamic form of the coupled evolution equations for the film height and surfactant concentration that are well established for small concentrations. Then we re-formulate the basic model as a gradient dynamics based on an underlying free energy functional that accounts for wettability and capillarity. Based on this re-formulation in the framework of nonequilibrium thermodynamics, we propose extensions of the basic hydrodynamic model that account for (i) nonlinear equations of state, (ii) surfactant-dependent wettability, (iii) surfactant phase transitions, and (iv) substrate-mediated condensation. In passing, we discuss important differences to most of the models found in the literature.Comment: 31 pages, 2 figure

Surfactant effects in the Landau–Levich problem

In this work we study the classical Landau–Levich problem of dip-coating. While in the clean interface case and in the limit of low capillary numbers it admits an asymptotic solution, its full study has not been conducted. With the help of an efficient numerical algorithm, based on a boundary-integral formulation and the appropriate set of interfacial and inflow boundary conditions, we first study the film thickness behaviour for a clean interface problem. Next, the same algorithm allows us to investigate the response of this system to the presence of soluble surface active matter, which leads to clarification of its role in the flow dynamics. The main conclusion is that pure hydrodynamical modelling of surfactant effects predicts film thinning and therefore is not sufficient to explain the film thickening observed in many experiments

On a thin film model with insoluble surfactant

This paper studies the existence and asymptotic behavior of global weak solutions for a thin film equation with insoluble surfactant under the influence of gravitational, capillary, and van der Waals forces. We prove the existence of global weak solutions for medium sized initial data in large function spaces. Moreover, exponential decay towards the flat equilibrium state is established, where an estimate on the decay rate can be computed explicitly

An adaptive moving mesh method for two-dimensional thin film flow equations with surface tension

In this paper, we extend our previous work [A. Alharbi and S. Naire, An adaptive moving mesh method for thin film flow equations with surface tension, J. Computational and Applied Mathematics, 319 (2017), pp. 365-384.] on a one-dimensional r-adaptive moving mesh technique based on a mesh density function and moving mesh partial differential equations (MMPDEs) to two dimensions. As a test problem, we consider the gravitydriven thin film flow down an inclined and pre-wetted plane including surface tension and a moving contact line. This technique accurately captures and resolves the moving contact line and associated fingering instability. Moreover, the computational effort is hugely reduced in comparison to a fixed uniform mesh

Surfactant induced flows in thin liquid films : an experimental study

The topic of the experimental work summarized in my thesis is the flow in thin liquid films induced by non-uniformly distributed surfactants. The flow dynamics as a consequence of the deposition of a droplet of an insoluble surfactant onto a thin liquid film covering a solid substrate where discussed as a starting point in Chapter 2. A strong focus in this context was on the effect of the conditions in the vicinity of the surfactant source. It was shown, by application of interference and fluorescence microscopy, that the radially outwards directed displacement of the subphase, induced by the surfactant induced Marangoni stresses, is strongly influenced by the conditions near the surfactant source, i.e. the supply of surfactant from the source as the spreading proceeds. A novel oscillatory contact line instability of the surfactant droplet was described that modulates the flow rate of liquid from under the droplet. Considering conditions relevant to surfactant spreading in an oil reservoir in Chapter 3 the influence of a chemically imposed confinement on the sub-phase, along the surface of which a surfactant spreads, was investigated. A pronounced transition in the morphology evolution of the flowing thin film was found to be induced by the spatial restriction imposed through chemical surface patterns. The experimental results are in excellent agreement with numerical simulations reported by Myroslava Hanyak. Considering conditions in an oil reservoir, results for the spreading of surfactants along liquid-air interfaces can only give a first order approximation. The studies of Chapter 3 were therefore extended to the interface between two thin liquid films in Chapter 4. Here the spreading of a surfactant, soluble in one phase, is studied along the liquid-liquid interface of thin films. Resembling reservoir conditions, the films were subject to both, physical confinement as well as confinement imposed by a wettability pattern. In the context of surfactant spreading, it is a conceptually entirely new discovery, that surfactant induced Marangoni flows cannot only transport surfactants along fluid interfaces but can also efficiently transport surfactants along interfaces exhibiting considerably sized discontinuities. All existing literature in the field of surfactant spreading exclusively regarded continuous fluid interfaces. This novel phenomenon was the topic of Chapter 5. The convective surfactant spreading along discontinuous interfaces is directly relevant to the spreading of surfactants in an oil reservoir. In these porous underground rock formations the oil-water interface is not necessarily connected, such that surfactant spreading through a reservoir involves transport over interface discontinuities. Besides the spreading of surfactants, I also studied the self-propulsion of surfactant droplets. The results of my experimental studies were presented in Chapter 6 and 7. Self-propulsion dynamics exhibited by insoluble surfactant droplets on thin liquid films are systematically investigated in Chapter 6. Several modes of motion were described from directed continuous propulsion over a meandering mode of propulsion, that can also be exhibited by a pair of droplets in a synchronized fashion, to an intermittent form of propagation. The systematic study of the various modes of propulsion is complemented with the outline of a potential application in microfluidic devices in Chapter 7. In this context I am describing the novel phenomenon of transporting solid cargo particles using these self-propelling droplets which can be routed across micro-fluidic networks by controlling the temperature field around the drop e.g. using an infrared laser. The independence from external power sources, integrated electrodes or heating elements to propel the droplets, makes the concept specifically interesting for applications in inexpensive, single-use-type devices. In this thesis surfactant induced flows are studied in a wide range of system configurations. Confinement effects on the spreading dynamics are investigated systematically. These studies are complemented by the presentation of novel phenomena such as the Marangoni driven convective transport of surfactants along discontinuous interfaces