Fluid-fluid Interface Research Articles

Influence of interface on nondeformable micropolar drop migration

Abstract In this article, an analytical approach is considered to study the issue of specifying Stokesian motion due to a micropolar sphere drop translating at a concentric instantaneous position within a spherical fluid-fluid interface that divides two immiscible fluids, one of which is bounded and the other is unbounded. Here, the focus is on the situation where there are two microstructure-related fluid phases (micropolar fluids) out of the three. The motion is considered to have low Reynolds numbers; thus, the drop's surface and fluid-fluid interface have insignificant deformation. For both the components of the microrotation and velocity, general solutions to the slow axisymmetric motion of the micropolar/viscous fluid in a spherical coordinate system are obtained based on a concentric position. Boundary conditions are fulfilled at the drop's surface and the fluid-fluid interface. Especially, the boundary condition for the microrotation-vorticity is utilised at the fluid-fluid interface; while the continuity of tangential couple stress and microrotation are also utilised at the drop's surface. Findings indicate that the normalised hydrodynamic force increases monotonically as the droplet-to-interface radius ratio increases, acting on a moving micropolar sphere droplet and becoming unlimited when the drop's surface touches the fluid-fluid interface. The numerical findings for the normalised force operating on the micropolar sphere droplet at different values of the suitable parameters are introduced in both graphical and tabular form. Our numerical findings are compared with the suitable data for the special cases stated in the literature. This current investigation is significant within the domains of industrial, biological, medicinal, and natural processes, for example, liquid-liquid extraction, raindrop formation, blood cells moving through a vein or artery, suspension rheology, sedimentation, and coagulation.

Hybrid particle-phase field model and renormalized surface tension in dilute suspensions of nanoparticles

We present a two-phase field model and a hybrid particle-phase field model to simulate dilute colloidal sedimentation and flotation near a liquid-gas interface (or fluid-fluid interface in general). Both models are coupled to the incompressible Stokes equation, which is solved numerically using a combination of sine and regular Fourier transforms to account for the no-slip boundary conditions at the boundaries. The continuum two-phase field model allows us to analytically solve the equilibrium interfacial profile using a perturbative approach, demonstrating excellent agreement with numerical simulations. Notably, we show that strong coupling to particle dynamics can significantly alter the liquid-gas interface, thereby modifying the liquid-gas interfacial tension. In particular, we show that the renormalized surface tension is monotonically decreasing with increasing colloidal particle concentration and decreasing buoyant mass. Published by the American Physical Society 2024

Molecular dynamics study of the thermal radiatively pressure-driven flow of two immiscible hybrid nanofluids through a curved pipe with viscous dissipation

Hybrid nanomaterials significantly enhance thermal systems through improved thermal conductivity, efficient energy storage, and customized thermomechanical properties. Due to their superior thermophysical characteristics, hybrid nanofluids are crucial in fields such as industry, biomedicine, transportation, and pharmaceuticals. Therefore, the current article scrutinizes the characteristics of heat transfer on the thermally radiative flow of two immiscible hybrid nanofluids through a curved pipe induced due to a pressure gradient in an axial direction. The pipe is divided into two distinct regions: namely, (i) Region 1 (core) is filled with base fluid kerosene oil containing copper (Cu) and carbon nanotube (CNT) nanoparticles, while (ii) Region 2 (peripheral) is filled with base fluid water containing zinc oxide (ZnO) and aluminum oxide (Al2O3) nanoparticles. The complex curvilinear coordinates called toroidal coordinates are used to form a mathematical model for the present problem. The fluid in the core region is assumed to be more viscous than that of the peripheral region as such types of flows are observed in real life (viz. blood flow through arteries). Equations governing the flow are considered without ignoring any curvature ratio terms and are solved analytically by considering the perturbation series. The continuity of velocities and shear stresses at the fluid-fluid interface is taken into account along with no-slip, symmetric, and regularity conditions while solving the two-fluid flow problem under consideration. The effect of various fluid parameters such as curvature ratio, Reynolds number, viscosity ratio, and density ratio on the axial velocity and temperature is studied through 2-dimensional graphs, contour plots, and streamlines. The results show that the axial velocity of immiscible fluids flow decreases with an increase in the concentration of nanomaterials. Heat transport characteristics of nanofluid are increased by the addition of nanomaterials.

A coupled local front reconstruction and immersed boundary method for simulating 3D multiphase flows with contact line dynamics in complex geometries

Multi-phase flows in the presence of complex solid geometries are encountered widely throughout industrial processes to intensify mass and heat transfer processes. The efficiency of these processes relies largely on the predominant fluid dynamics regime inside the reaction vessel (e.g. trickle bed, bubble column reactor). The prevailing flow structure is influenced by many factors including the nature of the fluid-solid interactions (i.e. wetting or non-wetting). Such flows are often studied using front-capturing techniques to capture the fluid-fluid interface in combination with an auxiliary model to account for fluid-solid interactions. However, these front-capturing methods have difficulties in accurately representing the interface. Therefore, we adopted a front-tracking method: the Local Front Reconstruction Method (LFRM). In this study, LFRM is coupled with the Immersed Boundary method to incorporate the no-slip boundary condition at the solid surface. The model performance is assessed using droplet spreading simulations, where the equilibrium droplet shape (i.e. radius, height, and outline), the interfacial pressure difference, and the surface tension force are compared to analytical solutions and literature data. The results show an excellent match with the analytical solutions, and additionally superior performance to state-of-the-art volume tracking models.

Nanoparticle transport in partially saturated porous media: Attachment at fluid interfaces

Like the solid-water interface (SWI), air-water and oil-water interfaces (AWI and OWI) also act as collectors for nano-sized particles in porous media. The attachment of hydrophobic nanoparticles, which is often favorable and irreversible, is of particular interest because the transport and retention of such particles is closely linked to the fate of nanoplastics in unsaturated subsurface environments and the success of nanoremediation practices. Here, we show how a pore-network model (PNM) can be used to upscale the kinetics and extent of irreversible nanoparticle attachment at a single fluid-fluid interface under conditions of advection and dispersion in a sphere packing. By focusing on a trapped (immobile) non-wetting phase, we highlight a fundamental difference between the single-collector contact efficiency of AWI/OWI and SWI. Namely, AWI/OWI collectors, which are largely by-passed by the flowing aqueous phase, are exposed to a hydrodynamic environment dominated by diffusion. This difference has profound implications for the modelling of nanoparticle transport in porous media at the continuum (Darcy) scale. This study reveals the potential of pore network modelling as an essential complement to continuum models for upscaling the behavior of nanocolloids in porous media.

Rheological impact of viscous fluid in the core region of heated curved pipe surrounded by Casson rheological fluid

The immiscible fluids can help design more efficient systems for drug delivery and understanding the blood flow through diseased arteries. It can also have implications for the design of flow control devices or medical implants that involve curved geometries. Therefore, the current article scrutinizes the characteristics of heat transfer on the flow of two immiscible Casson and Newtonian fluids through a curved pipe induced due to a pressure gradient in an axial direction. The pipe is divided into two distinct regions: namely, (i) Region 1 (core) is filled with Newtonian fluid while (ii) Region 2 (peripheral) is filled with non-Newtonian Casson fluid. The complex curvilinear coordinates called toroidal coordinates are used to form a mathematical model for the present problem. Equations governing the flow are considered without ignoring any curvature ratio terms and are solved analytically by considering the perturbation series. The continuity of velocities and shear stresses at the fluid-fluid interface is taken into account along with no-slip, symmetric, and regularity conditions while solving the two-fluid flow problem under consideration. The effect of various fluid parameters such as curvature ratio, Casson fluid parameter, Reynolds number, viscosity ratio, density ratio, Eckert number, and conductivity ratio on the axial velocity and temperature is studied through 2-dimensional graphs and contour plots. In addition, the volumetric flow rate and shear stress are also presented to evaluate the effects of various key parameters. The results show that the axial velocity of immiscible fluids flow increases with an increase in the values of the viscosity ratio parameter and the fluid temperature is decreased by increasing the conductivity ratio parameter.

Marangoni flows triggered by cationic-anionic surfactant complexation

HypothesisThe gradients in surfactant distribution at a fluid-fluid interface can induce fluid flow known as the Marangoni flow. Fluid interfaces found in biological and environmental systems are seldom clean, where mixtures of various surfactants are present. The presence of multi-component surfactant mixtures introduces the possibility of interactions among constituents, which may impact Marangoni flows and alter flow dynamics. ExperimentsWe employed flow visualization, surface tension and reaction kinetic measurements, and numerical simulations to quantitatively investigate the Marangoni flows induced by the reacting surfactant mixtures. Different binary surfactant mixtures were utilized for comparative analysis. FindingsThe impact of surfactant interactions on Marangoni flows is confirmed through the observation of diverse complex flow patterns that result from the combination of oppositely charged surfactants in varying composition ratios and concentrations. Unique flow patterns originate from the composition-dependent interfacial phenomena upon mixing surfactants. Our findings provide vital insights that could be used to guide the development of effective oil remediation or the spreading of waterborne pathogens in contaminated regions.

A coupled VOF/embedded boundary method to model two-phase flows on arbitrary solid surfaces

We present an hybrid VOF/embedded boundary method allowing to model two-phase flows in presence of solids with arbitrary shapes. The method relies on the coupling of existing methods: a geometric Volume of fluid (VOF) method to tackle the two-phase flow and an embedded boundary method to sharply resolve arbitrary solid geometries. Coupling these approaches consistently is not trivial and we present in detail a quad/octree spatial discretization for solving the corresponding partial differential equations. Modelling contact angle dynamics is a complex physical and numerical problem. We present a Navier-slip boundary condition compatible with the present cut cell method, validated through a Taylor–Couette test case. To impose the boundary condition when the fluid–fluid interface intersects a solid surface, a geometrical contact angle approach is developed. Our method is validated for several test cases including the spreading of a droplet on a cylinder, and the equilibrium shape of a droplet on a flat or tilted plane in 2D and 3D. The temporal evolution and convergence of the droplet spreading on a flat plane is also discussed for the moving contact line given the boundary condition (Dirichlet or Navier) used. The ability of our numerical methodology to resolve contact line statics and dynamics for different solid geometries is thus demonstrated.

Oscillations of a spherical particle in the presence of a flat interface separating two fluid phases

An analytical–numerical approach based on collocation techniques is introduced to examine the challenge of characterizing Stokes flow induced by a spherical particle in perpendicular motion to a plane interface that divides two semi-infinite, immiscible viscous fluid phases. The movement is examined under the conditions of low Reynolds and capillary numbers, where the interface undergoes negligible deformation. We contemplate both the rectilinear oscillations along and the rotational oscillation around an axis that is perpendicular to the interface. A comprehensive solution is formed by combining basic solutions in both cylindrical and spherical coordinate systems through superposition. Firstly, the boundary conditions at the fluid–fluid interface are fulfilled through Fourier–Bessel transforms, followed by addressing the conditions at the particle’s surface using a boundary collocation scheme. The drag force and torque coefficients, both in-phase and out-of-phase, acting on the particle are determined with satisfactory convergence across different geometric and physical parameter values. These results are illustrated through graphs and tables. We compare our results of drag force and torque coefficients with existing data in the literature, specifically for the limiting cases. The outcomes of this study highlight the substantial impact of the interface on both drag force and torque coefficients. This inquiry is driven by the necessity to enhance our comprehension of the fluid tapping mode in atomic force microscope devices, particularly when this mode involves an interface substrate with another fluid.

Effect of Micromixer Design on Lipid Nanocarriers Manufacturing for the Delivery of Proteins and Nucleic Acids.

Lipid-based nanocarriers have emerged as helpful tools to deliver sensible biomolecules such as proteins and oligonucleotides. To have a fast and robust microfluidic-based nanoparticle synthesis method, the setup of versatile equipment should allow for the rapid transfer to scale cost-effectively while ensuring tunable, precise and reproducible nanoparticle attributes. The present work aims to assess the effect of different micromixer geometries on the manufacturing of lipid nanocarriers taking into account the influence on the mixing efficiency by changing the fluid-fluid interface and indeed the mass transfer. Since the geometry of the adopted micromixer varies from those already published, a Design of Experiment (DoE) was necessary to identify the operating (total flow, flow rate ratio) and formulation (lipid concentration, lipid molar ratios) parameters affecting the nanocarrier quality. The suitable application of the platform was investigated by producing neutral, stealth and cationic liposomes, using DaunoXome®, Myocet®, Onivyde® and Onpattro® as the benchmark. The effect of condensing lipid (DOTAP, 3-10-20 mol%), coating lipids (DSPE-PEG550 and DSPE-PEG2000), as well as structural lipids (DSPC, eggPC) was pointed out. A very satisfactory encapsulation efficiency, always higher than 70%, was successfully obtained for model biomolecules (myoglobin, short and long nucleic acids).

Lattice Boltzmann method for particulate multiphase flow system

This study proposes a numerical model for particulate three-phase flow in microchannels based on multiphase lattice Boltzmann method (LBM). The model combines the color-gradient method to track the immiscible fluid-fluid interface and the two-fluid model (TFM) to describe particle-particle and particle-fluid interactions, which can efficiently simulate transport and displacement processes involving large amounts of particles. A mixture-rheology TFM algorithm is proposed by introducing a mixture phase with rheology properties obtained from experiments instead of the conventional TFM particle phase with artificial viscosity models. Multi-relaxation-time (MRT) collision operator and GPU computing are adopted to enhance the numerical stability and efficiency. Various theoretical benchmarks for particle transport and two-phase flow are performed respectively to verify the accuracy of the proposed model. Exceptional consistency between results from particulate three-phase flow simulation and microfluidic experiments further confirms the reliability of our model, especially in capturing the inertial lagging and accumulation phenomena under multiphase and porous flow conditions. The proposed numerical framework will benefit our understanding of multiphase displacement with microgels in microchannels with complex geometries.

Detachment of a Soluble Particle at the Slag-Argon Interface: CFD Study and Experimental Observations

The behavior of non-metallic inclusions at interfaces of high-temperature melt and molten slag affects the removal of inclusions and the consequent melt cleanness. This study presents real-time in situ observations on the behavior of an oxide particle in the vicinity of the slag-argon interface by means of high-temperature confocal scanning laser microscopy (HT-CSLM). On top of that, CFD simulations are conducted to investigate the underlying mechanisms of particle-interface interactions. In addition to revealing the particle motion process from the argon phase toward the slag, a significant particle morphology alteration associated with its dissolution in the slag is experimentally observed. Particularly, upon detachment from the slag-argon interface, the particle exhibits more dissolution at the near-interface area. By combining with numerical simulations, this study indicates that particle separation at the interface can be characterized as two stages. First, a short-term capillary force-driven motion stage happens until the particle initially settles at the interface. The settling position estimated by simulation shows good consistency with experimental measurement. Second, the particle takes a relatively long time to eventually detach from the interface, and this period is accompanied by particle dissolution. Investigations suggest that the concentration variation near the interface arising from particle dissolution triggers a Marangoni flow. This flow, in turn, enhances the local dissolution rate, consequently causing a significant particle morphology change that influences the detachment. This study provides new insight into the mechanism of inclusion removal through slag absorption in metallurgical processes. Both particle dynamics and dissolution kinetics, especially the effect of solutal Marangoni convection, are highlighted in detaching a small-scale particle from the fluid-fluid interface.

BIMBAMBUM: A potential flow solver for single cavitation bubble dynamics

In the absence of analytical solutions for the dynamics of non-spherical cavitation bubbles, we have implemented a numerical simulation solver based on the boundary integral method (BIM) that models the behavior of a single bubble near an interface between two fluids. The density ratio between the two media can be adjusted to represent different types of boundaries, such as a rigid boundary or a free surface. The solver allows not only the computation of the dynamics of the bubble and the fluid-fluid interface, but also, in a secondary processing phase, the computation of the surrounding flow field quantities. We present here the detailed implementation of this solver and validate its capabilities using theoretical solutions, experimental observations, and results from other simulation softwares. This solver is called BIMBAMBUM which stands for Boundary Integral Method for Bubble Analysis and Modeling in Bounded and Unbounded Media. Program summaryProgram Title: BIMBAMBUMCPC Library link to program files:https://doi.org/10.17632/89vv35pmhr.1Licensing provisions: GPLv3Programming language: C++ and PythonNature of problem: The code solves the axisymmetric dynamics of single cavitation bubble in the vicinity of different types of boundaries. The boundaries are treated as an interface between two fluids, where the fluids can have different density ratios. The two fluids are considered inviscid and incompressible and the associated flows irrotational so that Laplace's equation is valid everywhere.Solution method: A boundary integral method is used to calculate the velocities on the discretized bubble surface and the fluid-fluid interface. The position of these boundaries can then be updated in time using a Lagrangian approach. In the fluid domain surrounding the bubble, the velocities and pressure are estimated using a combination of the boundary integral method and finite differences.Additional comments including restrictions and unusual features: The code solves the bubble dynamics as long as its surface remains simply connected.

Buckling of a monolayer of platelike particles trapped at a fluid-fluid interface.

Particles trapped at a fluid-fluid interface by capillary forces can form a monolayer that jams and buckles when subject to uniaxial compression. Here we investigate experimentally the buckling mechanics of monolayers of millimeter-sized rigid plates trapped at a planar fluid-fluid interface subject to uniaxial compression in a Langmuir trough. We quantified the buckling wavelength and the associated force on the trough barriers as a function of the degree of compression. To explain the observed buckling wavelength and forces in the two-dimensional (2D) monolayer, we consider a simplified system composed of a linear chain of platelike particles. The chain system enables us to build a theoretical model which is then compared to the 2D monolayer data. Both the experiments and analytical model show that the wavelength of buckling of a monolayer of platelike particles is of the order of the particle size, a different scaling from the one usually reported for monolayers of spheres. A simple model of buckling surface pressure is also proposed, and an analysis of the effect of the bending rigidity resulting from a small overlap between nanosheet particles is presented. These results can be applied to the modeling of the interfacial rheology and buckling dynamics of interfacial layers of 2D nanomaterials.

Subphase Exchange Cell for Studying Fluid-Fluid Interfaces with Optical Microscopy.

A subphase exchange cell was designed to observe fluid-fluid interfaces with a conventional optical microscope while simultaneously changing the subphase chemistry. Materials including phospholipids, asphaltenes, and nanoparticles at fluid-fluid interfaces exhibit unique morphological changes as a function of the bulk-phase chemistry. These changes can affect their interfacial material properties and, ultimately, the emergent bulk material properties of the films, foams, and emulsions produced from such interfacial systems. In this work, we combine experiments, computational fluid dynamics simulations, and modeling to establish the operating parameters for a subphase exchange cell of this type to reach a desired concentration. We used the experimental setup to investigate changes to a graphene film during a common wet-etching transfer process. Observations reveal that capillary interactions can induce defects and deformations in the graphene film during the wet-etching process, an important finding that must be considered for any wet-etching transfer technique for 2D materials. More generally, conventional optical microscopy was shown to be able to image the dynamics of interfacial systems during a bulk-phase chemistry change. Potential applications for this equipment and technique include observing morphological dynamics of phospholipid film structure with subphase salinity, asphaltene film structure with subphase pH, and particle film synthesis with subphase chemistry.

Electrically mediated self-assembly and manipulation of drops at an interface.

The fluid-fluid interface is a complex environment for a floating object where the statics and dynamics may be governed by capillarity, gravity, inertia, and other external body forces. Yet, the alignment of these forces in intricate ways may result in beautiful pattern formation and self-assembly of these objects, as in the case of crystalline order observed with bubble rafts or colloidal particles. While interfacial self-assembly has been explored widely, controlled manipulation of floating objects, e.g. drops, at the fluid-fluid interface still remains a challenge largely unexplored. In this work, we reveal the self-assembly and manipulation of water drops floating at an oil-air interface. We show that the assembly occurs due to electrostatic interactions between the drops and their environment. We highlight the role of the boundary surrounding the system by showing that even drops with a net zero electric charge can self-assemble under certain conditions. Using experiments and theory, we show that the depth of the oil bath plays an important role in setting the distance between the self-assembled drops. Furthermore, we demonstrate ways to manipulate the drops actively and passively at the interface.

Dynamics of spreading of an asymmetrically placed droplet near a fluid-fluid interface.

Two-dimensional numerical simulations are carried out to study the spreading dynamics of a droplet placed in the vicinity of a fluid-fluid interface. Simulations are performed using the hybrid lattice-Boltzmann technique and the diffuse-interface model by considering three immiscible fluids of the same density and viscosity. In contrast to the well-studied spreading of drops placed symmetrically across fluid-fluid interfaces, this work considers the simultaneous migration, spreading and eventual adsorption of an asymmetrically placed drop. These processes, which are solely driven by interfacial forces, are characterised by monitoring the temporal evolution of geometric parameters, such as the centre of mass, radius and height of the drop, the surface energy of the three interfaces and the associated flow fields inside and outside the droplet. The rate of spreading and rate of adsorption are also calculated to determine the dominant processes that drive the dynamics of the system.

Impact of a spherical interface on a concentrical spherical droplet

<p>In this paper, an analytical and numerical technique are examined in order to analyse the Stokes flow determination problem due to a viscous sphere droplet moving at a concentric instantaneous position inside a spherical interface separating finite and semi-infinite immiscible fluid phases. Here, when only one of the three phases of the fluid (micropolar fluid) has a microstructure, attention is focused on this case. The motion is considered when Reynolds- and capillary-numbers are low, and the droplet surface and the fluid-fluid interface have insignificant deformation. A general solution is obtained in a spherical coordinate system based on a concentric position to analyse the slow axisymmetric movement of the micropolar fluid, considering microrotation and velocity components. Boundary conditions are initially fulfilled at the fluid-fluid interface and subsequently at the droplet surface. The normalised hydrodynamic drag force applying to a moving viscous droplet appears to be a function of the droplet-to-interface radius ratio, which increases monotonically and becomes unbounded when the droplet surface touches the fluid-fluid interface. The numerical outcomes of the normalised drag force acting on the viscous droplet are derived for different values of the parameters, and are presented in a tabular and graphical framework. A comparison was made between our numerical outcomes for the drag force and the pertinent data for the special cases found in the literature.</p>

Thermocapillary migration of a drop with a thermally conducting stagnant cap

Hypothesis The thermocapillary migration of a spherical drop with a stagnant cap in the presence of a constant applied temperature gradient can be strongly affected by the finite thermal conductivity of the stagnant cap.Numerics The heat conduction of the stagnant cap is analytically modeled. The effects of the additional interfacial stresses generated by the disturbances to the local temperature field due to the presence of the cap at the fluid-fluid interface and the corresponding velocity of migration of the drop are evaluated by solving for the temperature and hydrodynamic field equations in and around the drop. An asymptotic model is derived to predict the terminal velocity in the presence of an infinitely conducting stagnant cap.Findings The effects of the surface conductivity and size of the stagnation region alongside the bulk thermal conductivities and viscosities of the drop and surrounding media are evaluated. The terminal velocity of the drop is shown to have a monotonic dependence on the conductivity of the stagnant cap. The bounds to the terminal velocity increment due to the stagnant cap are derived. These bounds can be of significance to multiphysics problems involving particle laden drops, Pickering emulsions and other multi-phase technologies where the conductivity of the surface adsorbents is non-negligible.

Reduced-Order Model for Surfactant-Laden Electrified Sessile Droplets.

A comprehensive understanding of the physics of electrowetting of a surfactant-laden droplet is important for applications in rapid healthcare diagnostics. A majority of biological samples examined during point-of-care (POC) diagnostics are biofluids with dissolved surfactants, such as the respiratory droplets containing protein (mucin) and surfactant molecules like dipalmitoylphosphatidylcholine. The presence of these surfactant molecules is anticipated to have a significant impact on the performance of electrowetting-based POC diagnostic devices. A reduced-order model is developed using the weighted residual integral boundary layer theory for the electrowetting of a surfactant-laden sessile droplet in a parallel plate electrode configuration. Thin film evolution equations are obtained for the fluid-fluid interface, the surfactant concentration, the depth-integrated flow rate, and the interfacial charge density. We show that the presence of surfactants opposes and decreases the strength of the electrohydrodynamic flow due to Marangoni stress-driven convection. The droplet then responds to an AC field with a suppressed amplitude of oscillation and the same mean deformation as that under DC forcing. Thus, low-frequency AC forcing with a suitable surfactant can plausibly be employed as a viable alternative to more energy-intensive high-frequency AC forcing.