Session J39: Multiphase Flows: General II

Singular effect of small slip an otherwise stable two fluid shear flowSaleh Tanveer, The Ohio State University, Columbus, OH&Demetrios Papageorgiou, Imperial College, London, UK

A Navier-slip boundary condition between two immiscible fluids had been proposed to account for polymer disentanglement at the interface between two fluids that causes apparent slip [Zhao & Macosko, 2002]. Indeed, Koplik & Banavar [2006] used Molecular Dynamics simulations with interaction potentials supporting repulsion of molecules at the liquid-liquid interface, to demonstrate slip and propose a Navier-slip condition with an apparent slip coefficient that they computed.  

We consider the consequences of introducing an arbitrarily small slip in the highly stable configuration of Yih (1971), when a thin layer of less viscous fluid resides next to a moving wall in a two-layer fluid flow with very small viscosity ratio. We find that even when the viscosity ratio $m$ and a non-dimensional slip length $L$ tend to zero in some particular manner in a nonlinear thin-film model, we have destabilization of a planar interface to short wavelength (Turing type) instability. These waves were continued to finite amplitude traveling waves.

Existence of solutions was confirmed for finite amplitude waves and global smooth solutions were also shown to exist for the initial value problem. Numerical work with the Orr-Sommerfeld equations in each fluid, confirm that this Turing type instability transcends the thin-layer approximation [Katsavria & Papageorgiou, submitted, 2023].   

Direct simulations of droplets impacting oil slicks

2D and 3D computations of water droplets impacting oil slicks at the surface of water have been performed for different conditions of Weber number, Reynolds number, and oil layer thickness. These calculations have improved the understanding of high energy impacts, and it has also shown the requirements in terms of local mesh to capture the mechanisms in play, both in 2D and 3D. Comparisons with existing experiments have shown a reliable agreement regarding the time evolution of the cavity and crown created by the splash. The statistics about droplets and bubbles generated by the impact can be also partially reproduced, depending on the mesh resolution.   

Numerical Investigation of non-head-on collision and coalescence in oil-in-water emulsions

The stability of oil-in-water emulsions depends on the ease with which the dispersed oil phase droplets come in contact (or collide) with each other, and subsequently coalesce. Whether a phase separation is desired or not, controlling this coalescence process requires a thorough understanding of the approach dyanmics of the dispersed phase droplets, which in turn, governs the drinage (of the thin continuous film between the droplets) dynamics. Theoretical and Experimental studies mainly focus on head-on collisions between such droplets and the subsequent coalescence process. In reality, however, concentrated emulsions consist of a large number of droplets in a small amount of space, resulting in non-head-on contact/collision among droplets where the dynamics is surely different to that for head-on collisions. In this work, the effect of the angle of attack, θ, on coalescence in oil-in-water emulsions has been investigated using the Lattice Boltzmann Method. We notice that an increase in the angle of attack leads to a decrease in the collision time and the coalescence time. The decrease in the collision time is due to the geometric layout of the collision course and a local flow caused by the shear stress exerted by the droplets on the thin film in between. Once the film has drained enough, film rupture occurs, and a thin bridge forms between them, which defines the moment of collision. Finally, we also incorporate local changes in viscosity and interfacial tension during the non-head-on collisions.   

Diffusion-mediated Spinodal Decomposition in Ternary Mixtures

Ternary mixtures can undergo phase separation in response to concentration changes. It has been observed that a ternary mixture of oil-water-ethanol in a microchannel with water leads to the formation of a phase separating front, leaving oil- and water-rich stripes in its wake due to ethanol diffusion out of the mixture. We explore these dynamics via a system that is comprised of a stable ternary mixture and a stable single-component phase in contact. This interface allows for the preferential diffusion of component 3 out of the mixture (mimicking ethanol), causing the mixture to become unstable and undergo spinodal decomposition from the interface. By rewriting a Flory-Huggins free energy, assuming for simplicity that the interaction parameters involving component 3 are zero, we get an effective binary mixture description, parameterized by component 3. This allows the ternary mixture to potentially become unstable once component 3 concentration goes below a cut-off value. Using Cahn-Hilliard dynamics, we explore features of diffusion-mediated patterns such as length scale, phase composition, and front velocity. We can then extend this model to microfluidic systems for industrial use such as aqueous two-phase co-flows, where advection can affect the phase-separated patterns.   

Phase Distribution in a Sheared High-Viscosity Two-Fluid Immiscible Mixture

Mixing immiscible fluids where the volume fraction of one phase is much lower than for the other phase usually results in a mixture where the low volume fraction phase consists of drops or bubbles dispersed in a contiguous phase. When the volume fractions are comparable, however, the structure of the phase boundary is much more complex, often resulting in a co-continuous mixture. Understanding the structure of a mixture of immiscible fluids is important for many reasons, including the formation of polymer mixtures, which motivates the present study. The effect of volume fraction on the mixing and phase distribution in a sheared high viscosity immiscible mixture of two Newtonian fluids is examined by fully resolved numerical simulations. The densities of the phases are the same, but one is more viscous than the other. The results show that when the volume fraction of the phases is different, the low-volume fraction phase consists of drops dispersed in the high-volume fraction phase, but when the volume fraction of the phases are the same, the distribution is co-continuous. We show how the various measures of the mixture change with volume fraction and viscosity contrast. Preliminary results for more complex non-Newtonian material models are also discussed.   

Plunging jets and three phase flow: Modeling foundry physics in the laboratory

Metal casting, a prominent example of two phase flow, is susceptible to defects from air entrainment. Air entrainment is the capturing of air by a plunging jet, pulling it under the surface where it can be trapped. However, for some alloys, contact between the molten metal and even trace amounts of gaseous oxygen rapidly forms a solid oxide film at the interface, which can alter the physics substantially. Such a phenomenon warrants closer investigation, yet is difficult to model under conditions amenable to room temperature optical measurement methods commonly used in fluid dynamic analysis. We have found a specific liquid phenolic urethane resin, which when exposed to an amine vapor catalyst, will rapidly form a thin solid film, enabling analog laboratory investigations of a phenomenon previously limited to high-temperature foundry environments. The current work utilizes a disturbed plunging jet flow system to induce air entrainment into this three phase system. Using a high speed camera, we examine interactions between the solid film, gaseous, and liquid phases, revealing new air entrainment and multiphase flow phenomena.   

Hydrophilic oil-absorbent with macroscopic pores for recovery of high-viscosity oil

Oleophilic absorbents are widely utilized in most oil spills for cleaning up, small pore size of these oleophilic absorbents presents challenges in recovering high-viscosity oil from the ocean. Additionally, the difficulty in taking back the recovered oil from the absorbent causes a secondary pollution that they are supposed to be burnt. In this talk, we present a hydrophilic absorbent that can recover high-viscosity oils by its millimeter-scaled pore. To determine the optimal pore size, we systematically tuned the pore size in a millimeter scale by 3d printing technology. Polydopamine coating was then applied to provide a hydrophilic surface. To present, hydrophilic oil-absorbent have a better oil-recovery capability than conventional oleophilic absorbents. They also show unique reusability by virtue of the water film which helps to detach oil from the absorbent when an impulsive vibration is applied. Moreover, it is observed that the hydrophilic oil-absorbent can recover more oil as the absorbent thickness increases, which is hard to be realized by using the oleophilic absorbent. Hydrophilic oil-absorbents have an additional advantage in oil-recovery compared to oleophilic absorbents as the thickness of the absorbent increases.   

Oil-mineral aggregate formation: effects of concentration and flow

Multiphase flows are ubiquitous in various industries, and in nature. Dispersed oil droplets in these flows can capture sediment to form oil-mineral aggregates (OMAs). OMAs can be detrimental to industrial processes (e.g. buildup in pipes), but can also facilitate marine oil spill cleanup. While the formation of OMAs has been studied in some depth, it remains unclear how aggregation rate and aggregate properties vary with constituent concentrations and turbulence intensity. To begin to fill this gap, we aggregate oil and kaolinite clay at various concentrations via differential sedimentation in a cylindrical roller tank. After several hours, we measure the resulting size distribution of OMAs and quantify size, shape, and other properties. These results provide insight into formation rate and other environmentally impactful quantities such as settling/rising velocities. We also establish a baseline for studying the effects of turbulence intensity on OMA formation, presenting the design of a new experimental facility and procedure for investigating this problem. Our approach will enable a more detailed and definitive investigation of the formation rates and characteristics of OMAs, yielding a greater understanding of their behavior in both industrial and environmental flows.   

Computational Studies of the Dynamics of Disperse Gas-Liquid-Solid Mixtures

Froth flotation, where buoyant bubbles are used to separate hydrophobic particles from hydrophilic ones in a slurry and bring them to the top of a tank where they can be skimmed off, is the most widely used mineral separation technique. While many of the processes involved are reasonably well understood, their complex interactions make it difficult to predict the overall selectivity. Here, fully resolved numerical simulations, where the bubbles are followed using a front-tracking/finite volume method and the solid particles are included as rigid regions of different density, are used to examine the rate of capture of hydrophobic particles by a buoyant bubble. Heavy hydrophobic particles colliding with a gas bubble attach to the bubble and are carried with it as it rises and here a single bubble in a periodic domain containing several particles is followed for a long enough time for the bubble to gather most of the particles. The effect of the volume fraction and size of solid particles, and the deformability of the bubble on the rate of accumulation of particles on the bubble is examined for modest bubble Reynolds numbers. Preliminary results for several bubbles rising through a suspension of both hydrophobic and hydrophilic particles are also shown.