High Viscosity Ratios Research Articles

Suppressing Viscous Fingering in Porous Media with Wetting Gradient.

The viscous fingering phenomenon often occurs when a low-viscosity fluid displaces a high-viscosity fluid in a homogeneous porous media, which is an undesirable displacement process in many engineering applications. The influence of wetting gradient on this process has been studied over a wide range of capillary numbers (7.5 × 10-6 to 1.8 × 10-4), viscosity ratios (0.0025 to 0.04), and porosities (0.48 to 0.68), employing the lattice Boltzmann method. Our results demonstrate that the flow front stability can be improved by the gradual increase in wettability of the porous media. When the capillary number is less than 3.5 × 10-5, the viscous fingering can be successfully suppressed and the transition from unstable to stable displacement can be achieved by the wetting gradient. Moreover, under the conditions of high viscosity ratio (M > 0.01) and large porosity (Φ > 0.58), wetting gradient improves the stability of the flow front more significantly.

In vitro evaluation of viscosity of facial hyaluronic acid fillers through shear tension analysis. Preliminary data

To analyze and describe the viscosity and the stress in relation to the shear rate of eleven facial fillers of four commercial HA brands with authorized use in Brazil through the flow sweep rheological analysis method. The rheological parameter of viscosity (η) was analyzed by rheometry tests through flow sweep. The behavior of shear stress showed that Rennova Fill Lido® and Lift Lido® have higher viscosity ratios (ƞ = 336 Pa.s and ƞ = 406 Pa.s, respectively). In contrast, Hialurox® brand fillers showed the lowest viscosity value (ƞ) (Hialurox Ultra Soft 8 mg/g® ƞ= 9 Pa.s, Fine 16 mg/g ƞ= 29 Pa.s, Fill 24 mg/g ƞ= 36 Pa.s, Lift 26 mg/g ƞ= 50 Pa.s). The flow sweep showed variations in the viscosity (ƞ) of the eleven HA dermal fillers. Rennova Fill Lido® and Lift Lido® have a lower degree of spreadability and are less susceptible to shear forces and yield strength, making them ideal candidates for the intended treatment.

A hybrid immersed interface and phase-field-based lattice Boltzmann method for multiphase ferrofluid flow

In this study, we developed a hybrid immersed interface and phase-field lattice Boltzmann (LB) method to simulate multiphase ferrofluid flows. The Laplace equation for the magnetic potential with an interface jump condition was numerically solved using a phase-field-based immersed interface method. The phase interface was tracked by the conservative Allen–Cahn equation. One LB equation was used to capture the interfaces between the two immiscible fluids and another to solve for the hydrodynamic properties. The magnetic stress was treated as an interfacial force at the interface, and thus both the magnetic and capillary forces could be formulated in a unified phase-field method framework. Several typical problems, including a circular cylinder in a uniform magnetic field, deformation of a ferrofluid droplet under a uniform magnetic field, two bubbles merging in the ferrofluid, and a ferrofluid droplet suspension under a shear flow to study the rheological characteristics, were simulated to test the accuracy, applicability, and numerical stability of the present model. The numerical examples demonstrated that the present model is able to capture basic phenomenological features in magnetic multiphase flow problems with high density and high viscosity ratios.

Experimental study of viscous fingering in sand-pack model for heavy oil reservoir

Viscous fingering phenomenon in porous media has a great impact on industrial processes, such as enhanced oil recovery processes. The previous experimental works mainly used Hele-Shaw models and micromodels to investigate viscous fingering mechanisms. However, Hele-Shaw models simulate porous media flow in a narrow gap with no pore structure. Micromodels’ pore structures are simplified, and the material used to make micromodel generally has different wettability compared with real rocks. Therefore, a large-dimensions of 40 cm × 20 cm× 0.5 cm sand-pack model with a vertical well in the center is used in this study to mimic real reservoir in terms of pore structure, wettability conditions and real radial flow. To the best of our knowledge, there is no reported literature on viscous fingering experimental study for radial flow in real sand-pack models. Immiscible flooding processes with high viscosity ratios ranging from 853.9 to 32080 and different injection rates ranging from 0.01 to 0.5 ml·min−1 were conducted. The viscous fingering phenomena were captured and analyzed qualitatively and quantitatively. As capillary number increases, more unstable interfaces and complicated finger structures were visually observed and validated through fractal dimension analysis. These experimental results are in well agreement with previously reported results obtained from Hele-Shaw models and micromodels. The dimensionless number (Ca*µr2) analysis suggests viscosity has a greater effect on viscous fingering compared with injection rate, which was consistent with the conclusion of micromodel studies. Besides critical injection rate (0.01–0.05 ml∙min−1), increasing the viscosity ratio to a critical viscosity ratio (2946) leads to a significant decrease of breakthrough time, which was not reported in the literature. And different from linear displacement in which the viscous fingering followings two stages, additional pseudo-stable displacement could be generated after the rapid finger generation stage and combination stage for the radial displacement.

Effects of injection directions and boundary exchange times on adaptive pumping in heterogeneous porous media: Pore-scale simulation

Adaptive pumping, changing pumping rates or exchanging injection and extraction wells, is an enhancement of traditional Pump-and-Treat (P&T) technology. Since most previous studies on adaptive pumping are conducted through field-scale simulations, the mechanism behind it is not fully understood. An in-depth investigation of the pore-scale remediation mechanism of adaptive pumping is undoubtedly helpful in combining it with other decontamination methods to further enhance the remediation efficiency. In this study, coupling the Cahn–Hilliard phase field method and the Navier-Stokes equations, the dynamic displacement process in a heterogeneous porous medium is obtained. The effects of initial injection direction, boundary exchange times, and displacement regimes on the interface evolution and the remediation efficiency are systematically investigated. The results present that a significant increase in phase interface area is the most critical remediation mechanism for adaptive pumping. The effects of injection directions and boundary exchange times on remediation performance are mainly determined by the differences in pore connectivity and flow parameters. Higher pore connectivity under high and low viscosity ratios inhibits and promotes remediation performance, respectively. At high viscosity ratios, the residual oil morphology in the matrix after adaptive pumping is similar to that obtained by positive pumping with the opposite initial injection direction. The improvement in remediation performance of adaptive pumping is more significant under low viscosity ratio conditions. These results provide new pore-scale insights into the remediation mechanism of adaptive pumping, which contribute to the design and application of innovative remediation methods.

Probing the influence of inertia, viscosity, and initial offset on the hydrodynamic interaction of droplet pairs in confined shear flow

The collision behavior of droplet pairs subjected to confined shear flows at high density and viscosity ratios remains unexplored and unquantified, and therefore, the critical density and viscosity ratios for the collision mode of droplets under geometric parameters were unknown. Simulations have been performed using a free-energy-based lattice Boltzmann method, with the aim of determining new regimes compared to the previous study. The results demonstrate that the interaction between viscous and inertia forces plays a vital role in the coalescence nature of droplets, their deformation, course of trajectory, as well as their expedition toward the steady state.

Prediction of spontaneous imbibition with gravity in porous media micromodels

In this work, theoretical modelling, quasi-three-dimensional (quasi-3D) simulations and micromodel experiments are conducted to study spontaneous imbibition with gravity in porous media micromodels. By establishing the force balance governing the spontaneous imbibition process, we develop a theoretical model for predicting the imbibition length against time in a rectangular capillary. The theoretical model is then extended to the prediction of a compact displacement process in a micromodel by using an equivalent width, which is derived by analogising the micromodel to a rectangular capillary. By simulating spontaneous imbibition in a rectangular capillary with various aspect ratios ( $\varepsilon$ ), we show that the application condition of the quasi-3D method is $\varepsilon \leqslant 1/3$ . Next, we simulate spontaneous imbibition in micromodels with various geometries and flow conditions. Fingering and compact displacement are identified for varying viscosity ratios and gravitational accelerations. At low (high) viscosity ratio of wetting to non-wetting fluids, an upward (downward) gravity can promote the stability of the wetting front, favouring the transition from fingering to compact displacement. In addition, we find that the depth-oriented interface curvature dominates the capillary effect during the imbibition, and such a mechanism is considered by introducing an equivalent contact angle into the theoretical model. With the help of equivalent width and contact angle, the theoretical model is shown to provide satisfactory prediction of the compact displacement process. Finally, a micromodel experiment is presented to further verify the developed theoretical model and the quasi-3D simulation.

MPS-based axisymmetric particle method for bubble rising with density and pressure discontinuity

Numerical simulation of gas bubble rising in liquid is challenging due to high density and viscosity ratios. This study proposes to model the liquid and gas phases separately by the incompressible and Weakly Compressible Moving Particle Semi-implicit (MPS) methods with the aim of preserving the interfacial discontinuity. The liquid-gas interface is explicitly represented by a series of discrete nodes. By adequately enforcing the stress conditions on these moving interface nodes, the MPS and WC-MPS methods are coupled. The surface tension is considered as a pressure jump rather than the volume force. Without applying any smoothing or averaging scheme, the density, viscosity and pressure are discontinuous across the interface. The axisymmetric formulation is directly introduced based on the least squares method to save computational cost. In addition, a multi-time step algorithm is proposed so that independent time increments can be adopted for different phases. Furthermore, the particle shifting technique is extended to control the multi-spatial resolution dynamically. Several numerical tests, including hydrostatic pressure problems, droplet deformation and bubble rising benchmark are conducted to show the accuracy, efficiency and stability. Finally, validations are performed using experimental results with wide ranges of Reynolds number and Bond number, which dominate the bubble shape.

A partitioned continuous surface stress model for multiphase smoothed particle hydrodynamics

A density partitioned continuous surface-stress (CSS) model is presented within a multi-phase smoothed particle hydrodynamics (SPH) framework. We follow the original work of Adami et al. (2010) [1] to partition the surface-tension force from a zeroth-order consistent continuum surface-stress model. As a consequence of the scaled surface-tension force, both the surface-tension based artificial speed of sound and the numerical time step criteria can be relaxed for phase interfaces with high density ratio. A new color-gradient treatment and a static contact angle based surface-stress boundary condition is introduced to incorporate wetting behavior. All models are validated by comparison to analytical solutions of several surface-tension dominated flows. The resulting scheme is demonstrated to handle both capillary and Marangoni forces for high density and viscosity ratios.

Micromixing performance of a miniaturized annular rotating flow mixer (MARFM)

Miniaturization of mixers is becoming an increasingly significant topic in process intensification. In this work, we develop a novel miniaturized annular rotating flow mixer (MARFM) by integrating the rotating flow field and micro-scale effect. The micromixing performance of MARFM is evaluated by the Villermaux/Dushman reaction system. Effects of various structural parameters on the micromixing performance are investigated. Two flow regions named stratification region and entrainment region have been firstly distinguished. Increasing rotational speed can remarkably improve micromixing performance under the stratification region rather than the entrainment region. In addition, the mixing performance at extreme flow conditions including high fluid viscosity and high flow rate ratio can be substantially improved in the MARFM. Segregation index is at least an order of magnitude smaller than that without the rotating flow field. Moreover, the micromixing time could range from 10−5 to 10−3 s in the MARFM, which is 1-3 orders of magnitude smaller than that of conventional mixers. Relationship between micromixing time and mean energy dissipation rate is established, which shows that higher energy utilization efficiency has been reached.

An improved lattice Boltzmann model for fluid–fluid–solid flows with high viscosity ratio

In this paper, we present an improved lattice Boltzmann model for fluid–fluid–solid (FFS) flows with a high viscosity ratio. The bounce-back particle model is combined with the Shan–Chen (SC) multicomponent model. We extend the bounce-back scheme based on velocity interpolation and a fresh-node initialization approach with second-order accuracy to moving particles within the framework of the multicomponent model. An improved virtual solid density model for wetting boundary conditions is employed to implement contact angles on curved boundaries. We examine the factors that lead to the violation of mass conservation, and an easy redistributing method is developed to fix the mass leakage issue. The combined multiphase particle model is able to simulate FFS flows with a high viscosity ratio of up to 1000 while preserving the total mass of the two fluids. The performance of the approach is tested by a variety of numerical experiments. The dynamic behaviors of moving contact lines on the curved boundary are validated by a droplet wetting on a solid particle. The model is then applied to simulate dynamic FFS problems, such as particle wetting at the fluid interface and particle motion through a fluid–fluid interface. According to the simulation results, the present model is capable of capturing the total force exerted on a particle by the fluid and the interface. However, the SC-type fluid–solid interaction force does not equal the capillary force in the present model. Finally, the self-assembly process of two floating particles on a liquid–liquid interface is investigated.

Mixing in density- and viscosity-stratified flows

The lock-exchange problem is used extensively to study the flow dynamics of density-driven flows, such as gravity currents, and as a canonical problem to mixing in stratified flows. Opposite halves of a domain are filled with two fluids of different densities and held in place by a lock-gate. Upon release, the density difference drives the flow causing the fluids to slosh back and forth. In many scenarios, density stratification will also impose a viscosity stratification (e.g., if there are suspended sediments or the two fluids are distinct). However, numerical models often neglect variable viscosity. This paper characterizes the effect of both density and viscosity stratification in the lock-exchange configuration. The governing Navier–Stokes equations are solved using direct numerical simulation. Three regimes are identified in terms of the viscosity ratio μ2/μ1=(1+γ) between the dense and less dense fluids: when γ≪1, the flow dynamics are similar to the equal-viscosity case; for intermediate values (γ∼1), viscosity inhibits interface-scale mixing leading to a global reduction in mixing and enhanced transfer between potential and kinetic energy. Increasing the excess viscosity ratio further (γ≫1) results in significant viscous dissipation. Although many gravity or turbidity current models assume constant viscosity, our results demonstrate that viscosity stratification can only be neglected when γ≪1. The initial turbidity current composition could enhance its ability to become self-sustaining or accelerating at intermediate excess viscosity ratios. Currents with initially high excess viscosity ratio may be unable to dilute and propagate long distances because of the decreased mixing rates and increased dissipation.

The Effect of Viscosity Ratio and Peclet Number on Miscible Viscous Fingering in a Hele-Shaw Cell: A Combined Numerical and Experimental Study

The results from a series of well characterised, unstable, miscible displacement experiments in a Hele-Shaw cell with a quarter five-spot source-sink geometry are presented, with comparisons to detailed numerical simulation. We perform repeated experiments at adverse viscosity ratios from 1 to 20 and Peclet numbers from 10\(^4\) to 10\(^6\) capturing the transition from 2D to 3D radial fingering and experimental uncertainty. The open-access dataset provides time-lapse images of the fingering patterns, transient effluent profiles, and meta-information for use in model validation. We find the complexity of the fingering pattern increases with viscosity ratio and Peclet number, and the onset of fingering is delayed compared to linear displacements, likely due to Taylor dispersion stabilisation. The transition from 2D to 3D fingering occurs at a critical Peclet number that is consistent with recent experiments in the literature. 2D numerical simulations with hydrodynamic dispersion and different mesh orientations provide good predictions of breakthrough times and sweep efficiency obtained at intermediate Peclet numbers across the range of viscosity ratios tested, generally within the experimental uncertainty. Specific finger wavelengths, tip shapes, and growth are hard to replicate; model predictions using velocity-dependent longitudinal dispersion or simple molecular diffusion bound the fingering evolution seen in the experiments, but neither fully capture both fine-scale and macroscopic measures. In both cases, simulations predict sharper fingers than the experiment. A weaker dispersion stabilisation seems necessary to capture the experimental fingering at high viscosity ratio, which may also require anisotropic components. 3D models with varying dispersion formulations should be explored in future developments to capture the full range of effects at high viscosity ratio and Peclet number.

Effects of high viscosity ratio and interfacial tension on droplet formation

Effects of high viscosity ratio and interfacial tension on droplet formation

Study of Rayleigh-Taylor instability in viscosity-stratified fluid layers

The Rayleigh-Taylor instability in viscosity varying fluid layers is studied. A heavier fluid layer is superimposed on a lighter fluid layer. Both the fluid layers are bounded between two parallel isothermal horizontal walls. Out of the two walls, one wall is isothermally heated, while the other wall is isothermally cooled. The Rayleigh-Taylor instability is studied for axisymmetric configuration. Viscosities of both the fluids are considered to be varying with temperature. The effect of viscosity ratio, temperature ratio, heating location, Prandtl number and Weber number on the instability is studied. When the viscosity of fluid layers vary with temperature, the configuration becomes more unstable compared to that for constant viscosity fluid layers. For varying viscosity fluid layers the spike undergoes large deformations. At lower viscosity ratios, mushroom shaped spike is formed with elongated skirt structure. Whereas, at higher viscosity ratios, spike with fluid column structure is formed. It is found that increasing viscosity ratio shows stabilizing effect. Increasing temperature ratio is found to show destabilizing effect with complex spike structure formation at high temperature ratios. In top wall heating configuration, formation of mushroom shaped spike and skirt of the spike occurs earlier in a thinner and elongated form compared to that of bottom wall heating configuration. Prandtl number showed insignificant effect on the instability. For the parameter values of the study, when Weber is lower than 55 the configuration is stable and does not undergo instability. Overall, surface tension has shown stabilizing effect on the instability.

Effect of lubricant addition on bubble motion of refrigerant CO2 in the nucleate boiling process

In this study, the influence mechanism of lubricating oil on the heat transfer of CO2 flow boiling was investigated from a mesoscopic perspective. A multiphase and multicomponent lattice Boltzmann model was proposed to simulate the rising motion of CO2 bubbles in CO2 with a small amount of lubricating oil based on the pseudopotential model. There are few simulations of multicomponent with different chemical compositions in existing studies. Moreover, the original pseudopotential model exhibited increasing instabilities at higher viscosity ratios. The model proposed in this study realized the mesoscopic simulation of a CO2/lubricant system by using an explicit forcing model to achieve numerical calculation under a high viscosity ratio and solve the evolution of the number density of each component to obtain the evolution of the macro parameters. The effectiveness of the model was verified using a Laplace's law simulation. Based on this model, the rising motions of single bubbles, double bubbles, and bubble groups under different oil concentrations were simulated. The effects of the lubricant on the rising velocity, morphology, and interaction of bubbles during bubble motion were analyzed in detail. The numerical results indicated that the variations in bubble shape decreased and drag force increased with the addition of oil. At an oil concentration of 0.05, the drag coefficient was 1.14 times higher than that under the oil-free condition. In addition, the presence of oil weakened the flow field disturbance caused by bubble interactions and resulted in the suppression for nucleate boiling.

Density-modification displacement using colloidal biliquid aphron for entrapped DNAPL contaminated aquifer remediation

Colloidal biliquid aphron (CBLA) is a strong density modifier for dense nonaqueous phase liquids (DNAPLs). However, the underlying mechanisms responsible for density modification and displacement is not yet clear. Here, a series of batch column and sandbox experiments were conducted to achieve substantial removal and irreversible density reduction of tetrachloroethylene (PCE). The mass of PCE retained in the column and sandbox was less than 1% under suitable injection conditions, and the density of PCE in the effluent was less than that of water (fluctuated in the range of 0.74–0.96 g/cm3). The displacement process was controlled by the high viscosity ratio of CBLA to PCE (52.3). The emulsified and dissolved phase of PCE formed after reaction with CBLA, and the light nonaqueous phase liquid (LNAPL) phase formed after injecting demulsifier solution. The phase analysis played a significant role in monitoring the changes in concentration and density of PCE. The density-modification displacement technique using CBLA reduced the mass of residual PCE by a factor of 165 compared to surfactant flushing, and there was no risk of downward migration of PCE. This study contributes to a better remediation of entrapped DNAPL in contaminated aquifer.

Shear-induced migration of a viscous drop in a viscoelastic liquid near a wall at high viscosity ratio: Reverse migration

• A drop under shear migrates laterally away from a wall in shear. • Medium viscoelasticity and viscosity ratio affects the migration. • High viscosity ratio and high Deborah number leads to migration towards the wall. • The critical viscosity ratio varies inversely with the capillary number. • The critical Deborah number also varies inversely with the capillary number. Wall-induced migration of a viscous drop in a viscoelastic fluid subjected to a plane shear is numerically simulated to investigate the effects of drop/matrix viscosity ratio. In a Newtonian system, drop migration away from the wall is inhibited as the viscosity ratio is increased. Here, we show that the introduction of the matrix viscoelasticity further decreases the migration and can even reverse its direction ‘from away’ to ‘towards the wall’, a phenomenon not seen in Newtonian systems. The migration towards or away from the wall eventually settles in a quasi-steady state that only depends on the instantaneous wall separation independent of the initial position of the drop. Drops migrating towards the wall initially increase their velocity, but as they approach the wall, they decelerate, showing a non-monotonic variation. The migration direction depends on the viscosity ratio, viscoelasticity (Deborah number), and the capillary number. We compute phase diagrams in the parameter space showing boundaries where migration changes direction. The critical Deborah number (at a fixed viscosity ratio) and the critical viscosity ratio (at a fixed Deborah number) for direction reversal approximately scales with the inverse of the capillary number.

Enhancing thermal conductivity of segregated structural PE/PVDF/BN composites: Role of viscosities

It is challenging to fabricate polymer composites with high thermal conductivity at a low concentration of fillers. In this work, Polyethylene (PE)/Poly (vinylidene fluoride) (PVDF)/Boron nitride (BN, average size of 25 μm and specific surface area of 2–4) segregated structural composites were prepared to investigate the effect of microstructure evolution along with a wide range of matrix viscosity ratios (0.08–20.96) on the thermal conductivities. The PE/PVDF/BN composite with a viscosity ratio of 20.96 shows a high thermal conductivity of 2.36 W/(m·K), outperforming the composite with a viscosity ratio near 1 (1.34 W/(m·K)) by 177%. Moreover, the orientation of BN was characterized by the X-ray diffractometer, which demonstrated that I100/I002 could be altered by different viscosity ratios, indicating a higher alignment in the vertical direction. Besides, infrared thermal images and energy harvest measurements further confirmed the composite with high viscosity ratio presents a stronger capability to dissipate the heat. The obtained results enlightened to the valuable fundamental design and the fabrication of the highly thermal-conductive polymer-matrix composites by controlling viscosity ratio, expecting to be applied as advanced thermal management materials.

Pore-scale study of drainage processes in porous media with various structural heterogeneity

Multiphase flow in porous media is widely encountered in many scientific and engineering fields. In this work, Voronoi diagram is used to reconstruct porous structures with low permeability and high heterogeneity, and the color-gradient lattice Boltzmann method is employed to simulate two-phase displacement with high viscosity ratio. Three benchmarks are utilized to validate the model, which are the Young-Laplace test, the contact angle test and the relative permeability in a 2D channel. Effects of capillary number, structural heterogeneity and wettability are analyzed. The results show that a higher capillary number leads to viscous fingering with a higher recovery rate. The connectivity rate is used to quantify the continuous wide pores, showing that structure heterogeneity will increase the probability of continuous wide pores, which promotes the formation of gas channeling, thus reducing the recovery rate. However, local structure modifications, providing that the overall homogeneity is retained, would not induce significant differences in recovery rates and displacement patterns. Complex pore structures will also cause capillary snap off, leading to more dead-end fingerings and more complicated two-phase dynamic behaviors. Meantime, a more wetting invading phase would induce a stop-wait-overlap phenomenon, which would increase the recovery rate and render the displacement more compact.