The drainage of a foam lamella

We present a mathematical model for the drainage of a surfactant-stabilised foam lamella, including capillary, Marangoni and viscous effects and allowing for diffusion, advection and adsorption of the surfactant molecules. We use the slender geometry of a lamella to formulate the model in the thin-film limit and perform an asymptotic decomposition of the liquid domain into a capillary-static Plateau border, a time-dependent thin film and a transition region between the two. By solving a quasi-steady boundary-value problem in the transition region, we obtain the flux of liquid from the lamella into the Plateau border and thus are able to determine the rate at which the lamella drains. Our method is illustrated initially in the surfactant-free case. Numerical results are presented for three particular parameter regimes of interest when surfactant is present. Both monotonic profiles and those exhibiting a dimple near the Plateau border are found, the latter having been previously observed in experiments. The velocity field may be uniform across the lamella or of parabolic Poiseuille type, with fluid either driven out along the centre-line and back along the free surfaces or vice versa. We find that diffusion may be negligible for a typical real surfactant, although this does not lead to a reduction in order because of the inherently diffusive nature of the fluid-surfactant interaction. Finally, we obtain the surprising result that the flux of liquid from the lamella into the Plateau border increases as the lamella thins, approaching infinity at a finite lamella thickness

Biological applications of kinetics of wetting and spreading

Wetting and spreading kinetics of biological fluids has gained a substantial interest recently. The importance of these fluids in our lives has driven the pace of publications. Globally scientists have ever growing interest in understanding wetting phenomena due to its vast applications in biological fluids. It is impractical to review extremely large number of publications in the field of kinetics of complex biological fluids and cosmetic solutions on diverse surfaces. Therefore, biological and cosmetic applications of wetting and spreading dynamics are considered in the following areas: (i) Spreading of Newtonian liquids in the case of non-porous and porous substrates. It is shown that the spreading kinetics of a Newtonian droplet on non-porous and porous substrate can be defined through theoretical relations for droplet base radius on time, which agree well with the experimental results; (ii) Spreading of blood over porous substrates. It is shown that blood, which has a complex non-Newtonian rheology, can be successfully modelled with the help of simple power-law model for shear-thinning non-Newtonian liquids; (iii) Simultaneous spreading and evaporation kinetics of blood. This part enlightens different underlying mechanisms present in the wetting, spreading, evaporation and dried pattern formation of the blood droplets on solid substrates; (iv) Spreading over hair. In this part the wetting of hair tresses by aqueous solutions of two widely used by industry commercially available polymers, AculynTM 22 and AculynTM 33, are discussed. The influence of non-Newtonian rheology of these polymer solutions on the drainage of foams produced from these solutions is also briefly discussed

The dynamics of static bubbles: the drainage and rupture of quiescent bubbles can enrich, aerosolize, and stress suspended microorganisms

Bubbles are ubiquitous influencing a multitude of biological processes in natural and industrial environments; this influence is especially relevant during and after bubble rupture. Indeed, the influence of a bubble can extend well beyond its lifetime via the droplets produced when it ruptures. These droplets are known to effectively transport nearby particulates including bacteria and viruses into the surroundings, which in addition to affecting human health can influence global climate by acting as cloud condensation nuclei. Further, the bubble's rupture is a violent event that has been linked to decreased cell viability in bioreactors. However, in all these applications many of the studies have taken an empirical approach, making the results difficult to generalize. Here we combine theory and experiment to investigate the static and dynamic interactions between bubbles and the surrounding microorganisms at a free interface. Our first study focuses on the equilibrium shape a bubble forms after reaching the surface of a liquid. Existing literature is limited to a bubble resting on a flat interface; for example, the surface of a pool or calm lake. However, there are instances where this assumption no longer applies -- a bubble bursting on a raindrop, for example. By relaxing this assumption, we show how a curved boundary alters the final shape of the bubble. Our next study focuses on the enrichment of particulates in the cap of a bursting bubble. As a bubble rises to a free surface, particulates in the bulk liquid are frequently transported to the surface by attaching to the bubble's interface. When the bubble ruptures, a fraction of these particulates are often ejected into the surroundings in film droplets with particulate concentrations higher than the liquid from which originate. However, the precise mechanisms responsible for this enrichment are unclear. By simultaneously recording the drainage and rupture events with high-speed and standard photography, we directly measure the concentrations in a thin bubble film. Based on our results, we develop a physical model and provide evidence that the enrichment is due to a combination of scavenging and film drainage. Our next study focuses on the conditions necessary for a jet droplet to be produced. Past research shows that droplet production is halted when either gravitational or viscous effects are significant. Through systematic experimentation we uncover an intermediate region where both effects are significant, leading to an early end of droplet production. By numerically decoupling the gravitational effects into before and after rupture, we find that the equilibrium shape is responsible for the existence of this intermediate region. Our last study focuses on quantifying the localized stresses produced during spontaneous bubble bursting. Directly simulating each bubble and its effect on the suspended cells in a bioreactor is currently infeasible. Here we illustrate how the results of past works, which disagree by several orders of magnitude for similarly sized bubbles, are primarily a result of the chosen numerical mesh, not the underlying physics. By implementing a particle tracking method, we eliminate this mesh dependence and quantify the extent or volume effected by a single bubble bursting event. Based on our results, we develop a generalizable framework that could be integrated into existing models as a parameterization, removing the need to simulate both phases.2019-07-09T00:00:00

Non-Newtonian and non-isothermal effects in the gravity-driven draining of a vertically-aligned thin liquid film

The drainage and thinning of liquid films are important in a variety of applications,such as in liquid and solid foam networks, relevant in the manufacture of metallic and ceramic foams, the food industry, processing in the petro-chemical industry, and the biological and life sciences. In a liquid foam network, there are gas bubbles separated by thin liquid lamellae. If one is interested in predicting the lifetime of a foam or its overall stability then, as a starting point, understanding the drainage within the lamella is important.Motivated by the above, in this thesis, we consider a two-dimensional model system to investigate the draining and thinning of the lamella relevant to metallic and polymeric melts. Lubrication theory is employed to derive two master Partial Differential Equa-tions (PDEs) for a generalised Newtonian liquid describing the evolution of the film thickness and the extensional flow speed. The PDEs include the effects due to gravity, extensional viscous and surface tension forces. We use the non-Newtonian (Power-law and Carreau) and viscoplastic (Bingham and Herschel-Bulkley) constitutive laws to describe the flow rheology.We first describe the evolution of a Newtonian liquid film in the limit of large Capillary number, Ca=ρ*g*L*2/(eγ*)>>1. We derive early and late-time similarity solutions for the draining and thinning of the lamella. A new power law thinning rate of t−2.25 in the lamella is identified at late times. This is in comparison to a thinning rate of t−2 predicted for a Newtonian film without gravity, suggesting a weak-dependence on gravity.Next, we perform numerical simulations to investigate the influence of non-Newtonian and viscoplastic effects by varying the power-law index and the yield stress. We observe that the power law index and the yield stress affects the time scale of the thinning, but has weak dependence on the late-time thinning rate relative to the Newtonian thinning rate. We identify the limitations of the power-law model when the shear rate is low and how these can be resolved using the Carreau model.We extend the Newtonian model to include non-isothermal effects, such as temperature-dependent viscosity and surface tension. We perform numerical simulations to describe the evolution for a variety of parameter values, such as the reduced P ́eclet number and those related to the exponential viscosity-temperature model and the linear surface tension-temperature model. Our results indicate that the resulting temperature drop in the film due to cooling from the free surface, particularly in the lamella, and the corresponding viscosity and surface tension contrast, significantly influence the draining and thinning of the film. Preliminary results show that the viscosity variation has greater influence compared to surface tension variations; however additional work is required to confirm this.The new knowledge will enhance the current understanding to a wider class of thin liquid film draining flows associated with metallic and polymeric melts

An experimental study on the buoyancy-driven motion of air bubbles in square channels

The motion of drops and bubbles in confined domains is encountered in several applications such as oil recovery, solvent extraction, paper-making, and microfluidics, among others. In this thesis, the motion of air bubbles in square capillaries moving under the influence of gravity is studied at finite Reynolds numbers. The steady shapes, deformations, film thickness, and velocities of the bubbles as a function of the bubble size are determined experimentally. The bulk fluid phase is either Newtonian, viscoelastic, or a surfactant solution. Bubbles rising in a Newtonian fluid are nearly spherical at lower bubble volumes and become prolate losing their fore and aft symmetry at larger bubble volumes. At lower bulk viscosities, a reentrant cavity develops at the rear of bubble. The critical viscosity at which this shape transition occurs depends on the size of the capillary. The terminal velocity of bubbles increases with volume for small bubble volumes. Even at small bubble volumes, the terminal velocity of the bubbles is much less than the Hadamard-Rybczinski velocity of a spherical bubble with the same volume. (Abstract shortened by UMI.)

Dynamics of bubbles in microchannels : theoretical, numerical and experimental analysis

This thesis aims at contributing to the characterization of the dynamics of bubbles in microfluidics through modeling and experiments. Two flow regimes encountered in microfluidics are studied, namely, the bubbly flow regime and the Taylor flow regime (or slug flow). In particular, the first part of this thesis focuses on the dynamics of a bubbly flow inside a horizontal, cylindrical microchannel in the presence of surfactants using numerical simulations. A numerical method allowing to simulate the transport of surfactants along a moving and deforming interface and the Marangoni stresses created by an inhomogeneous distribution of these surfactants on this interface is implemented in the Level set module of the research code. The simulations performed with this code regarding the dynamics of a bubbly flow give insights into the complexity of the coupling of the different phenomena controlling the dynamics of the studied system. Fo example it shows that the confinement imposed by the microchannel walls results in a significantly different distribution of surfactants on the bubble surface, when compared to a bubble rising in a liquid of infinite extent. Indeed, surfactants accumulate on specific locations on the bubble surface, and create local Marangoni stresses, that drastically influence the dynamics of the bubble. In some cases, the presence of surfactants can even cause the bubble to burst, a mechanism that is rationalized through a normal stress balance at the back of the bubble. The numerical method implemented in this thesis is also used for a practical problem, regarding the artisanal production of Mezcal, an alcoholic beverage from Mexico. The second part of the thesis deals with the dynamics of a Taylor flow regime, through experiments and analytical modeling. An experimental technique that allows to measure the thickness of the lubrication film forming between a pancake-like bubble and the microchannel wall is developed. The method requires only a single instantaneous bright-field image of a pancake-like bubble translating inside a microchannel. In addition to measuring the thickness of the lubrication film, the method also allows to measure the depth of a microchannel. Using the proposed method together with the measurment of the bubble velocity allows to infer the surface tension of the interface between the liquid and the gas. In the last chapter of this thesis, the effect of buoyancy on the dynamics of a Taylor flow is quantified. Though often neglected in microfluidics, it is shown that buoyancy effects can have a significant impact on the thickness of the lubrication film and consequently on the dynamics of the Taylor flow. These effects are quantified using experiments and analytical modeling. This work was performed at Princeton University with Professor Howard A. Stone during a seven month stay

Physical Model Study of the Effects of Wettability and Fractures on Gas Assisted Gravity Drainage (GAGD) Performance

The Gas-Assisted Gravity Drainage (GAGD) process was developed to take advantage of the natural segregation of injected gas from crude oil in the reservoir. It consists of placing a horizontal producer near the bottom of the reservoir and injecting gas using existing vertical wells. As the injected gas rises to the top to form a gas cap, oil and water drain down to the horizontal producer. Earlier experimental work using a physical model by Sharma had demonstrated the effectiveness of the GAGD process in improving the oil recovery when applied in water-wet porous media. The current research is an extension of that work and is focused on evaluating the effect of the wettability of the porous medium and the presence of a vertical fracture on the GAGD performance. The effect of the injection strategy (secondary and tertiary mode) on the oil recovery was also evaluated in the experiments. In the physical model experiments a Hele-Shaw type model was used (dimensions: 13 7/8” by 5/16” by 1”) along with glass beads and silica sand as the porous media. Silanization with an organosilane (dimethydichlorosilane) was used to alter the wettability of the glass beads from water-wet to oil-wet. The experiments showed a significant improvement of the oil recovery in the oil-wet experiments versus the water-wet runs, both in the secondary and the tertiary modes. The fracture simulation experiments have also shown an increase in the effectiveness of the GAGD process

Non-Newtonian and viscoplastic models of a vertically-aligned thick liquid film draining due to gravity

We consider theoretically the two-dimensional flow in a vertically-aligned thick liquid film supported at the top and bottom by wire frames. The film gradually thins as the liquid drains due to gravity. We focus on investigating the influence of non-Newtonian and viscoplastic effects, such as shear thinning and yield stress, on the draining and thinning of the liquid film, important in metallic and polymeric melt films. Lubrication theory is employed to derive coupled equations for a generalised Newtonian liquid describing the evolution of the film’s thickness and the extensional flow speed. We use the non-Newtonian (Power-law and Carreau)and viscoplastic (Bingham and Herschel-Bulkley) constitutive laws to describe the flow rheology. Numerical solutions combined with asymptotic solutions predict late-time power-law thinning rate of the middle section of the film. For a Newtonian liquid, a new power law thinning rate of t -2.25 is identified. This is in comparison to a thinning rate of t -2 predicted for a thin Newtonian liquid film neglecting gravity, suggesting a weak dependence on gravity for the drainage of thicker films. For a non-Newtonian and viscoplastic liquid, varying the power law index and the yield stress influences the time scale of the thinning, but has weak dependence on the late-time thinning rate relative to the Newtonian thinning rate. The shortcomings of the Power-law model are exposed when the shear rate is low and these are resolved using the Carreau model