Effect Of Interfacial Tension Research Articles

Influence of the thermophysical properties of working liquids on heat transfer performance during flow boiling in microchannels

A thorough understanding of the governing interfacial interactions during flow boiling in a microchannel would provide important insights into the underlying physics of fluid dynamics and heat transfer mechanisms. In this study, flow-boiling experiments were performed in a single rectangular microchannel with hydraulic diameter of 0.18 mm. Three working fluids (water, ethanol, and HFE7100) with significantly different thermo-physical properties were tested under an inlet subcooling of 25°C, mass flux of 50–330 kg·m−2·s−1, and effective heat fluxes up to 400 kW·m−2. Non-dimensional groups were used to quantify the relative effects of the forces governing the liquid–vapor interface. The bubble dynamics, flow pattern transition, heat transfer, and pressure drop were compared for the three different working fluids, and a mechanistic explanation of the flow boiling performance was proposed based on a force scaling analysis. Meanwhile, through investigating the influence of dimensionless parameters on heat transfer coefficient, a new basic heat transfer correlation that applies to a wide range of working fluids was developed, with 92.5% of data points falling within ±30% error bands and with a mean absolute error of 14.7%. HFE7100 exhibited the minimum increase in pressure drop with heat flux owing to its smallest liquid-to-vapor density ratio, low viscosity, and lowest interfacial tension effect. This study lays the foundation for the development of more reliable theoretical correlations and provides important insights into optimal design principles.

Impact of cationic surfactant-coated hydrophilic nanoparticles on polymeric solution performance in chemical enhanced oil recovery (CEOR) from a two-dimensional porous medium

This study aims to investigate the mechanisms underlying enhanced oil recovery (EOR) through chemical injection and explore the key parameters influencing these mechanisms in a two-dimensional porous medium. Distilled water, polyacrylamide (PAM), α-Al2O3 nanoparticles, and cetyltrimethylammonium bromide (CTAB) surfactant were employed for this purpose. The effects of interfacial tension (IFT), viscosity, and zeta potential measurement were also examined. The results revealed that the injection of PAM polymer increased the viscosity of the displacing fluid, and enhanced the sweep efficiency. This resulted in a 35 % increase in the oil recovery factor compared to the water injection alone. Furthermore, the introduction of alumina (α-Al2O3) nanoparticles altered the wettability and stabilized the emulsion, leading to a further increase in the oil recovery factor. In the optimal state, the oil recovery factor reached 63.2 %. Moreover, the study of various concentrations of polymer and nanoparticles illustrated that low concentrations of polymer and high concentrations of nanoparticles in the base fluid resulted in higher oil recovery factors. Furthermore, adding CTAB surfactant ended a significant reduction in IFT, with a decrease from 45.03 to 10.33 mN/m. This reduction resulted in the highest oil recovery factor of 69 %. Consequently, the highest oil recovery factor was achieved using PAM polymer at a concentration of 500 ppm, α-Al2O3 nanoparticles at a concentration of 0.1 wt%, and CTAB surfactant at a critical micelle concentration of 1 mM in the base fluid (pure water), with a constant injection flowrate of 0.1 ml/min.

Numerical study of capillary-dominated drainage dynamics: Influence of fluid properties and wettability

Drainage in porous media, crucial in various engineering, industrial, and pharmaceutical contexts, is influenced by the instability of fluid interfaces, leading to diverse displacement efficiencies. This study employs a color gradient model based on the lattice Boltzmann method for pore-scale simulations, examining effects of fluid viscosity, interfacial tension, and wettability on fluid distribution and pressure variations. Results reveal that higher viscosity ratios intensify the imbibition interface, making the invading fluid more compact early in displacement. Increased interfacial tension amplifies pressure difference fluctuations and enhances imbibition, affecting the displacement front's morphology by enhancing lateral evolution but reducing finger-like structures. A greater contact angle in the defending fluid heightens pressure difference volatility, lowers imbibition interfaces, and improves the displacement front's compactness, thereby boosting overall displacement efficiency. These insights offer foundational theoretical support for optimizing mining and industrial processes considering subtle variations in fluid property and wettability.

Simulation of collision behaviour between droplet and solid surface in liquid phase environment

AbstractProcesses involving dispersed immiscible fluids occur across the traditional onshore and offshore crude oil development phases, including oil exploitation and production, gathering and transportation, and station and field processing. The stabilities of such processes are deeply influenced by the collision and film drainage between separated phase interfaces. Due to factors such as gravity as well as buoyancy and resistance, droplets usually collide with the wall at a relatively high speed and experience one or several rebounds before gradually stabilizing and staying on the surface. Though work related to this aspect has raised significant attention, further research on the force‐deformation behaviour between microsized (r ≈50 μm) droplets and solid surface under the influence of the above factors is still lacking and strongly demanded. In this paper, under the comprehensive influence of flow driving, an emulsified water droplet colliding with a solid surface in silicon oil is modelled. The dynamic behaviour of the droplet was analyzed by coupling the Stokes–Reynolds drainage equation, the generalized Young–Laplace equation, and the force situation of the deformable droplet. Furthermore, the effects of interfacial tension, collision velocity, and viscosity of continuous phase on the collision characteristics of droplet were analyzed, and it was found that these factors could significantly change the collision characteristics of droplet.

Fluctuations and Shape Dependence of Microphase Separation in Systems with Long-Range Interactions.

The combination of phase separation and long-ranged, effective, Coulomb interactions results in microphase separation. We predict the sizes and shapes of such microdomains and uniquely their dependence on the macroscopic sample shape which also affects the effective interfacial tension of fluctuations of the lamellar phase. These are applied to equilibrium salt solutions and block copolymers. Nonequilibrium phase separation in the presence of chemical reactions (e.g., cellular condensates) is mapped to the Coulomb theory to which our predictions apply. In some cases, the effective interfacial tension can be ultralow.

Construction of cholesteric liquid crystal microlens array at air/CLC/air and water/CLC/air interfaces

This study addressed the limitations of cholesteric liquid crystal (CLC) based microlens arrays, which required submersion of the CLC in water for their formation. We successfully constructed microlens arrays at both the air/CLC/air and water/CLC/air interfaces by doping E7, a nematic host, with a strong chiral dopant, (S)− 1-Phenylethane-1, 2-diyl bis(4-(trans-4-pentyl cyclohexyl) benzoate) (S1011) at different concentrations (0.3, 0.5, and 1 wt%). By spreading the mixture on transmission electron microscopy square-geometry grids, we observed that the lenses thickened at the water/CLC/air interface and thinned at the air/CLC/air interface with increasing dopant concentrations. A non-inverted image on the same side as the object was analyzed, created from the inverted virtual image of the object on the opposite side of the lens. The non-inverted image's focal length ranged from 6–6.24 mm for air/CLC/air and 4.8–3.6 mm for water/CLC/air, corresponding at 0.3, 0.5, and 1 wt% of S1011. Furthermore, the effect of interfacial tension on focal length was also observed by replacing water with sodium dodecyl sulfate (SDS) solution, and it was found that the focal length increased by 60 µm with increasing SDS from 0.1 to 1 mM. These findings suggest that the S1011 doped E7 microlens array can be easily constructed and potentially used in optical technologies.

Role of Temperature-Dependent Interfacial Tension on Shear Wave Velocity for Energy Geosystems.

Interfacial tension varies with temperature. This paper investigates the effects of temperature-dependent interfacial tension on shear wave velocity. We designed a nylon cell equipped with bender elements in a cross-hole configuration to measure the shear wave velocity of nine sand-silt mixtures with different degrees of saturation (S = 0%, 2.5%, 5%, 10%, and 100%). All specimens were subjected to a temperature change from 10 °C to 1 °C. The results demonstrate that shear wave velocity tends to be very sensitive to changes in temperature at a low degree of saturation. Particle-scale analyses overlapped with the experimental results and captured the critical role of temperature-dependent interfacial tension in small-strain skeletal stiffness. In fact, the temperature should be considered during laboratory and field shear modulus measurements of the long-term performance of energy geosystems subjected to thermally induced repetitive loads.

Further Study on the Effect of Interfacial Tension on Cocurrent Spontaneous Imbibition Based on Direct Simulation and NMR

Further Study on the Effect of Interfacial Tension on Cocurrent Spontaneous Imbibition Based on Direct Simulation and NMR

Investigation of Ferrofluid Sessile Droplet Tensile Deformation in a Uniform Magnetic Field

A significant growth of research on digital microfluidics has been achieved over the past several decades, and the field is still attracting increasing attention for fulfilling relevant mechanisms and potential applications. Numerous studies have been devoted to actively manipulating droplets in a variety of fundamental and applicational scenarios. In this work, the deformation of ferromagnetic fluid droplets is studied under an external uniform magnetic field. The droplets are precisely dispersed on the bottom surface of a container assembled with polymer methacrylate (PMMA) plates. Mineral oil is applied instead of air as the surrounding medium for easy stretching and preventing water solvent evaporation in ferrofluid. The design and processing of the container are firstly carried out to observe the shape and characterize the wettability of the droplets in the immiscible mineral oil medium. Furthermore, the droplets’ deformation and the working mechanism are given under the action of the horizontal uniform magnetic field. At different magnetic field intensities, the droplet is stretched in the horizontal direction parallel to the applied field. Due to volume conservation, the dimension in the height reduces correspondingly. With the coupling effect of magnetic force, viscous force and interfacial tension, the contact angle first increases with the magnetic field and then basically remains unchanged upon magnetization saturation. Consistent with the experimental results, the numerical method clearly reveals the field coupling mechanism and the nonlinear deformation of the sessile droplet.

Immiscible thermoplastic polymer blends with alternative layered encapsulation structure: Modeling and processing

“Encapsulation” is a common phenomenon during polymer melting processing, which supplied great opportunities for fabricating high-performance polymer products. In this work, two immiscible polymers, high density polyethylene (HDPE) and polyketone (PK), were used for preparing polymer blends with viscous encapsulation structures. Moreover, the effects of interfacial tension, viscosity ratio, and shear rate on the phase morphology evolution of HDPE/PK blends were investigated by numerical simulation and high-pressure capillary extrusion (HCE). Meanwhile, the formation mechanisms of HDPE/PK alternating layered encapsulation structure were explored by tracking the trajectory of PK droplets via numerical simulation. The results show that an alternative layered encapsulation structure of HDPE/PK was formed under the shear rate from 50 to 1000 s−1 with the interfacial tension over 1.35 mN/m. Moreover, it was found that the revealed mechanism in HCE was also applicable to the injection molding process. Therefore, this unique “microstructure-intelligent prediction-control” strategy of polymer blends is suitable for the industrial processing of high-performance polymer blends for desired applications.

Macroscopic model for generalised Newtonian inertial two-phase flow in porous media

A closed macroscopic model for quasi-steady, inertial, incompressible, two-phase generalised Newtonian flow in rigid and homogeneous porous media is formally derived. The model consists of macroscopic equations for mass and momentum balance as well as an expression for the macroscopic pressure difference between the two fluid phases. The model is obtained by upscaling the pore-scale equations, employing a methodology based on volume averaging, the adjoint method and Green's formulation, only assuming the existence of a representative elementary volume and the separation of scales between the microscale and the macroscale. The average mass equations coincide with those for Newtonian flow. The macroscopic momentum balance equation in each phase expresses the seepage velocity in terms of a dominant and a coupling Darcy-like term, a contribution from interfacial tension effects and another one from interfacial inertia. Finally, the expression of the macroscopic pressure difference is obtained in terms of the macroscopic pressure gradient and body force in each phase, and interfacial terms that account for capillary effects and inertia, if present when the interface is not stationary. All terms involved in the macroscale equations are predicted from the solution of adjoint closure problems in periodic representative domains. Numerical predictions from the upscaled models are compared with direct numerical simulations for two-dimensional configurations, considering flow of a Newtonian non-wetting fluid and a Carreau wetting fluid. Excellent agreement between the two approaches confirms the pertinence of the macroscopic models derived here.

Experimental and numerical analysis of the emulsification of oil droplets in water with high frequency focused ultrasound

Focused high frequency ultrasound emulsification provides significant benefits such as enhanced stability, finer droplets, elevated focal pressure, lowered power usage, minimal surfactant usage and improved dispersion. Hence, in this study, the high frequency focused ultrasound emulsification of oil droplets in water was investigated through experiments and numerical modeling. The effect of transducer power (74–400 W), frequency (1.1 and 3.3 MHz), oil viscosity (10.6–512 mPas), interfacial tension (25–250 mN/m) and initial droplet radius (10–750 µm) on the emulsification process was assessed. In addition, the mechanism of droplet break-up was examined. The experiments showed that the acoustic pressure increased from 9.01 MPa to 26.24 MPa as the power was raised from 74 W to 400 W. At 74 W, the Weber number (We) at the surface and focal zone are 0.5 and 939.8, respectively. However, at 400 W, the We at the transducer surface and focal region reached 2.7 and 6451.8, respectively. Thus, bulb-like and weak catastrophic break up dominates the emulsification at 74 W. The catastrophic break up at 400 W is more vigorous because the ultrasound disruptive stress and We are higher. The time for the catastrophic dispersion of a single droplet at We = 939.8 and We = 6451.8 are 1.01 ms and 0.45 ms, respectively. The numerical model gives reasonable prediction of the trend and magnitude of the experimental acoustic pressure data. The surface and focal pressure amplitudes were estimated with errors of ∼ 6.5% and ∼ 10%, respectively. The predicted Reynolds number (Re) between 74 and 400 W were 8442 and 21364, respectively. The acoustic pressure at the focal region were ∼ 26 MPa and ∼ 69 MPa at frequencies of 1.1 MHz and 3.3 MHz, respectively. Moreover, the acoustic velocities were ∼ 16 m/s and ∼ 42 m/s at 1.1 MHz and 3.3 MHz, respectively. Hence, smaller droplets could be attained at higher frequency excitation under intense catastrophic modes. The Ohnesorge number (Oh) increased from 0.062 to 3.12 with the viscosity between 10.6 mPas and 530 mPas. However, the We remained constant at 856.14 for the studied range. Generally, higher critical We is required for the different breakup stages as the viscosity ratio is elevated. Moreover, the We increased from 25.68 to 1284.22 as the droplet radius was elevated from 15 to 750 µm. Larger droplets allow for higher possibility and intensity of breakup due to diminished viscous and interfacial resistance.

The Effect of Interfacial Tension and Emulsification in Enhancing Oil Recovery During Surfactant Flooding

Abstract The effectiveness of various surfactants in improving crude oil displacement efficiency was evaluated using one-dimensional homogeneous core and three-dimensional heterogeneous models. Emulsification of the crude oil was simulated using an ultrasonic instrument, and the emulsification degree was evaluated based on droplet dispersion, droplet number density, interfacial tension, external phase viscosity, internal phase volume, and demulsification time. Six surfactants could be divided into five emulsifying types: non-emulsification, emulsification inversion, early emulsification, late emulsification, and whole process emulsification. The results showed that the surfactants had varying levels of effectiveness in improving displacement efficiency. The whole process emulsification system can effectively start the residual oil in the pore throat and reduce the free-state and bound-state residual oil saturation. The area of the mainstream zone between the injection and production wells was significantly expanded after the whole process emulsification system was injected. The whole process emulsification is more important than interfacial tension for enhancing oil recovery.

Direct prediction of relative permeability curve from 3D digital rock images based on deep learning approaches

The relative permeability curve is one of the key features to evaluate the flow property of a porous medium, which is important in petroleum and gas industry, yet it is not easy to obtain. In this study, we proposed a new intelligent way to predict the relative permeability curves directly from 3D digital rock images, compared with other existing artificial intelligence (AI) methods that usually used indirect geometrical parameters as inputs. The inputs of our AI model are the digital rock images and fluid/rock physical properties such as wettability and interfacial tension; the outputs (relative permeability curves) are obtained by an improved pore-network model. We test three deep learning methods (CNN, ConvLSTM-FC, and ConvLSTM-CNN) and compare their accuracy in the predictions for both sandstone and volcanic rock types. The results show that the overall prediction accuracy of the deep hybrid ConvLSTM-CNN method is the highest, reaching 95%. The well-trained model is further applied to successfully predict the effects of wettability and interfacial tension on the relative permeability curves of a Berea sandstone.

Triumfetta cordifolia Gum as a Promising Bio-Ingredient to Stabilize Emulsions with Potentials in Cosmetics.

The cosmetics industry is searching for efficient and sustainable substances capable of stabilizing emulsions or colloidal dispersions that are thermodynamically unstable because of their high surface energy. Therefore, surfactants are commonly used to stabilize the water/oil interface. However, the presence of a surfactant is not always sufficient to obtain stable emulsions on the one hand, and conventional surfactants are often subject to such controversies as their petroleum origin and environmental concerns on the other hand. As a consequence, among other challenges, it is obvious that research related to new-natural, biodegradable, biocompatible, available, competitive-surfactants are nowadays more intensive. This study aims to valorize a natural gum from Triumfetta cordifolia (T. cordifolia) as a sustainable emulsifier and stabilizer for oil-in-water (O/W) emulsions, and to evaluate how the nature of the fatty phase could affect this potential. To this end, O/W emulsions were prepared at room temperature using three different oils varying in composition, using a rotor-stator mixer. Resulting mixtures were characterized using optical microscopy, laser granulometry, rheology, pH and stability monitoring over time. The results demonstrated good potential for the gum as an emulsifying agent. T. cordifolia gum appears efficient even at very low concentrations (0.2% w/w) for the preparation and stabilization of the different O/W emulsions. The best results were observed for cocoglyceride oil due to its stronger effect of lowering interfacial tension (IFT) thus acting as a co-emulsifier. Therefore, overall results showed that T. cordifolia gum is undoubtedly a highly promising new bio-sourced and environmentally friendly emulsifier/stabilizer for many applications including cosmetics.

Numerical study of the effect of Péclet number on miscible viscous fingering with effective interfacial tension

Viscous fingering or Saffman–Taylor instability shows fingering interfacial patterns when a more mobile fluid displaces a less mobile one in porous media. The effective interfacial tension (EIT) is like capillary force, acting at the miscible interface on time scales shorter than interface relaxation. It has been numerically reported so far that the fingers are wider with EIT compared with those without EIT. A recent experiment observed finger widening with increasing flow rate in a miscible system with EIT, which is not observed in classical immiscible and miscible systems. In this study, we have numerically investigated the effect of $Pe$ (which corresponds to the injection flow rates in the experiment) on miscible viscous fingering with/without EIT. We have shown that the fingers are monotonically thinner with an increase in $Pe$ in the system without EIT, while finger widening with increasing $Pe$ is observed in the system with EIT. Furthermore, we have also examined a one-dimensional underlying concentration profile and EIT profile by using a one-dimensional diffusion–convection model because EIT is proportional to the squared concentration gradient. We have then shown that the concentration gradient is steeper and, thus, the EIT is larger as $Pe$ is larger. Therefore, this is the first numerical study that can theoretically verify finger widening with increasing flow rate, which occurs only in a miscible system with EIT to the extent of our targeting EIT values, and explain the mechanism by one-dimensional analysis.

The pore-network modeling of gas-condensate flow: Elucidating the effect of pore morphology, wettability, interfacial tension, and flow rate

The gas-condensate flow in the near-well region is significantly influenced by phase behavior, flow regimes, and pore geometries. In conventional gas-condensate reservoirs the key pore-scale parameters affecting gas and condensate relative permeabilities include velocity (i.e., pressure gradient), interfacial tension (IFT), wettability, and pore structure. To examine the impact of these parameters, three-dimensional (3D) and two-dimensional (2D) pore-network models (PNMs) were developed. A proposed compositional model was used to implement the cyclic process of condensate corner flow (film flow for circular tubes) and condensate blockage. Response surface methodology (RSM) was employed to achieve high accuracy in phase equilibrium calculations and to enhance computational speed.The 3D PNM simulations of gas-condensate core-flood experiments confirmed the consistency and accuracy of the implemented methodology. A parametric study of governing factors such as pore shapes, wettability, IFT, and flow rate was conducted using the developed PNMs. The findings revealed that pore geometry and contact angle dictate the condensate meniscus curvature and snap-off process in pore throats. The unblocking of throats by condensate bridges was primarily controlled by contact angle, IFT, and pore cross-section. A shift to neutral wetting substantially improved gas-condensate flow in higher IFTs and angular pore shapes.The positive velocity effect on low-IFT gas-condensate flow, known as the coupling rate effect, was more pronounced in simulations with lower contact angles, and its impact was negligible at neutral wettability, similar to the IFT effect. The simulation results and findings underscore the influence of each factor and offer a method for incorporating the effects of pore shape (i.e., formation type and structure), contact angle, velocity, and IFT in continuum scale simulations.

A Systematic Experimental Study to Understand the Performance and Efficiency of Gas Injection in Carbonate Reservoirs

Summary Gas injection is the most widely applied recovery method in light, condensate, and volatile oil carbonate reservoirs. Gas has high displacement efficiency and usually results in a low residual oil saturation in the part of the reservoir that is contacted with gas. The displacement efficiency increases when the injected gas is near-miscible or miscible with the oil. In addition to nitrogen and hydrocarbon gas projects, carbon dioxide (CO2) enhanced oil recovery (EOR) has been the dominant gas EOR process. Gas-based EOR has been implemented in both mature and waterflooded carbonate reservoirs. In this paper, we present the results of a detailed experimental study aimed at understanding the performance and efficiency of gas injection in carbonate reservoirs. A series of immiscible and miscible gas injection coreflood experiments were performed using limestone reservoir cores under different injection strategies. To minimize laboratory artifacts, long cores were used in the experiments, and to observe the effect of gravity, both 2 in. diameter and 4 in. diameter (whole core) were used. The experiments were performed under reservoir conditions using live crude oil. The core wettability was restored by aging the core in crude oil for several weeks under reservoir temperature. Hydrocarbon gas (methane) was used as the immiscible injectant, and both CO2 and a mixture of 50% C1 and 50% CO2 were used as miscible injectant. All gas injection experiments were performed using vertically oriented cores, and the gas was injected from the top unless it is stated otherwise. The main parameters investigated in this study are as follows: The effect of miscibility on oil recovery for both continuous gas injection and water alternating gas (WAG). The effect of gravity on gas sweep efficiency compared to waterflooding. The effect of gas-oil interfacial tension (IFT) on oil recovery when using the same oil. The effect of oil type on oil recovery using the same injected gas at miscible and immiscible conditions. The effect of immiscible gas injection on subsequent miscible gas injection performance. Impact of CO2 cycle length on ultimate oil recovery. The impact of the order of fluid injection where multiple WAG injection cycles were performed in separate experiments after water or gas injection. The main conclusions of this study are as follows: As expected, miscibility has a significant impact on displacement efficiency and oil recovery where miscible gas recovered more than 20% extra oil compared to immiscible gas. A significant variation in oil recovery is observed for miscible gas injection (i.e., more than 10 saturation units difference) depending on the minimum miscibility pressure (MMP) between the injected gas and crude oil, even when both experiments are performed at miscible conditions using the same injected gas. The performance of tertiary CO2 flood was adversely affected by the slug of immiscible gas injected. Therefore, it is not recommended to have immiscible gas injection before miscible gas injection. Regardless of injected gas type, gas injection with similar IFTs achieved similar oil recovery. During WAG experiments, starting the injection cycles with water or gas did not have any impact on the ultimate oil recovery for both miscible and immiscible cases for one of the reservoirs, while WAG_G (WAG starting with gas injection) recovered more oil for another reservoir. Gravity has a significant impact on oil recovery for both miscible and immiscible gas injections. A significant difference is observed in oil recovery when comparing CO2 injection on 2-in.- and 4-in.-diameter core samples or when comparing horizontal vs. vertical immiscible gas injection and WAG experiment. The longer the CO2 slug size, the higher the oil recovery observed in gas injection experiments. The results of this study provide a rich and rarely available set of experimental data that can help improve and optimize gas and WAG injection in oil-wet carbonates.

Two-dimensional numerical modelling of viscous emulsion drops coalescence in a constricted capillary channel

We study numerically the coalescence of viscous emulsion drops in a two-dimensional semi-elliptical shape constricted channel. The Navier-Stokes equations are solved using the finite element method and the oil-water interface is tracked using the level-set techniques. Effects of interfacial tension, inertia, viscosity ratio, droplet size, and constriction shape on the droplet coalescence and average viscous pressure drop along the channel are investigated. It is found that at high interfacial tension, droplets are circular, approach each other more quickly, coalesce at the constriction entrance, and give higher pressure drops. At intermediate interfacial tension, the onset of coalescence occurs downstream of the constriction entrance while at very low interfacial tension, no coalescence of the droplets was observed. Inertia is found to be negligible effects on the coalescence of the droplets. High inertia gives less viscous pressure drop. Less viscous droplets are more likely to quickly coalesce compared to high viscous drops. Higher viscous drops create more resistance to flow. Moreover, larger size drops are responsible for more quick coalescence and tend to create more viscous pressure drops. In addition, we found that circular constriction offers less resistance to fluid flow. We hope that these numerical results would be beneficial while displacing oil from the underground reservoirs.

Hydrodynamic simulation of metal droplet settlement in molten slag

A mathematical model of the metal droplet settlement process of smelting slag was established. The effect of interfacial tension between the metal and slag phases on the droplet settlement velocity and drag force under different viscosity models was studied. The results showed that the Laminar and RNG k–ɛ turbulence models accurately predict the final settlement velocity of smaller diameter droplets. The interfacial tension affects the settlement velocity of the droplet, and the effect gradually increases as the droplet size is increased. The “RNG + CSS” model accurately describes the droplet settlement process and the change in the droplet settlement velocity. The drag force coefficient formula under coupling interfacial tension was derived with the established mathematical model and experimental data. This model reveals the mechanism of the settlement process of metal droplets in smelting slag and provides theoretical guidance for reducing the content of valuable metals in slag in actual production.