Increasing Viscosity Ratio Research Articles

Interaction of a Taylor bubble with the liquid–liquid interface in a notched tube

Injection of air into stratified liquids for improved mixing and for the removal of oil droplets from water is some well-established applications for augmentation of heat and mass transfer and purification of water. The present study investigates the dynamics of a Taylor bubble passing through the liquid–liquid interface in a vertical tube provided with rounded notch of different radii using the Eulerian approach-based volume of fluid method. The complete bypass of the Taylor bubble across the liquid–liquid interface and the notch is observed for dimensionless notch radius, r* = 0.0388, whereas the Taylor bubble has bypassed in the form of smaller volumes periodically pinched-off near the notch for higher notch radius. The drag coefficient has significantly increased during the bypass of the bubble across the liquid–liquid interface, its peak has an order of magnitude ≅102 for r* = 0.0388, and it is ≅ 103 for a larger notch radius. This increase in the drag coefficient is also manifested in terms of significant increase in the wall shear stress and capillary pressure drop across the notch. The increase in liquid viscosity ratio has resulted in a slight increase in pinched-off bubble volumes and their surface oscillations.

Improved lattice Boltzmann model for immiscible multicomponent systems with high viscosity gradients at the interface.

We propose alternative discretization schemes for improving the lattice Boltzmann pseudopotential model for incompressible multicomponent systems, with the purpose of modeling the flow of immiscible fluids with a large viscosity ratio. Compared to the original model of Shan-Chen [Phys. Rev. E 47, 1815 (1993)1063-651X10.1103/PhysRevE.47.1815], the present discretization schemes consider: (i) an explicit force term, (ii) a second-order discretization of the stream term, (iii) a moments-based model for the kinetic nonequilibrium distributions, and (iv) a high-order discretization of the spatial derivative terms. To verify the accuracy of the proposed model, the effects of varying the viscosity ratio as well as both fluid's viscosities on spurious currents and capillary number are investigated for the problems dealing with a static bubble, two-component Poiseuille flow, and immiscible fluid-fluid displacement. The resulting algorithm maintains the simplicity of the pseudopotential model while allowing an easy implementation for multicomponent systems. The results of the model herein proposed show improved control of the interface region and interfacial tension, relatively smaller magnitudes of spurious current values with increasing viscosity ratio, and also a significantly wider stability range with respect to the previously best results in the literature.

Modelling the effect of soluble surfactants on droplet deformation and breakup in simple shear flow

A hybrid lattice Boltzmann and finite difference method is applied to study the influence of soluble surfactants on droplet deformation and breakup in simple shear flow. First, the influence of bulk surfactant parameters on droplet deformation in two-dimensional shear flow is investigated, and the surfactant solubility is found to influence droplet deformation by changing average interface surfactant concentration and non-uniform effects induced by non-uniform interfacial tension and Marangoni forces. In addition, the droplet deformation first increases and then decreases with Biot number, increases significantly with adsorption number $k$ and decreases with Péclet number or adsorption depth; and among the parameters, $k$ is the most influential one. Then, we consider three-dimensional shear flow and investigate the roles of surfactants on droplet deformation and breakup for different capillary numbers and viscosity ratios. Results show that in the soluble case with $k=0.429$ , the droplet exhibits nearly the same deformation as in the insoluble case due to the balance between surfactant adsorption and desorption; upon increasing $k$ from 0.429 to 1, the average interface surfactant concentration is greatly enhanced, leading to significant increase in droplet deformation. The critical capillary number of droplet breakup $C{{a}_{cr}}$ is identified for varying viscosity ratios in clean, insoluble and soluble ( $k=0.429$ and 1) systems. As the viscosity ratio increases, $C{{a}_{cr}}$ first decreases and then increases rapidly in all systems. The addition of surfactants always favours droplet breakup, and increasing solubility or $k$ could further reduce $C{{a}_{cr}}$ by increasing average interface surfactant concentration and local surfactant concentration near the neck during the necking stage.

Improvement of the properties of poly (L-lactide)/ethylene-ethyl acrylate-glyceryl methacrylate terpolymer (EGA) by the introduction of stereocomplex polylactide crystals

Ternary blends comprising poly(L-lactide) (PLLA), ethylene-ethyl acrylate-glyceryl methacrylate terpolymer (EGA), and poly(D-lactide) (PDLA) were melt blended using low-temperature method to obtain blends with balanced properties. The formation of stereocomplex polylactide (SC-PLA) crystals was verified by torque changes and differential scanning calorimetry (DSC) results. The SC-PLA crystals formed a percolating network in the PLLA matrix at a concentration of 2 wt% PDLA, and blend melt presented solid-like rheological behavior. Attributing to the increased viscosity ratio between PLLA and EGA, the size of dispersed EGA phase increased. The crystallization of PLLA was significantly promoted because of the nucleation effect of SC-PLA crystals. The PLLA/EGA/2 %PDLA ternary blends with elongation at break of 138 % and impact strength of 72.3 kJ/m2 exhibited excellent toughness. These ternary blends demonstrated exceptional crystallization ability and tailored rheological and mechanical properties, opening a new path for developing high-performance PLLA-based materials in packaging industry.

Numerical simulation investigation of the mechanism of lacquer curtain formation in curtain coating

To study the key factors on integrated curtain formation and breakup in curtain coating production process, we used the numerical simulation method to analyze the various stages of the curtains from full curtain to full thread state by changing the inlet flow rate, which is, changing the Weber number (We). The numerical model was based on an actual production machine, and the physical properties of the lacquer were accurately measured for the simulation. It is found that with the gradual breakup of the curtain, the oscillation of the curtain gradually increased, there was obvious distortion and increase in Turbulent Viscosity Ratio (TVR) at the breakup, and there was a decrease in Dynamic Pressure (DP) at the top of the breakup. Different curtain state reflects a shift from inertia force dominance to a balance of forces and finally to surface tension dominance. The finding from the simulation, also the comparison between the results of simulation and experiments provided the basis to understand the mechanism of curtain coating, also inspired the engineers to optimize the geometry of curtain coater and the coating production parameters for easier integrated curtain forming.

Two‐Phase Relative Permeability Curves of Bingham Heavy Oil Under Different Types of Wettability: A Theoretical Model

As an important and universal petrophysics of heavy oil reservoirs, the two‐phase flow ability inside porous medium is vital for heavy oil development. Utilizing the laminar flow theory and an ideal pore structure, especially cylinder model, the function of the relative permeability of heavy oil–water with water saturation is derived by incorporating the principles of momentum conservation and the characteristics of Bingham fluids, which was modified by validated experiment. Two‐phase relative permeability, considering heavy oil as non‐Newtonian fluid, is the function of water saturation, pore size, oil–water viscosity ratio, and yield stress. The results of the validated experiment show that the theoretical values calculated employing the modified equation exhibit better agreement with the experimental values, particularly when the viscosities of two‐phase fluid are great. The results of the modified two‐phase relative permeability show a decrease in water saturation interval corresponding to the two‐phase flow area and a smaller value of permeability at equal two‐phase relative permeability. The oil–water viscosity ratio in the hydrophobic pores affects the water‐phase relative permeability, although the magnitude of its influence diminishes as the viscosity ratio increases. The behavior of relative permeability in hydrophilic pores is the opposite of that in hydrophobic pores. This work can afford good application prospects for mobility control in multilayered reservoirs through the heterogeneous‐phase‐composite fluid. The saturations of the remaining oil and irreducible water also play a vital role in the prediction of permeability. The work can afford good application prospects for the flow behavior of Bingham heavy oil in pores with different types of wettability.

Unsteady magneto-hydro-dynamics flow of Jeffrey fluid through porous media with thermal radiation, Hall current and Soret effects

In the present paper, Hall current and Soret reaction effects on unsteady natural convection MHD flow with viscous, incompressible, and electrically conducting fluid through a porous medium in the presence of chemical reaction and thermal radiation have been studied. The fluid has considered non-Newtonian fluid, which is Jeffrey fluid. The non-dimensional flow governing equations are solved analytically through the perturbation method, and obtained results of velocity, concentration, and temperature have been analyzed with the help of graphs drawn for different parameters. The numerical values of skin friction, Nusselt number, and Sherwood number have been tabulated. The study's results may find applications related to solar physics dealing with the solar cycle, Magnetohydrodynamics sensors, rotating MHD induction machine energy generators, sunspot development, the structure of rotating magnetic stars, etc. The velocity profiles are observed to increase with an increase in Hall parameters, but reverse effects are found with an increase in viscosity ratio and chemical reaction parameter. The thermal radiation parameter is to increase the temperature profiles, but the reverse effect is observed with an increase in the frequency of oscillations. Further, the concentration is decreased with an increase in the Schmidt number and increased with an increase in the chemical reaction parameter.

Dynamic mechanism of double emulsion droplets flowing through a microfluidic T-junction

A microfluidic chip is adopted to study the droplet dynamic behaviors when flowing through the T-junction. Large ranges of initial length (Lo/w = 0.8–2.8), capillary number (Cao = 0.030–0.165), and viscosity ratio (λo = 0.16–5.90) are considered to identify the deformation characteristics and the breakup results. Three flow patterns are categorized in the T-junction, and critical conditions are expressed as power law relations between the normalized length and the capillary number. The coupling competition exists between outer neck thinning and inner droplet shifting, which influences the deformation process. A state diagram indicating the number of breakups is built through two key features of the shifting behavior, namely, the shifting distance and the shifting velocity. With increasing viscosity ratio, thresholds of both breakups decrease due to the reduced deformation resistance caused by vortex flow and the weakened coupling effect, resulting from the suppressed shifting behavior. The shell thickness via twice-breakup pattern depends solely on the viscosity ratio.

Pore scale insights into the role of inertial effect during the two-phase forced imbibition

Fluid inertia could significantly alter the flow paths of fluids in multiphase flow. This study aims to quantify the role of the inertia effect in fluid flow through porous media using the modified color-gradient lattice Boltzmann method. Specifically, we focused on understanding the effects of fluid inertia on two-phase distribution, pore scale events, displacement patterns, transient behaviors of fluids, and the consumption of thermodynamic energy. Results show that the effect of fluid inertia on the two-phase distribution and the final invading wetting saturation is trivial under a low viscosity ratio. However, as the viscosity ratio increases, the inertia effect becomes more pronounced and cannot be ignored in the displacement process. This observation can also be found from the dependence of the invading saturation on the injected volume when the viscosity ratio and the Ohnesorge (Oh) number are varied. In addition, we found that the contribution from the post-breakthrough stage to the total invading saturation is increasingly significant with the increasing viscosity ratio, and its contribution varies depending on the fluid inertia for a given viscosity ratio. We also used the pressure difference between the inlet and outlet to identify the direction of energy conversion in multiphase flow. It is found that for the high viscosity ratio, there is a positive relationship between the dissipated energy and the invading saturation, and both exhibit a non-monotonic change with increasing Oh. However, for low viscosity ratios, fluid inertia does not significantly affect forced imbibition. In addition, the nonwetting phase becomes less connected with the injected wetting fluid, and there exists an almost linear relationship between the invading wetting saturation and the Euler characteristic, irrespective of the Oh numbers for a given viscosity ratio. The mechanism of inertial effect is that the local fluid velocity can be several orders of magnitude larger than the mean velocity despite the low capillary number, which leads to frequent release of surface energy and notably alters the flow paths, particularly under the unfavorable displacement pattern.

Effect of mechanical properties of red blood cells on their equilibrium states in microchannels

The equilibrium positions of red blood cells (RBCs) and their steady motions in microchannel affect the hemodynamics in vivo and microfluidic applications on a cellular scale. However, the dynamic behavior of a single RBC in three-dimensional cylindrical microchannels still needs to be classified systematically. Here, with an immersed boundary method, the phase diagrams of the profiles and positions of RBCs under equilibrium states are illustrated in a wide range of Capillary numbers. The effects of initial positions are explored as well. Numerical results present that the profiles of RBCs at equilibrium states transform from snaking, tumbling to slipper, or parachute with the increase in flow rates, and whether RBCs finally approach slipper or parachute motion under large shear rates is dependent on their initial positions. With the increase in tube diameters, the equilibrium positions of RBCs are closer to tube walls relatively. Although both the increase in membrane shear modulus and the viscosity ratio are regarded as the stiffening of RBCs, the change of membrane property does not affect the dependence of the profiles and positions of RBCs at equilibrium states on the shear rates of the flow obviously, but with the increase in viscosity ratio, RBCs move further away from the centerline of the tube associating with more asymmetric characteristics in their stable profiles. The present results not only contribute to a better understanding of the dynamic behavior and multiple profiles of single RBC in microcirculation, but also provide fundamentals in a large range of Capillary numbers for cell sorting with microfluidic devices.

Pore-scale study of three-phase reactive transport processes in porous media

Coupled three-phase flow and reactive transport processes are widely encountered in many scientific and engineering problems. In the present study, a pore-scale model based on the lattice Boltzmann method is developed to simulate coupled three-phase flow and reactive transport processes. The model is validated by contact angle test of droplets on a curved surface and confined reactive mass transport in a three-phase system. The pore-scale model validated is then employed to study the three-phase reactive transport in channels and porous media. The evolution of the three-phase distribution, the concentration field, and the contact line length are discussed in detail. For a two-channel structure, the result shows that as the viscosity ratio increases, the phase with higher viscosity is more difficult to be displaced. Moreover, as the surface tension force between two certain phases increases, the third phase tends to form a film between the two phases, thus suppressing the reactive transport between the two phases. Finally, pore-scale simulation results of three-phase flow in a two-dimensional porous medium show that as viscosity of the phase to be displaced increases, the recovery rate of the displaced phase decreases, and the displacing phase tends to follow the mechanism of viscous fingering. Finally, while the viscosity of the displaced phase can be reduced due to the existence of the species, the recovery rate does not necessarily increase and sometimes even reduces due to the combined bypass and lubrication effects.

Competition between main meniscus and corner film flow during imbibition in a strongly wetting square tube

Imbibition in a strongly wetting square tube with corner flow can be described by an interacting capillary bundle model, where the first sub-capillary describes the main meniscus flow while the others describe corner film flow. In this work, an advanced modified interacting capillary bundle model (MICBM) is developed to simulate imbibition dynamics in a strongly wetting square tube incorporating the viscous coupling effect. The flow conductances of each sub-capillary are obtained from two-phase lattice Boltzmann simulations with different viscosity ratios considering the viscous coupling effect. After verifying its accuracy, MICBM is used to analyze the imbibition dynamics of main meniscus and corner film flows under different conditions. The results show that, with increasing viscosity ratio between wetting and non-wetting fluids and increasing driving force, the wetting corner film development tends to be less significant compared with main meniscus flow. Interestingly, the corner film length first increases then decreases when the wetting fluid is less viscous than the non-wetting fluid in a long square tube. A phase diagram of dimensionless corner film length versus driving force and viscosity ratio is proposed to characterize the competition between main meniscus and corner film flow. Gravity and smaller contact angle make the corner film development more obvious. In addition, the tube length and width are shown to influence the interaction between main meniscus and corner film flow for a low viscosity ratio. The underlying physics of the above phenomena are explained in detail.

Dripping and jetting generation mode in T-junction microchannels with contractive structures

Droplet generation in T-junction microchannels with contractive structures is investigated under different flow rates and viscosity conditions by numerical simulation to improve the monodispersity and controllability of the microdroplets. Basic flow modes are observed, including dripping, transition, and jetting, under various flow rates and dispersed phase viscosities. The flow condition for the transition mode is modeled as a function of capillary number, flow rate ratio, and viscosity ratio to indicate the conversion of generation modes. Unlike ordinary T-junction microchannels, in this case, the droplet diameter first decreases and then increases with the increasing viscosity ratio in T-junction microchannels with contractive structures. By analyzing the velocity fields, pressure fields, and forces in droplet formation, the dynamic mechanism of the viscosity ratio on the generation mode and droplet size is achieved. The droplet volume in the dripping mode is analyzed to propose a prediction formula that takes into account the influence of the viscosity ratio.

Two local slip modes at the liquid–liquid interface over liquid-infused surfaces

A liquid–liquid interface (LLI) at liquid-infused surfaces (LISs) plays a significant role in promoting slip flow and reducing frictional drag. By employing the transverse many-body dissipative particle dynamics simulations, the behavior of local and effective slip at a flat LLI for shear flows over periodically grooved LISs has been studied. With increasing viscosity ratio between the working fluid and lubricant fluid, two local slip modes are identified. For a small viscosity ratio, the local slip length remains finite along the LLI, while a hybrid local slip boundary condition holds along the LLI for large viscosity ratios, i.e., the local slip length is finite near the groove edge and unbounded in the central region of the LLI. The vortical flow inside the groove can be enhanced by increasing viscosity ratio due to the change in the local slip mode from the finite state to the hybrid one. Moreover, the results suggest two scenarios for the variation of the effective slippage. For LISs with a large LLI fraction, the effective slip length increases significantly with increasing viscosity ratio, while for a small LLI fraction, the effective slippage is rather insensitive to the viscosity ratio. The underlying mechanism for the relationship between the effective slip length and the viscosity ratio for different LLI fractions is revealed based on the two slip modes. These results elucidate the effect of LLI on slip boundary conditions and might serve as a guide for the optimal design of LISs with enhanced slip properties.

Enhanced droplet formation in a T-junction microchannel using electric field: A lattice Boltzmann study

The electric field-driven droplet formation technique can effectively improve the formation throughput and control the droplet size, which is important for the application of microscale droplets in biopharmaceuticals and chemical analysis. In this paper, the droplet formation characteristics in T-junction microchannels under the action of electric field are investigated by coupling a three-dimensional lattice Boltzmann method (3 D LBM) with the leaky dielectric model, focusing on the effects of electric capillary number, a flow ratio, and a viscosity ratio on the droplet size. It is shown that as the electrical capillary number increases, the non-uniformly distributed electric force stretches the dispersed phase to form a Taylor cone and increases shear force at the interface of the two liquids to overcome the surface tension force. This facilitates the transition from squeezing to dropping and reduces the droplet size. At high flow ratios, increasing the electric capillary number leads to a pinning effect between the dispersed phase and the wall, which intensifies the compression of continuous phase on the neck of dispersed phase, resulting in a significant decrease in the droplet size. As the viscosity ratio increases, the vortex resistance caused by electrical force decreases, and thus, the electric field effect will dominate the droplet formation process.

Relative permeability estimation of oil−water two-phase flow in shale reservoir

Oil−water two-phase flow is ubiquitous in shale strata due to the existence of connate water and the injection of fracturing fluid. In this work, we propose a relative permeability model based on a modified Hagen−Poiseuille (HP) equation and shale reconstruction algorithm. The proposed model can consider the nanoconfined effects (slip length and spatially varying viscosity), oil−water distribution, pore size distribution (PSD), total organic matter content (TOC), and micro-fracture. The results show that the increasing contact angles of organic matters (OM) and inorganic minerals (iOM) increase the relative permeability of both oil and water. As the viscosity ratio increases, the relative permeability of oil phase increases while that of water phase decreases, due to the different water−oil distribution. The effective permeability of both oil and water decreases with the increasing TOC. However, the relative permeability of water phase increases while that of oil phase decreases. The increasing number and decreasing deviation angle of micro-fracture increase the effective permeability of oil and water. However, micro-fracture has a minor effect on relative permeability. Our model can help understand oil−water two-phase flow in shale reservoirs and provide parameter characterization for reservoir numerical simulation.

The role of viscosity ratio in Janus drop impact on macro-ridge structure

An interaction of liquid and solid surfaces upon impact has made great progress in understanding the principle behind impinging compound drops, such as single-interface Janus and core–shell configurations, for controlling drop mobility on the surfaces. Despite advancement of recent technologies, fundamentals of how viscosity ratios of Janus drops affect post-impact dynamics on anisotropic surfaces are still unknown. Here, we numerically investigate the asymmetric impact dynamics of Janus drops on a non-wettable ridged surface to demonstrate the feasibility of the separation of the low-viscosity part from the high-viscosity part by reducing the residence time. The separation is investigated for various viscosity ratios, Weber numbers (We), and initial angle, which are discussed in terms of the temporal evolution of the mass and momentum distributions. A regime map for the separation reveals that the low-viscosity parts are more likely to be separated from high-viscosity parts as the viscosity ratio increases. The phenomenon can be related to a retraction time, which is explained by a hydrodynamic model for the low-viscosity part. This study suggests that We thresholds for the separation can be significantly reduced with the help of center-assisted retraction along the ridge. The asymmetric bouncing of Janus drops on a ridged surface can open up possibilities for the efficient control of liquid separation.

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.

Inertial Effect on Oil/Water Countercurrent Imbibition in Porous Media from a Pore-Scale Perspective

Summary The color-gradient lattice Boltzmann (LB) method is used to investigate the inertial effect on oil/water countercurrent imbibition characteristics in a matrix-fracture system. The interplay between capillarity, fluid inertia, and viscous force during the imbibition under different viscosity ratios is delineated. Pore-scale dynamics, the interfacial front morphology, and oil recovery under the influence of fluid inertia are also elucidated. Additionally, we study the energy conversion during the imbibition displacement from the perspective of energy balance. Finally, the application of the theoretical scaling model is discussed based on the simulated data. Results show that the pore-scale events involved mainly consist of cooperative pore filling, oil expelled from large pores, and the motion of jetting-like oil clusters under high viscosity ratios. The curve of pressure difference between the fracture inlet and outlet vs. imbibition time can be regarded as a signal to discern the imbibition regime, which is taken together with the energy conversion analysis could further determine how capillarity, external pressure, and viscous dissipation contribute to water imbibition. Capillary force dominates in the cases of low viscosity ratios, and the majority of the surface energy is dissipated. The external pressure becomes increasingly significant and even governs the countercurrent imbibition as the viscosity ratio increases. Furthermore, the oil recovery, interfacial area, and fractal dimension of the nonwetting phase strongly rely on the Ohnesorge (Oh) number when the viscosity ratio is low. In contrast, the inertial effect can be neglected in the cases of high viscosity ratios. Besides, the relationship between the simulated imbibition recovery and imbibition time follows the theoretical scaling model as the external pressure is trivial. The comparable exponents fitted from different Oh numbers reveal that the inertial effect does not alter the imbibition dynamics. In sum, fluid inertia only affects the local fluid behaviors and thus the imbibition oil recovery when the viscosity ratio is low. These results could provide important implications for a range of energy-related and environmental applications, such as the evaluation of fracturing fluids loss, oil recovery by water huff n puff, microfluidic devices, and hydrological sciences.

Oil secondary migration simulation in tight reservoir and fingering factors analysis

In the tight reservoirs, the oil accumulation is characterized by ambiguous trap boundaries, complicated oil distribution and nano-scale pore-throat interconnection system. As one of significant process for understanding the oil trap in the tight reservoir, oil migration from source rocks to reservoirs is the key concern by geoscientist. Investigating the immiscible two-phase fluids displacement in porous media, especially the fingering problem during the hydrocarbon migration, has always been a challenge scientific topic. This study establishes PNMs (Pore Network Model) with multiple viable parameters. A fluid migration numerical program is built for the flow study by modifying Poiseuille equation. Sensitive studies have been conducted by several dimensionless numbers to investigate the control factors of the flow behavior. Five factors are identified as the key factors on the migration mode: 1) Fluid viscosity ratio; 2) Interface tension force; 3) Fluid density; 4) Pore structure of sediments; 5) Capillary number. Oil migration behavior is affected by pressure domain, buoyancy, and resistance forces, such as capillary resistance and viscous forces. As the distribution fractal dimension increases with a given viscosity ratio, the width of the front edge of oil-water interface gradually expands. Oil saturation increases in parallel with a rising capillary number. During the simulation, Haines Jump phenomenon is observed. When the capillary number increases, oil migration gravitates towards piston-like displacement. As the oil-water viscosity ratio increases, the front width reaches its maximum at a particular point in time, and plateaus.