Immiscible Fluids Research Articles

APPLICATION OF AN EXACT SOLUTION OF SPECIAL TYPE OF THERMOSOLUTAL CONVECTION EQUATIONS FOR THE INVESTIGATION OF EVAPORATIVE THREE-DIMENSIONAL FLOWS

The characteristics of gas-liquid flows with evaporation at the thermocapillary interface in an infinite rectangular duct, with a linearly distributed thermal load being applied on the upper and lower walls, are studied. The theoretical research of the three-dimensional convective flows is carried out within the framework of a two-sided model of evaporative convection based on the Navier-Stokes equations in the Oberbeck-Boussinesq approximation. A solution of a special type of governing stationary equations is used for describing the heat and mass transfer in a system of two immiscible fluids. We investigate the influence of the working (equilibrium) temperature of the system and intensity of the external thermal load on the structure of the velocity and temperature fields, as well as on changes in the evaporation mass flow rate and vapor content in the gas phase. The simulations are performed for the ethanol-air system. Based on the comparison of the calculated and experimental data, an effective way of nondimensionalization is proposed that allows one to consistently take into account the impact of the gas pumping velocity being a controlled parameter in experiments. It provides correct matching of the mathematical model to the experiment conditions, as well as a better qualitative and quantitative agreement between theoretical and measured values of evaporative mass flow rate. The results of the present study can aid in developing a theoretical basis for experimental research methods of evaporative convection and also in designing equipment for thermal coating or drying.

Flow and clogging of capillary droplets.

Capillary droplets form due to surface tension when two immiscible fluids are mixed. We describe the motion of gravity-driven capillary droplets flowing through narrow constrictions and obstacle arrays in both simulations and experiments. Our new capillary deformable particle model recapitulates the shape and velocity of single oil droplets in water as they pass through narrow constrictions in microfluidic chambers. Using this experimentally validated model, we simulate the flow and clogging of single capillary droplets in narrow channels and obstacle arrays and find several important results. First, the capillary droplet speed profile is nonmonotonic as the droplet exits the narrow orifice, and we can tune the droplet properties so that the speed overshoots the terminal speed far from the constriction. Second, in obstacle arrays, we find that extremely deformable droplets can wrap around obstacles, which leads to decreased average droplet speed in the continuous flow regime and increased probability for clogging in the regime where permanent clogs form. Third, the wrapping mechanism causes the clogging probability in obstacle arrays to become nonmonotonic with surface tension Γ. At large Γ, the droplets are nearly rigid and the clogging probability is large since the droplets can not squeeze through the gaps between obstacles. With decreasing Γ, the clogging probability decreases as the droplets become more deformable. However, in the small-Γ limit, the clogging probability increases since the droplets are extremely deformable and wrap around the obstacles. The results from these studies are important for developing a predictive understanding of capillary droplet flows through complex and confined geometries.

Swirling flow of two immiscible fluids in a cylindrical container: Lattice Boltzmann and volume-of-fluid study

An experimental and numerical study of a multicomponent swirl flow of a liquid in a closed cylinder is carried out for various values of the relative cylinder elongation and the Reynolds number. The experimental technique for flow characteristics measurement is based on the PIV (particle image velocimetry) technique. To study the flow characteristics in detail, we simulated the problem numerically using the Palabos and Basilisk software open-source packages. The current implementation of the Palabos package uses the LBM (lattice Boltzmann method) approach, in which the collision integral is determined by the MRT (multiple-relaxation-time) approximation, and the intercomponent interaction is established according to the Shan–Chen pseudopotential approximation. The Basilisk package uses VOF (volume-of-fluid) approach to approximate the fluid interface. In this paper, for the first time, the data considering the emergence conditions for the zone of axial isolated recirculation in a multicomponent vortex flow were obtained at different viscosity ratios of two fluids. It is shown that with a decrease in the viscosities ratio, the recirculation zone existence curve shifts closer to that corresponding to the case of a one-component flow. In the course of numerical analysis, we found that both numerical implementations of this problem describe flow characteristics with high accuracy. Both methods recreate the recirculation zone on the cylinder axis observed experimentally. However, the velocity shift on the interface is observed only in the LBM approach.

STABILITY OF THE INTERFACE OF LIQUIDS OSCILLATING IN A VERTICAL FLAT CHANNEL

The stability of an oscillating interface between two immiscible low-viscosity fluids of different densities in a vertical flat channel with a harmonic change in the liquid flow rate is studied experimentally. The limiting case of high dimensionless oscillation frequencies when the layer width exceeds the thickness of the Stokes layer is considered. It is found that a standing wave with a length significantly exceeding the gap width develops on the oscillating interface upon reaching a critical amplitude. It is shown that the discovered oscillations are gravity-capillary waves similar to Faraday ripples oscillating with the frequency of the driving force. The wavelength is determined by the interface oscillation frequency and the gravity acceleration and agrees well with the wavelength of gravity-capillary oscillations of the interface. A description of a new phenomenon is given.

Analytical and numerical investigation of viscous fluid-filled spherical slip cavity in a spherical micropolar droplet

<abstract><p>This article presents an analytical and numerical investigation on the quasi-steady, slow flow generated by the movement of a micropolar fluid drop sphere of at a concentrical position within another immiscible viscous fluid inside a spherical slip cavity. Additionally, the effect of a cavity with slip friction along with the change in the micropolarity parameter on the movement of the fluid sphere is introduced. When Reynolds numbers are low, the droplet moves along a diameter that connects their centres. The governing and constitutive differential equations are reduced to a computationally convenient form using appropriate transformations. By using the resulting linear partial differential equations for the stream functions and using the method of separation variables, we can obtain their solutions. General solutions for velocity fields are found using spherical coordinate systems, which are based on the concentric point of the cavity; this allows to obtain solutions to the Navier-Stokes equations internal and external to the spherical droplet. The vorticity-microrotation boundary condition is used in regard to the micropolar droplet case in a viscous fluid. The normalised drag forces acted upon the micropolar drop are illustrated via graphs and tables for diverse values of the viscosity ratio and drop-to-wall radius ratio, with the change of the spin parameter that attaches the microrotation to vorticity. The correction wall factor is shown to increase with an increase in the drop-to-wall radius ratio, when moving from the gas bubble case to the solid sphere case, with an increase in the micropolarity parameter, and with an increase in the slip frictional resistance. This study is relevant due to its potential uses in a variety of biological, natural, and industrial processes, including the creation of raindrops, the investigation of blood flow, fluid-fluid extraction, the forecasting of weather conditions, the rheology of emulsions, and sedimentation phenomena.</p></abstract>

Analytical solution of unsteady MHD immiscible fluid with thermal radiation and chemical reaction in a porous medium under heat source

Analytical solution of unsteady MHD immiscible fluid with thermal radiation and chemical reaction in a porous medium under heat source

Bubble Dynamics Within a Droplet: A New Mechanism for Mixing in Binary Immiscible Fluid Systems

Bubble Dynamics Within a Droplet: A New Mechanism for Mixing in Binary Immiscible Fluid Systems

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.

Pore-scale investigation on the effect of capillary barrier on two-phase displacement in dual-structure porous media

Although immiscible fluid–fluid displacement in porous media has received extensive attention, understanding the dynamics behavior within complex structures remains elusive. This study utilizes the direct numerical simulation by solving the Navier–Stokes equations and coupling with the volume of fluid method to examine oil–water flow in porous media across various contact angles θ and capillary number Ca. Three kinds of artificial porous media were generated with designed opening angle β, including single-structure and dual-structure models. A theoretical analysis of the capillary barrier phenomenon, as well as its occurrence conditions, is identified under water-wet conditions. Generally, when θ + β < 90°, the capillary force consistently drives oil displacement from throats to pores. Conversely, if θ + β > 90°, the direction of the capillary force can move toward the water phase side and prevent the fluid interface from continuing to move. For a single-structure porous medium, the dynamics behavior of fluids is controlled by the capillarity, wettability, and geometric structures. The greatest efficiency occurs when the condition θ + β = 90° is met, particularly at an intermediate Ca. For a dual-structure porous medium with smaller opening angles inside, the water phase tends to infiltrate the embedded pore structure due to weaker capillary barrier effects. Conversely, larger opening angles within the embedded structure lead to stronger capillary barrier effects, hindering water entry into the interior porous medium. This obstruction forces the water phase to bypass and traverse longer flow paths, resulting in the formation of a large amount of residual oil.

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>

Heat transport and flow structure in thermal convection with two liquid layers

We report an experimental investigation of the heat transport and flow field in a rectangular Rayleigh–Bénard convection (RBC) cell with two immiscible fluids: silicone oil and glycerol. The global heat transport of the system is divided into three ranges corresponding to the different flow structures formed in the glycerol layer. In range I, the glycerol layer is dominated by conduction, and no plume is formed over the interface. In range II, cellular rolls are formed in the glycerol layer and the horizontal motion of rolls causes an oscillation of temperature in the interface. In range III, the cellular pattern is time-independent, and the interface forms a group of wavelets with wave numbers consistent with the mode of the cellular pattern. In lower-thin glycerol, the Nusselt (Nu) grows from conduction to convection through an oscillating subcritical bifurcation at critical Rayleigh number $Ra_c$ . The value of $Ra_c$ in the present work is smaller than the theoretical prediction of both-rigid boundaries and greater than the prediction of one-rigid and one-free boundaries. In the upper-thick silicone oil layer, $Nu$ increases with increasing $Ra$ , but it is smaller than that of traditional RBC. For the silicone oil layer in two-layer RBC, the hot plumes emitting over the liquid–liquid interface showed different shape and different velocity from cold plumes emitting from the top rigid plate. This implies that the velocity boundary condition strongly influences the flow structure in turbulent convection.

Capillary-lubrication force exerted on a two-dimensional particle moving towards a thin fluid film

A rigid object moving in a viscous fluid and in close proximity to an elastic wall experiences self-generated elastohydrodynamic interactions. This has been the subject of intense research activity, with recent and growing attention given to the particular case of elastomeric and gel-like substrates. Here, we address the situation where the elastic wall is replaced by a capillary surface. Specifically, we analyse the lubrication flow generated by the prescribed normal motion of a rigid infinite cylinder near the deformable interface separating two immiscible and incompressible viscous fluids. Using a combination of analytical and numerical treatments, we compute the emergent capillary-lubrication force at leading order in capillary compliance, and characterize its dependencies with the interfacial tension, viscosities of the fluids, and length scales of the problem. Interestingly, we identify two main contributions: (i) a velocity-dependent adhesive-like force; (ii) an acceleration-dependant inertia-like force. Our results may have implications for the mobility of colloids near complex interfaces and for the motility of confined microbiological entities.

Surface tension effects between two immiscible Stokes fluids: a computational study using unfitted hybrid high-order methods and a level-set scheme

Surface tension effects between two immiscible Stokes fluids: a computational study using unfitted hybrid high-order methods and a level-set scheme

Design and operation of a von Kármán reactor for droplet breakage experiments

The dispersion of an immiscible fluid in a turbulent liquid flow is a frequent occurrence in various natural and technical processes, with particular importance in the chemical, pharmaceutical, mining, petroleum, and food industries. Understanding the dynamics and breakup of liquid droplets is crucial in many scientific and engineering applications, as poor control and optimization of droplet systems results in significant financial losses annually. Although a theoretical background for describing droplet breakup exists, many assumptions still require experimental verification. Numerous mathematical models have been proposed to describe the rate coefficient of droplet breakup and child distribution functions. However, the validation and discrimination between models have been hindered by the lack of experimental data gathered under well-controlled and well characterized conditions. Thus, to validate the current models, novel equipment and methodology for optical droplet breakage research are required. In this work, a von Kármán swirling flow apparatus was designed and constructed to carry out optical based droplet breakage experiments under low-intensity, homogeneous turbulent flow. The methodology presented here describes the procedure for generating and controlling the size of the droplets being injected into the homogeneous turbulent flow field. The experiments involved introducing single droplets into the test section, using peanut oil to be the droplet phase and the continuous phase is water. Automated image analysis algorithms were utilized to determine breakage time, breakage probability, and child droplet size distribution for different turbulence intensities.

Evaluation of advection schemes and surface tension model for algebraic and geometric VOF multiphase flow solvers

This paper addresses the validation and verification of numerical models for complex multiphase flows involving immiscible fluids. Specifically, the focus is on the dynamics of the interface between the fluids, which remains a challenge in many applications. Previous studies have primarily examined simpler flows with limited complexity, while real-world scenarios involve intricate interfaces and turbulent dynamics. To overcome this, a representative test case involving the motion of an oil cube within a water cube proposed by [12] is used. Different computational models using volume-of-fluid (VOF) approaches are validated and compared, with particular attention given to the influence of numerical schemes for convective terms. The impact of these schemes on integral quantities and interface dynamics is analyzed. Particular attention is paid at the surface tension contribution to the energy budgets, which is usually neglected in the available literature. Furthermore, it is shown here that, the model adopted for the surface tension is responsible for an additional contribution to numerical dissipation. To the authors' knowledge, it is the first time that a detailed analysis of such aspects is presented.

Marangoni-driven spreading of a droplet on a miscible thin liquid layer

HypothesisThe coalescence of droplets with liquid–gas interfaces of different surface tensions is common in nature and industrial applications, where the Marangoni-driven film spreading is an essential process. Unlike immiscible fluids governed by triple contact line dynamics, the mixing between two miscible fluids strongly couples with the film spreading process, which are expected to manifest distinct power-law relations for the temporal increase in the film radius. ExperimentsWe experimentally investigate the Marangoni-driven film spreading phenomenon for a droplet with lower surface tension dropping onto a miscible, thin liquid layer. The temporal growth of the film radius was detected by using a novel deep convolutional neural network, the U2-net method. Scaling analysis was performed to interpret the spreading dynamics of the film. FindingsWe find that the film radius exhibits a three-stage power-law relation over time, with the exponent varying from 1/2 to 1/8, and back to 1/2. The diffusion-affected Marangoni stresses in these three stages were derived, and two estimations of viscous stress were considered. Through estimating and balancing the viscous stress with the Marangoni stress, the three-stage power-law relation was derived and validated.

Robust surface light scattering spectroscopy for fluid interfaces

Surface Light Scattering Spectroscopy (SLSS) can characterize the dynamics of an interface between two immiscible fluids by measuring the frequency spectrum of coherent light scattered from thermophysical fluctuations—‘ripplons’. In principle, and for many interfaces, SLSS can simultaneously measure surface tension and viscosity, with the potential for higher-order properties, such as surface elasticity and bending moments. Previously, this has been challenging. We describe and present some measurements from an instrument with improvements in optical design, specimen access, vibrational stability, signal-to-noise ratio, electronics, and data processing. Quantitative improvements include total internal reflection at the interface to enhance the typically available signal by a factor of order 40 and optical improvements that minimize adverse effects of sloshing induced by external vibrations. Information retrieval is based on a comprehensive surface response function, an instrument function, which compensates for real geometrical and optical limitations, and processing of almost real-time data to report results and their likely accuracy. Detailed models may be fit to the power spectrum in real time. The raw one-dimensional digitized data stream is archived to allow post-experiment processing. This paper reports a system design and implementation that offers substantial improvements in accuracy, simplicity, ease of use, and cost. The presented data are for systems in regions of low viscosity where the ripplons are underdamped, but the hardware described is more widely applicable.

The Rosensweig instability at the interface between ferrofluids and immiscible fluids

In this study, the Rosensweig instability at the interface between ferrofluids and other immiscible fluids is systematically studied. Stable water based ferrofluids with saturated magnetization as high as 25.4 kA/m are successfully synthesized. The surface tension, density and viscosity of water based ferrofluids used in this study are systematically and scientifically studied. Concentrated coils magnetic field generator is constructed to evaluate the experimental results of Rosensweig instability at the interface between ferrofluids and immiscible fluids. Combined with the theoretical results, the simulation results are obtained from our model to evaluate the Rosensweig instability at the interfaces. The well accordance between experimental results and the theoretical simulation results indicates that the Rosensweig instability is easily generating at interfaces between ferrofluids and oils than the interfaces between ferrofluids and air. This result could be attributed to the surface tension and buoyance of liquids on the ferrofluids.

Free-energy-based lattice Boltzmann model for emulsions with soluble surfactant

We propose a diffuse interface model to simulate a system of two immiscible liquids with surfactant. This model is based on a modified Ginzburg-Landau free energy functional to account for non-ionic soluble surfactants and couples the Navier-Stokes equations with two Cahn-Hilliard transport equations to represent immiscible fluids and surfactant concentration. The governing equations are solved using a lattice Boltzmann framework. The proposed model is validated for Langmuir and Frumkin adsorption isotherms when applied to simulate a planar interface and a spherical drop equilibration. The model ensures numerical stability and accurate results for low and high surfactant concentrations, and the diffuse interface thickness remains constant even for high surfactant loads. The model also allows achieving a surface tension reduction of 45-50% compared to the clean system, even at low surfactant concentrations. The appropriate surfactant mobility and solubility values are recommended for different values of the strength of nonlinear surfactant coupling.

Influence of non-linear slip dependent zeta potential on the bi-layered electrohydrodynamic flow in an electrically actuated microsystem

In this paper, the electro-osmotic flow (EOF) of two immiscible fluids through an electrically actuated micro-slit with a non-linear slip-dependent zeta potential is considered. The main objective of this work is to enhance the EOF velocity of non-polar fluid with an intensive flow variation in micro-confinements. We present the comparison between the Poisson–Nernst–Planck (P–N–P) and the Poisson–Boltzmann model and illustrate the impact of different parameters, such as Debye–Hückel parameter, slip coefficient, and interfacial potential drop, on the ionic concentration and the induced potential in detail. In this study, the interface between two immiscible fluids is considered to be planar, and a potential drop is observed close to the interface due to the development of back-to-back diffuse layers. At the interface between two layers, the continuity of the velocity and total stresses (Maxwell stress and shear stress) are taken into account to investigate the flow field in the system of immiscible electrolytes. The P–N–P model, linked with the ion transport equation and the Poisson equation, is employed to describe the motion of electrolyte solutions. The non-linear governing equations are numerically computed using a pressure-correction-based finite volume technique based on a staggered grid algorithm. Closed-form analytical solutions are derived for both steady and unsteady EOF field of two immiscible fluids for the low wall zeta potential and non-overlapping electrical double layer. The analytical solutions are well validated with our numerical results under suitable assumptions. It is also observed that the slip-dependent zeta potential successfully provides a considerable enhancement in EOF velocity over a broad range of parameters such as zeta potential, Debye–Hückel parameter, as well as boundary slip parameter. The results for both layers are highly affected by unequal wall potential, and the ion concentrations are highly actuated by the external electric field.