Multiphase Fluid Systems Research Articles

Stability and thinning of liquid jets in the presence of soluble surfactants.

The dynamics of many multiphase fluid systems involve the thinning and eventual break up of a slender fluid filament or a liquid jet. The interfacial instability that controls the rate of jet thinning depends on the relative magnitudes of capillary, viscous, and inertial stresses. Surfactants add an additional layer of physicochemical dynamics by reducing the surface tension of the interface and introducing reverse Marangoni flows in response to surface concentration gradients. Surfactants may also introduce an intrinsic surface rheology that affects jet thinning. Quantifying these effects has been a significant problem in chemical physics and a topic of key research interest. Recent studies have shown that insoluble surfactants delay thread thinning and suppress instabilities in Newtonian jets. However, the role of surfactant solubility in liquid jet stability is still unknown. In this work, we use linear stability analysis to quantitatively show the stabilizing effects of Marangoni stresses, surfactant adsorption and desorption time, and intermolecular forces upon adsorption. We highlight the seemingly indistinguishable way in which various surfactant properties result in the same outcome. We also identify a surface dissipative contribution that arises from the interplay of Marangoni flows with finite adsorption and desorption, which acts as an "apparent" surface viscosity. We verify predictions of our linear stability results against numerical simulations and conclude by noting that tuning surface activity and kinetics of adsorbed surfactants or particles can potentially suppress droplet formation, which is of significant impact in the printing industry and in the control of the spread of aerosols.

On the influence of the natural shape of particles in multiphase fluid systems: Granular collapses

The collapse of natural granular particles is encountered in various scenarios, including landslides, tsunamis, avalanches, and industrial processes. However, our understanding of these phenomena is still limited due to the complex interactions and the wide range of parameters that influence such systems. Particle shape is one of the factors that can significantly impact granular collapse behavior. In this paper, we studied the role of particle morphology in the interaction between fluids and particles in collapse problems and wave generation in multiphase fluid systems. To achieve this, we employed an image-based Discrete Element Method coupled with the Volume-of-Fluid approach. Initially, the proposed method is validated using experimental data for spherical particles. Then, we increased the irregularity of the spherical particles in four incremental steps. Our study establishes a clear relationship between particle morphology and important characteristics such as displacement, velocity, inter-particle forces, and kinetic energy. We observed that as irregularity increases, interlocking between particles becomes more prominent, leading to reduced particle travel distances. Additionally, our findings demonstrate that interlocking also influences particle-fluid interactions, resulting in significant alterations in the formation of generated waves.

Fluid-structure interaction analysis on the response of open-top, squat, circular tank due to wind-driven rain

Wind-driven rain (WDR) is a natural phenomenon, which occurs, when rain droplets descend through a wind flow field, creating an angle with the vertical and affects any structure by impingement through the structural envelope. Existing literatures on wind-driven rain effect on structure, are focused on building envelop only. There is a huge scope, left unexplored, on studying the interaction response of squat, open top, circular tank with wind-driven rain. This available scope is the main motivation of the present authors behind this study. The present study has been conducted through fluid–structure interaction (FSI) analysis, by coupling computational fluid dynamics (CFD) analysis of a multi-phase fluid system involving air and water to simulate wind-driven rain, with the mechanical analysis of the tank structure, by importing the wall pressure, assessed from CFD model of WDR. This study is focused on ground-supported, open-top, squat, circular tank with a slenderness ratio of 0.5. The internal and external pressure distributions on the tank wall have been assessed for WDR and compared with the same caused by wind. The radius (R): thickness (t) ratio of the tank wall has been varied from 125 to 500, in order to understand the impact of wind-driven rain on the tank wall deformation. The comparative study of pressure distribution between WDR and wind (only) cases clearly demonstrates that the wall pressure (internal and external) due to wind-driven rain, is higher than wind (only). It has been observed that the wall deformation is showing an incremental pattern with the decrement of wall thickness. The maximum deformation zone has been observed at the upper half of the frontal area. Higher deformation zone for R/t ratios 500, 250, 166.67, and 125, can be seen for 0° to 40°, 0° to 37°, 0° to 35°, and 0° to 32°, peripherally.

Modeling droplets with slippery interfaces

Many multiphase fluid systems, such as those involving immiscible polymers or liquid-liquid systems with surfactants, have shown a breakdown of the no-slip condition at the material interface. This results in systems where the tangential velocity of the inner and outer fluid can differ, with the jump in velocity dependent not only on the material properties of the interface but also the stresses applied by the surrounding fluid. In this work a numerical model is presented which is capable of investigating general multiphase fluid systems involving interfacial slip in both two- and three-dimensions. To make the system computationally feasible, a hybrid Navier-Stokes projection method is used, whereby the viscosity, density, and pressure are assumed to be continuous across the interface while the velocity field can experience a jump, which is handled via the Immersed Interface Method. The numerical model is compared to experimental results involving polymer-polymer mixtures and computational results for droplets in extensional flows, showing excellent agreement with both. It is then used to explore the influence of interfacial slip in a number of common multiphase fluid systems, including the shearing of a planar interface, droplet and filament relaxation, and droplets in shear flow, both unbounded and wall-bound.

Dynamics of multiphase magnetic fluid systems in microchannels of different shapes in a nonhomogeneous magnetic field

We presented the results of a study of the dynamics of gas bubbles injected into a ferrofluid under the influence of an inhomogeneous magnetic field in microchannels of five configurations. The dependences of bubble sizes on the configuration of the magnetic field and the physical properties of the magnetic fluid are obtained. The results obtained can be used in gas meters and dispensers in microfluidics.

Modeling of droplet dynamics with soluble surfactant by multi-relaxation-time phase-field lattice Boltzmann method

The multiphase fluid system in the presence of surfactant is frequently encountered in numerous scientific and engineering applications. Developing a model for accurately simulating such a complex system is of great significance. In this work, we propose a multi-relaxation-time phase-field lattice Boltzmann model for simulating droplet dynamics with soluble surfactants. The accuracy and validity of the model are verified by benchmark cases including static droplet and Rayleigh–Taylor instability tests. The effects of surfactant, capillary number, and density ratio on single-droplet deformation and two-droplet interaction under shear flow are investigated. Simulation results indicate that the Marangoni stress generated by the inhomogeneous distribution of surfactant at the interface plays the role of promoting droplet deformation and hindering droplet coalescence. Within the studied range, it tends to be much easier for droplets to deform with the decrease in density ratio. The increase in the capillary number and surfactant concentration is conducive to promoting the deformation and breakup of droplets. In addition, a higher surfactant concentration is found to result in greater liquid film thickness between droplets, which would hinder the coalescence of the droplets.

A new approach to analyze the equilibrium and transient behaviors of particulate systems and the subsequent application to multiphase fluid systems

Fast and robust computation for population balance models is a crucial requirement for simulating particulate systems. Despite all the recent advances in developing relevant computational algorithms, either efficiency or robustness can only be achieved at the expense of the other. However, optimal compromise is possible by having prior estimates of the system's internal length and time scales. Thus, an approximation technique is introduced in this study to extract equilibrium and transient behaviors for a particulate system considering coalescence and breakage phenomena. The approximation method is developed by simplifying assumptions on the available analytical solution for a spatially homogeneous population balance equation with simple kernels. The derived equilibrium and transient equations suggest that the system is governed by a dimensionless group that can describe the equilibrium distribution of the system as well as the rate and the direction that the system is likely to evolve. The method is applied to two different sets of complex breakage and coalescence kernels used for liquid-liquid dispersed systems. The approximated time and length scales were validated with numerical results; thus, the approximation can be used to generate targeted element-based orthogonal collocation grids for fast and robust computation of transient and steady-state particulate systems. This approach can significantly decrease the computation time, typically by 40–70 % for steady-state conditions.

Vulnerability Analysis of Structural Systems under Extreme Flood Events

Vulnerability analyses of coastal or inland bridges in terms of flood actions and structural and fluid flow characteristics are carried out. In particular, a numerical model based on a two-phase fluid flow is implemented for the multiphase fluid system, whereas a three-dimensional formulation based on shell/volume finite elements is adopted for the structure. The governing equations can simulate the interaction between fluids and the structures, by using the Arbitrary Lagrangian–Eulerian (ALE) strategy. The results of the hydrodynamic forces, bridge displacements and dynamic amplification factors (DAFs) show that the existing formulas, available in the literature or in structural design codes, do not accurately predict the maximum design effects. For the investigated cases, the DAFs may vary from 1 to 4.5. The worst scenarios are observed for the upload vertical direction. Finally, the performance of the protection fairing system is investigated. The results show that such devices are able to efficiently reduce the effects of the wave load in terms of the applied hydraulic forces on the structure and bridge deformability, in particular, with 40% more accuracy than the unprotected configuration.

Physics-informed neural networks for phase-field method in two-phase flow

The complex flow modeling based on machine learning is becoming a promising way to describe multiphase fluid systems. This work demonstrates how a physics-informed neural network promotes the combination of traditional governing equations and advanced interface evolution equations without intricate algorithms. We develop physics-informed neural networks for the phase-field method (PF-PINNs) in two-dimensional immiscible incompressible two-phase flow. The Cahn–Hillard equation and Navier–Stokes equations are encoded directly into the residuals of a fully connected neural network. Compared with the traditional interface-capturing method, the phase-field model has a firm physical basis because it is based on the Ginzburg–Landau theory and conserves mass and energy. It also performs well in two-phase flow at the large density ratio. However, the high-order differential nonlinear term of the Cahn–Hilliard equation poses a great challenge for obtaining numerical solutions. Thus, in this work, we adopt neural networks to tackle the challenge by solving high-order derivate terms and capture the interface adaptively. To enhance the accuracy and efficiency of PF-PINNs, we use the time-marching strategy and the forced constraint of the density and viscosity. The PF-PINNs are tested by two cases for presenting the interface-capturing ability of PINNs and evaluating the accuracy of PF-PINNs at the large density ratio (up to 1000). The shape of the interface in both cases coincides well with the reference results, and the dynamic behavior of the second case is precisely captured. We also quantify the variations in the center of mass and increasing velocity over time for validation purposes. The results show that PF-PINNs exploit the automatic differentiation without sacrificing the high accuracy of the phase-field method.

Inexact methods for sequential fully implicit (SFI) reservoir simulation

The sequential fully implicit (SFI) scheme was introduced (Jenny et al. J. Comput. Phys. 217(2), 627–641 2006) for solving coupled flow and transport problems. Each time step for SFI consists of an outer loop, in which there are inner Newton loops to implicitly and sequentially solve the pressure and transport sub-problems. In standard SFI, the sub-problems are usually solved with tight tolerances at every outer iteration. This can result in wasted computations that contribute little progress towards the coupled solution. The issue is known as ‘over-solving’. Our objective is to minimize the cost of inner solvers while maintaining the convergence rate of SFI. We first extended a nonlinear-acceleration (NA) framework (Jiang and Tchelepi, Comput. Methods Appl. Mech. Eng. 352, 246–275, 2019) to multi-component compositional models, for ensuring robust outer-loop convergence. We then developed inexact-type methods that alleviate ‘over-solving’. It is found that there is no need for one sub-problem to strive for perfection, while the coupled (outer) residual remains high due to the other sub-problem. The new SFI solver was tested using several complex cases. The problems involve multi-phase and EoS-based compositional fluid systems. We compared different strategies such as fixed relaxations on absolute and relative tolerances for the inner solvers, as well as an adaptive approach. The results show that the basic SFI method is quite inefficient. Away from a coupled solution, additional accuracy achieved in inner solvers is wasted, contributing to little or no reduction of the overall outer residual. By comparison, the adaptive inexact method provides relative tolerances adequate for the current convergence state of the sub-problems. We show across a wide range of flow conditions that the new solver can effectively resolve the over-solving issue, and thus greatly improve the overall efficiency.

On the lattice Boltzmann method and its application to turbulent, multiphase flows of various fluids including cryogens: A review

Cryogenic fluids are used in a myriad of different applications not limited to green fuels, medical devices, spacecraft, and cryoelectronics. In this review, we elaborate on these applications and synthesize recent lattice Boltzmann methods (LBMs) including collision operators, boundary conditions, grid-refinement techniques, and multiphase models that have enabled the simulation of turbulence, thermodynamic phase change, and non-isothermal effects in a wide array of fluids, including cryogens. The LBM has reached a mature state over the last three decades and become a strong alternative to the conventional Navier–Stokes equations for simulating complex, rarefied, thermal, multiphase fluid systems. Moreover, the method's scalability boosts the efficiency of large-scale fluid flow computations on parallel clusters, including heterogeneous clusters with graphics card-based accelerators. Despite this maturity, the LBM has only recently experienced limited use in the study of cryogenic fluid systems. Therefore, it is fitting to emphasize the usefulness of the LBM for simulating computationally prohibitive, complex cryogenic flows. We expect that the method will be employed more extensively in the future owing to its simple representation of molecular interaction and consequently thermodynamic changes of state, surface tension effects, non-ideal effects, and boundary treatments, among others.

An adaptive time stepping algorithm for IMPES with high order polynomial extrapolation

Two-phase flows in oil reservoirs can be modeled by a coupled system of elliptic and hyperbolic partial differential equations. The transport velocity of the multiphase fluid system is related to the pressure through Darcy’s law and it is coupled to a conservation law for the saturation variable of one of the phases. A time step of the classical IMPES (IMplicit Pressure Explicit Saturation) method consists of first solving the elliptic problem for pressure and Darcy velocity, and then updating the saturation with an explicit numerical scheme for conservation laws. This method is very computationally costly, since the time-consuming elliptic solver must be invoked at time intervals defined by the stability limit of the hyperbolic solver. A popular variant is not to update the velocity at all hyperbolic time steps, but to skip a fixed number C of them, with C determined by the user. In this work we propose a more accurate and systematic procedure for time stepping in IMPES codes. The velocity is updated at all transport time steps, though the elliptic solver is only invoked every C steps. In the time steps at which the elliptic problem is not solved, the velocity is extrapolated from previously computed values with polynomials of high degree. Further, we introduce an error estimator that allows for the number C to be adaptively determined without user intervention. The algorithm was tested in several relevant benchmark problems. This allowed for the optimization of its parameters and comparisons with previous variants. The results show that the proposed algorithm is very stable, reliable and time-cost effective. It is also easily implemented in pre-existent IMPES codes.

Localized nonlinear solution strategies for efficient simulation of unconventional reservoirs

Accurate and efficient numerical simulation of unconventional reservoirs is challenging. Long periods of transient flow and steep potential gradients occur due to the extreme conductivity contrast between matrix and fracture. Detailed near-well/near-fracture models are necessary to provide sufficient resolution, but they are computationally impractical for field cases with multiple hydraulic-fracture stages.Previous works in the literature of unconventional simulations mainly focus on the gridding level that adapts to wells and fractures. Limited research has been conducted on nonlinear strategies that exploit locality across timesteps and nonlinear iterations. It was reported that an individual Newton update is typically sparse and nonlinear convergence is constrained by a small portion of the model. To perform localized computations, an a-prioristrategy is essential to first determine the active subset of simulation cells for the subsequent iteration. The active set flags the cells that will be updated, and then the corresponding localized linear system is solved.The objective of this work is to develop localization methods that are readily applicable to complex fracture networks and flow physics in unconventional reservoirs. By utilizing the diffusive nature of pressure updates, an adaptive algorithm is proposed to make adequate estimates for the active domains. In addition, we further develop a localized solver based on nonlinear domain decomposition (DD). Compared to a standard DD method, domain partitions are dynamically constructed. The new solver provides effective partitioning that adapts to flow dynamics and Newton updates.We evaluate the developed methods using several complex problems with discrete fracture networks. The problems consider multi-phase and compositional fluid systems with phase changes. The results show that large degrees of solution locality present across timesteps and iterations. Compared to a standard Newton solver, the new solvers enable superior computational performance. Moreover, Newton convergence behavior is preserved, without any impact on solution accuracy.

Prediction of fluid interface between dispersed and matrix phases by Lattice Boltzmann-adaptive network-based fuzzy inference system

ABSTRACT The integration of Lattice Boltzmann (LB) and adaptive-network-based fuzzy inference system was utilised to simulate mesoscale fluid interface in a multiphase fluid system. This method uses data generated by LB and based on the local population and density data. The interface between dispersed and matrix phases on the neural points was simulated. The neural mesh of interface was created by the ANFIS method and locally was compared by the CFD results. The results showed that there is a great agreement between ANFIS and numerical data when a particularly more number of rules are used in the learning step of simulations. Since this new overview of modelling can predict fluid flow based on existing data, less number of rules cause over prediction for the ANFIS method; however, by enhancing the number of rules, ANFIS can solve this over-prediction far from the curvature of the dispersed phase. This algorithm can be a promising tool for simulation of macroscopic parameters in the large-scale multi-phase reactors.

Wettability control on deformation: Coupled multiphase fluid and granular systems.

Understanding of multiphase flow in porous media is important for a wide range of applications such as soil science, environmental remediation, energy resources, and CO_{2} sequestration. This phenomenon depends on the complex interplay between the fluid and solid forces such as gravitational, capillary, and viscous forces, as well as wettability of the solid phase. Such interactions along with the geometry of the medium give rise to a variety of complex flow regimes. Although much research has been done in the area of wettability, its mechanical effect is not well understood, and it continues to challenge our understanding of the phenomena on macroscopic and microscopic scales. In this paper, therefore, the effect of wettability on the deformation of porous media and fluid-fluid patterns is studied through a series of three-dimensional (3D) simulations. To this end, the discrete element method (DEM) and volume of fluid (VOF) are coupled to accurately model free-surface flow interaction in a cylindrical pack of spheres. The fluid-particle interactions are modeled by exchanging information between DEM and VOF, while the effect of wettability is considered to study how it controls fluid displacement. The results indicate that the drag force and deformation in the pack vary with the change in wettability and capillary number. To demonstrate the effect of both wettability and capillary number, a series of numerical experiments were conducted with two capillary numbers and three wettability conditions. Our results show that the drag force was greatest for near extreme wettability conditions, which resulted in a larger deformation.

Cahn-Hilliard mobility of fluid-fluid interfaces from molecular dynamics

The Cahn-Hilliard equation is often used to model the temporospatial evolution of multiphase fluid systems including droplets, bubbles, aerosols, and liquid films. This equation requires knowledge of the fluid-fluid interfacial mobility γ, a parameter that can be difficult to obtain experimentally. In this work, a method to obtain γ from nonequilibrium molecular dynamics is presented. γ is obtained for liquid-liquid and liquid-vapor interfaces by perturbing them from their equilibrium phase fraction spatial distributions, using molecular dynamics simulations to observe their relaxation toward equilibrium, and fitting the Cahn-Hilliard model to the transient molecular simulations at each time step. γ is then compared to a different measure of interfacial mobility, the molecular interfacial mobility M. It is found that γ is proportional to the product of M, the interface thickness, and the ratio of thermal energy to interfacial energy.

Thermodynamic-consistent multiple-relaxation-time lattice Boltzmann equation model for two-phase hydrocarbon fluids with Peng-Robinson equation of state

In this work, a multiple-relaxation-time (MRT) lattice Boltzmann (LB) equation model with Beam-Warming (B-W) scheme is proposed to simulate a multi-phase fluid system with Peng-Robinson (P-R) equation of state (EOS). The mathematical model of the multi-phase fluid flow is derived based on the NVT-based framework, where the Helmholtz free energy of P-R EOS is introduced. The nonideal force in the multi-phase flow is directly computed from the free energy in order to obtain a more compact formulation of hydrodynamic equations, which is termed as potential form. The MRT-LB model is developed based on the potential form of hydrodynamic equations, which can eliminate spurious currents effectively. In addition, to capture the tiny nonconvex perturbation from the linear trend of P-R model precisely, the B-W scheme is utilized in the present MRT-LB model, which gives rise to an adjustable Courant-Friedrichs-Lewy (CFL) number. Also, the second order accuracy can be naturally achieved by this scheme without any other requirements and numerical boundary conditions. In the numerical experiments, a realistic hydrocarbon component (isobutane) in three dimensional space is simulated by the proposed MRT-LB model. Numerical results show that the magnitude of spurious currents can be significantly reduced by the present MRT-LB model. In addition, our numerical predictions of surface tension agree well with the experimental data, which verify the effectiveness of the proposed MRT-LB model.

An evaluation of in-silico methods for predicting solute partition in multiphase complex fluids – A case study of octanol/water partition coefficient

Solute partition in multiphase fluids is an important thermodynamic phenomenon and performance attribute for a wide range of product formulations of foods, pharmaceuticals and cosmetics. Experimental evaluation of partition coefficients in complex product formulations is empirical, difficult and time consuming. In-silico methods such as fragment constant method and group contribution method require parameter fitting to the experimental data and are limited to relatively simple fluids. Recently, a method combining molecular dynamics (MD) and quantum chemical (QC) calculation of screening charge density function has been reported. The method does not only use fundamental properties of intermolecular force and charge density function, which does not require parameter fitting to the experimental data, but also applies to complex fluid structures such as micelles. In this work, the predictive accuracy of the combined method of MD and QC is evaluated. Using widely available octanol-water partition coefficients as a case study, the performance of the combined MD and COSMOmic for predicting octanol/water partition coefficients has been compared with those of the EPI Suite™ fragment constant method, UNIFAC group contribution method and COSMOtherm. The prediction of the combined MD/COSMOmic method is the closest to the best performing fragment constant method which was specifically designed for the octanol-water system. The combined MD/QC method proves to be the most promising and robust method applicable to a wide range of complex structures of multiphase fluid systems.

Simulating the gas hydrate behavior at equilibrium dissociation: A study from Mahanadi basin of eastern offshore, India

Abstract A suitable model is developed by analyzing the effects of external stimuli such as changes in pressure and temperature on the gas production behavior for the multi-phase fluid system. Our ultimate goal was to assess and understand the response of the Mahanadi basin of eastern India, which is already identified as a prospective zone for gas hydrate exploration, while subjected to dissociation through numerical simulation. Further, a series of simulations were conducted to understand the spatial distributions of several key parameters including hydrate saturation, gas and aqueous phase velocities, heat flux, enthalpy changes, within the system. In this case, we have considered only the equilibrium reaction model to simulate the natural gas production during two vital hydrate dissociation mechanisms such as thermal stimulation and depressurization methods. Coupled equations of heat and mass balance were used in every subdomain of the simulation and the integral difference equations were used to model the hydrate-bearing geologic system of the studied region at different physicochemical environments. The simulation results suggest that the studied field has a great prospect for commercial gas production. Further, we identified that the speed of dissociation front varies with the boundary pressure, and depressurization is the suitable dissociation method to produce more gas from the studied field when compared to the thermal stimulation. The developed model can be used as an avenue for further detailed study of natural gas production from the hydrate reservoir of this region.

Effect of surfactants on the deformation of single droplet in shear flow studied by dissipative particle dynamics

ABSTRACTThe behaviour of a single droplet in shear flow is a fundamental problem in immiscible liquid–liquid multiphase fluid systems. In this article, the deformation and inclination angle of single droplet covered with surfactants in shear flow at moderate Reynolds number, when both the inertial effects and interfacial tension are the key governing factors, were simulated by dissipative particle dynamics (DPD). Weber number We was adopted to indicate the force state of the droplet and a linear relationship between the deformation parameter D and We was found when Reynolds number Re is about 1–10, which is similar to the relation of D and Capillary number Ca when Re ≪ 1. When the surfactant concentration is lower than the critical micelle concentration (CMC), the distribution of surfactants, the droplet inclination angle θ and the droplet deformation parameter D were investigated at different surfactant density at interface ds and shear rate . When the droplet size is close to the characteristic size of surfactant molecules, phase interfaces of water in oil (W/O) and oil in water (O/W) systems have different microstructures, which result in differences in the surfactant distribution, the droplet inclination angle and deformation of the two systems.