scholarly journals Color-gradient lattice Boltzmann modeling of immiscible two-phase flows on partially wetting surfaces

2017 ◽  
Vol 232 (3) ◽  
pp. 416-430 ◽  
Author(s):  
Yuan Yu ◽  
Haihu Liu ◽  
Yonghao Zhang ◽  
Dong Liang
Keyword(s):  
Lattice Boltzmann ◽  
Capillary Number ◽  
Viscosity Ratio ◽  
High Viscosity ◽  
Contact Angles ◽  
Displacement Velocity ◽  
Two Dimensional ◽  
Change Rate ◽  
Finger Length ◽  
Color Gradient

A zero-interfacial-force condition is derived and implemented to improve the wetting boundary scheme for a lattice Boltzmann color-gradient model. This new wetting boundary scheme is validated by two static problems, i.e. a droplet resting on a flat surface and a cylindrical surface, and one dynamic problem, i.e. the capillary filling in a two-dimensional channel. In these simulations, we observe that non-physical mass transfer is suppressed and spurious velocities become smaller. Meanwhile, accurate results including dynamic contact line movement are achieved for a broad range of contact angles. The model is then applied to study the displacement of immiscible fluids in a two-dimensional channel. Both the displacement velocity and the change rate of finger length are found to exhibit a linear dependence on the contact angle at the viscosity ratio of unity. The displacement velocity decreases but the change rate of finger length increases with increasing capillary number, while the displacement velocity tends to be constant, i.e. two-thirds of the maximum inlet velocity, at high viscosity ratios or low capillary numbers. In contrast to the displacement velocity, the change rate of finger length is negligible at high viscosity ratios or low capillary numbers, where the finger length is in an equilibrium state, while the equilibrium finger length itself is smaller at a higher viscosity ratio or a lower capillary number.

Study of Fingering Dynamics of Two Immiscible Fluids in a Homogeneous Porous Medium with Considering Wettability Effects Using a Pore-Scale Multicomponent Lattice Boltzmann Model

2021 ◽  
Author(s):  
Eslam Ezzatneshan ◽  
Reza Goharimehr
Keyword(s):  
Porous Medium ◽  
Dynamic Viscosity ◽  
Lattice Boltzmann ◽  
Capillary Number ◽  
Viscosity Ratio ◽  
Viscous Fingering ◽  
Immiscible Fluids ◽  
Pore Scale ◽  
Homogeneous Porous Medium ◽  
Wetting Fluid

In the present study, a pore-scale multicomponent lattice Boltzmann method (LBM) is employed for the investigation of the immiscible-phase fluid displacement in a homogeneous porous medium. The viscous fingering and the stable displacement regimes of the invading fluid in the medium are quantified which is beneficial for predicting flow patterns in pore-scale structures, where an experimental study is extremely difficult. Herein, the Shan-Chen (S-C) model is incorporated with an appropriate collision model for computing the interparticle interaction between the immiscible fluids and the interfacial dynamics. Firstly, the computational technique is validated by a comparison of the present results obtained for different benchmark flow problems with those reported in the literature. Then, the penetration of an invading fluid into the porous medium is studied at different flow conditions. The effect of the capillary number (Ca), dynamic viscosity ratio (M), and the surface wettability defined by the contact angle (θ) are investigated on the flow regimes and characteristics. The obtained results show that for M<1, the viscous fingering regime appears by driving the invading fluid through the pore structures due to the viscous force and capillary force. However, by increasing the dynamic viscosity ratio and the capillary number, the invading fluid penetrates even in smaller pores and the stable displacement regime occurs. By the increment of the capillary number, the pressure difference between the two sides of the porous medium increases, so that the pressure drop Δp along with the domain at θ=40∘ is more than that of computed for θ=80∘. The present study shows that the value of wetting fluid saturation Sw at θ=40∘ is larger than its value computed with θ=80∘ that is due to the more tendency of the hydrophilic medium to absorb the wetting fluid at θ=40∘. Also, it is found that the magnitude of Sw computed for both the contact angles is decreased by the increment of the viscosity ratio from Log(M)=−1 to 1. The present study demonstrates that the S-C LBM is an efficient and accurate computational method to quantitatively estimate the flow characteristics and interfacial dynamics through the porous medium.

scholarly journals Lattice Boltzmann Simulation of Immiscible Two-Phase Displacement in Two-Dimensional Berea Sandstone

2018 ◽  
Vol 8 (9) ◽  
pp. 1497 ◽  
Author(s):  
Qingqing Gu ◽  
Haihu Liu ◽  
Yonghao Zhang
Keyword(s):  
Interfacial Tension ◽  
Lattice Boltzmann ◽  
Viscosity Ratio ◽  
Immiscible Fluids ◽  
Lattice Boltzmann Model ◽  
Immiscible Fluid ◽  
Two Dimensional ◽  
Berea Sandstone ◽  
Fluid Saturation ◽  
Wetting Fluid

Understanding the dynamic displacement of immiscible fluids in porous media is important for carbon dioxide injection and storage, enhanced oil recovery, and non-aqueous phase liquid contamination of groundwater. However, the process is not well understood at the pore scale. This work therefore focuses on the effects of interfacial tension, wettability, and the viscosity ratio on displacement of one fluid by another immiscible fluid in a two-dimensional (2D) Berea sandstone using the colour gradient lattice Boltzmann model with a modified implementation of the wetting boundary condition. Through invasion of the wetting phase into the porous matrix, it is observed that the viscosity ratio plays an important role in the non-wetting phase recovery. At the viscosity ratio ( λ ) of unity, the saturation of the wetting fluid is highest, and it linearly increases with time. The displacing fluid saturation reduces drastically when λ increases to 20; however, when λ is beyond 20, the reduction becomes less significant for both imbibition and drainage. The front of the bottom fingers is finally halted at a position near the inlet as the viscosity ratio increases to 10. Increasing the interfacial tension generally results in higher saturation of the wetting fluid. Finally, the contact angle is found to have a limited effect on the efficiency of displacement in the 2D Berea sandstone.

Displacement of a two-dimensional immiscible droplet adhering to a wall in shear and pressure-driven flows

1999 ◽  
Vol 383 ◽  
pp. 29-54 ◽  
Author(s):  
ANTHONY D. SCHLEIZER ◽  
ROGER T. BONNECAZE
Keyword(s):  
Capillary Number ◽  
Contact Angles ◽  
Fluid Viscosity ◽  
Diffusive Transport ◽  
Two Dimensional ◽  
Parallel Plates ◽  
Contact Lines ◽  
Critical Capillary Number ◽  
Pressure Driven Flow ◽  
Pressure Driven

The dynamic behaviour and stability of a two-dimensional immiscible droplet subject to shear or pressure-driven flow between parallel plates is studied under conditions of negligible inertial and gravitational forces. The droplet is attached to the lower plate and forms two contact lines that are either fixed or mobile. The boundary-integral method is used to numerically determine the flow along and dynamics of the free surface. For surfactant-free interfaces with fixed contact lines, the deformation of the interface is determined for a range of capillary numbers, droplet to displacing fluid viscosity ratios, droplet sizes and flow type. It is shown that as the capillary number or viscosity ratio or size of the droplet increases, the deformation of the interface increases and above critical values of the capillary number no steady shape exists. For small droplets, and at low capillary numbers, shear and pressure-driven flows are shown to yield similar steady droplet shapes. The effect of surfactants is studied assuming a fixed amount of surfactant that is subject to convective–diffusive transport along the interface and no transport to or from the bulk fluids. Increasing the surface Péclet number, the ratio of convective to diffusive transport, leads to an accumulation of surfactant at the downstream end of the droplet and creates Marangoni stresses that immobilize the interface and reduce deformation. The no-slip boundary condition is then relaxed and an integral form of the Navier-slip model is used to examine the effects of allowing the droplet to slip along the solid surface in a pressure-driven flow. For contact angles less than or equal to 90°, a stable droplet spreads along the wall until a steady shape is reached, when the droplet translates across the wall at a constant velocity. The critical capillary number is larger for these droplets compared to those with pinned contact lines. For contact angles greater than 90°, the wetted area between a stable droplet and the wall decreases until a steady shape is reached. The critical capillary number for these droplets is less than that for pinned droplets. Above the critical capillary number the droplet completely detaches for a contact angle of 120°, or part of it is pinched off leaving behind a smaller attached droplet for contact angles less than or equal to 90°.

scholarly journals Lattice Boltzmann Simulation of Droplet Generation in a Microfluidic Cross-Junction

2011 ◽  
Vol 9 (5) ◽  
pp. 1235-1256 ◽  
Author(s):  
Haihu Liu ◽  
Yonghao Zhang
Keyword(s):  
Droplet Size ◽  
Flow Rate ◽  
Lattice Boltzmann ◽  
Capillary Number ◽  
Rate Ratio ◽  
Viscosity Ratio ◽  
Droplet Formation ◽  
Continuous Phase ◽  
Viscous Force ◽  
Flow Rate Ratio

AbstractUsing the lattice Boltzmann multiphase model, numerical simulations have been performed to understand the dynamics of droplet formation in a microfluidic cross-junction. The influence of capillary number, flow rate ratio, viscosity ratio, and viscosity of the continuous phase on droplet formation has been systematically studied over a wide range of capillary numbers. Two different regimes, namely the squeezinglike regime and the dripping regime, are clearly identified with the transition occurring at a critical capillary number Cacr. Generally, large flow rate ratio is expected to produce big droplets, while increasing capillary number will reduce droplet size. In the squeezing-like regime (Ca ≤ Cacr), droplet breakup process is dominated by the squeezing pressure and the viscous force; while in the dripping regime (Ca ≤ Cacr), the viscous force is dominant and the droplet size becomes independent of the flow rate ratio as the capillary number increases. In addition, the droplet size weakly depends on the viscosity ratio in both regimes and decreases when the viscosity of the continuous phase increases. Finally, a scaling law is established to predict the droplet size.

Study of the Effect of Wetting on Viscous Fingering Before and After Breakthrough by Lattice Boltzmann Simulations

2021 ◽  
Author(s):  
Peter Mora ◽  
Gabriele Morra ◽  
Dave Yuen ◽  
Ruben Juanes
Keyword(s):  
Reynolds Number ◽  
Oil Recovery ◽  
Lattice Boltzmann ◽  
Capillary Number ◽  
Viscosity Ratio ◽  
Viscous Fingering ◽  
Wetting Angle ◽  
Recovery Factor ◽  
Transition To Turbulence ◽  
Two Phase

Abstract We present a suite of numerical simulations of two-phase flow through a 2D model of a porous medium using the Rothman-Keller Lattice Boltzmann Method to study the effect of viscous fingering on the recovery factor as a function of viscosity ratio and wetting angle. This suite involves simulations spanning wetting angles from non-wetting to perfectly wetting and viscosity ratios spanning from 0.01 through 100. Each simulation is initialized with a porous model that is fully saturated with a "blue" fluid, and a "red" fluid is then injected from the left. The simulation parameters are set such that the capillary number is 10, well above the threshold for viscous fingering, and with a Reynolds number of 0.2 which is well below the transition to turbulence and small enough such that inertial effects are negligible. Each simulation involves the "red" fluid being injected from the left at a constant rate such in accord with the specified capillary number and Reynolds number until the red fluid breaks through the right side of the model. As expected, the dominant effect is the viscosity ratio, with narrow tendrils (viscous fingering) occurring for small viscosity ratios with M ≪ 1, and an almost linear front occurring for viscosity ratios above unity. The wetting angle is found to have a more subtle and complicated role. For low wetting angles (highly wetting injected fluids), the finger morphology is more rounded whereas for high wetting angles, the fingers become narrow. The effect of wettability on saturation (recovery factor) is more complex than the expected increase in recovery factor as the wetting angle is decreased, with specific wetting angles at certain viscosity ratios that optimize yield. This complex phase space landscape with hills, valleys and ridges suggests the dynamics of flow has a complex relationship with the geometry of the medium and hydrodynamical parameters, and hence recovery factors. This kind of behavior potentially has immense significance to Enhanced Oil Recovery (EOR). For the case of low viscosity ratio, the flow after breakthrough is localized mainly through narrow fingers but these evolve and broaden and the saturation continues to increase albeit at a reduced rate. For this reason, the recovery factor continues to increase after breakthrough and approaches over 90% after 10 times the breakthrough time.

scholarly journals Modeling Immiscible Fluid Displacement in a Porous Medium Using Lattice Boltzmann Method

Fluids ◽  
2021 ◽  
Vol 6 (2) ◽  
pp. 89
Author(s):  
Magzhan Atykhan ◽  
Bagdagul Kabdenova (Dauyeshova) ◽  
Ernesto Monaco ◽  
Luis R. Rojas-Solórzano
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Lattice Boltzmann ◽  
Capillary Number ◽  
Viscosity Ratio ◽  
Penetration Rate ◽  
Surface Wettability ◽  
Gas Viscosity ◽  
Boltzmann Method ◽  
Gas Penetration

The numerical investigation of the interpenetrating flow dynamics of a gas injected into a homogeneous porous media saturated with liquid is presented. The analysis is undertaken as a function of the inlet velocity, liquid–gas viscosity ratio (D) and physical properties of the porous medium, such as porous geometry and surface wettability. The study aims to improve understanding of the interaction between the physical parameters involved in complex multiphase flow in porous media (e.g., CO2 sequestration in aquifers). The numerical simulation of a gaseous phase being introduced through a 2D porous medium constructed using seven staggered columns of either circular- or square-shaped micro-obstacles mimicking the solid walls of the pores is performed using the multiphase Lattice Boltzmann Method (LBM). The gas–liquid fingering phenomenon is triggered by a small geometrical asymmetry deliberately introduced in the first column of obstacles. Our study shows that the amount of gas penetration into the porous medium depends on surface wettability and on a set of parameters such as capillary number (Ca), liquid–gas viscosity ratio (D), pore geometry and surface wettability. The results demonstrate that increasing the capillary number and the surface wettability leads to an increase in the effective gas penetration rate, disregarding porous medium configuration, while increasing the viscosity ratio decreases the penetration rate, again disregarding porous medium configuration.

Effects of Various Parameters on the Coating of Substrates with Trenches

2012 ◽  
Vol 569 ◽  
pp. 219-222
Author(s):  
Ali Mazloomi ◽  
Ali Moosavi
Keyword(s):  
Contact Angle ◽  
Lattice Boltzmann ◽  
Capillary Number ◽  
Close Agreement ◽  
Critical Size ◽  
Thin Liquid Film ◽  
Film Coating ◽  
Contact Angles ◽  
Critical Depth ◽  
Boltzmann Method

We investigate thin liquid film coating of substrates with trenches via lattice Boltzmann method. The effects of different parameters such as the capillary number, the contact angles and geometric parameters on the results are studied. Our results indicate that for trench depths greater than a critical size coating of the trench is not successful. The critical depth increases by decreasing the capillary number. Moreover we find height, width, capillary number and contact angle under which the coating is successful. The results have been compared with the available results and very close agreement has been achieved.

Lattice Boltzmann Models without Underlying Boolean Microdynamics

2018 ◽  
Author(s):  
Sauro Succi
Keyword(s):  
Lattice Boltzmann ◽  
High Viscosity ◽  
Top Down ◽  
Bottom Up ◽  
Low Reynolds ◽  
Lattice Boltzmann Models ◽  
Exponential Complexity ◽  
Statistical Noise ◽  
Collision Rule

Chapter 12 showed how to circumvent two major stumbling blocks of the LGCA approach: statistical noise and exponential complexity of the collision rule. Yet, the ensuing LB still remains connected to low Reynolds flows, due to the low collisionality of the underlying LGCA rules. The high-viscosity barrier was broken just a few months later, when it was realized how to devise LB models top-down, i.e., based on the macroscopic hydrodynamic target, rather than bottom-up, from underlying microdynamics. Most importantly, besides breaking the low-Reynolds barrier, the top-down approach has proven very influential for many subsequent developments of the LB method to this day.

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