scholarly journals Growth morphology and symmetry selection of interfacial instabilities in anisotropic environments

Soft Matter ◽  
2021 ◽  
Vol 17 (5) ◽  
pp. 1202-1209
Author(s):  
Qing Zhang ◽  
Amin Amooie ◽  
Martin Z. Bazant ◽  
Irmgard Bischofberger
Keyword(s):  
Viscosity Ratio ◽  
Viscous Fingering ◽  
Growth Morphology ◽  
Interfacial Instabilities ◽  
Fingering Instability ◽  
Degree Of Anisotropy ◽  
Selection Of

We show that both the viscosity ratio between the inner and outer fluid and the degree of anisotropy control the symmetry of dendritic patterns in the viscous fingering instability.

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 Numerical investigation of controlling interfacial instabilities in non-standard Hele-Shaw configurations

2019 ◽  
Vol 877 ◽  
pp. 1063-1097 ◽  
Author(s):  
Liam C. Morrow ◽  
Timothy J. Moroney ◽  
Scott W. McCue
Keyword(s):  
Viscous Fluid ◽  
Linear Prediction ◽  
Applied Mathematics ◽  
Viscous Fingering ◽  
Time Dependent ◽  
Linear Stability Theory ◽  
Inviscid Fluid ◽  
Interfacial Instabilities ◽  
Hele Shaw Cell ◽  
Injection Rates

Viscous fingering experiments in Hele-Shaw cells lead to striking pattern formations which have been the subject of intense focus among the physics and applied mathematics community for many years. In recent times, much attention has been devoted to devising strategies for controlling such patterns and reducing the growth of the interfacial fingers. We continue this research by reporting on numerical simulations, based on the level set method, of a generalised Hele-Shaw model for which the geometry of the Hele-Shaw cell is altered. First, we investigate how imposing constant and time-dependent injection rates in a Hele-Shaw cell that is either standard, tapered or rotating can be used to reduce the development of viscous fingering when an inviscid fluid is injected into a viscous fluid over a finite time period. We perform a series of numerical experiments comparing the effectiveness of each strategy to determine how these non-standard Hele-Shaw configurations influence the morphological features of the inviscid–viscous fluid interface. Surprisingly, a converging or diverging taper of the plates leads to reduced metrics of viscous fingering at the final time when compared to the standard parallel configuration, especially with carefully chosen injection rates; for the rotating plate case, the effect is even more dramatic, with sufficiently large rotation rates completely stabilising the interface. Next, we illustrate how the number of non-splitting fingers can be controlled by injecting the inviscid fluid at a time-dependent rate while increasing the gap between the plates. Our simulations compare well with previous experimental results for various injection rates and geometric configurations. We demonstrate how the number of non-splitting fingers agrees with that predicted from linear stability theory up to some finger number; for larger values of our control parameter, the fully nonlinear dynamics of the problem leads to slightly fewer fingers than this linear prediction.

NUMERICAL ANALYSIS OF VISCOUS FINGERING INSTABILITY DUE TO MISCIBLE DISPLACEMENT

2020 ◽  
Vol 61 (4) ◽  
pp. 539-545
Author(s):  
A. Nemati ◽  
H. Saffari ◽  
B. Z. Vamerzani ◽  
R. Azizi ◽  
S. M. Hosseinalipoor ◽  
...  
Keyword(s):  
Numerical Analysis ◽  
Viscous Fingering ◽  
Miscible Displacement ◽  
Fingering Instability

Numerical simulations of a viscous-fingering instability in a fluid with a temperature-dependent viscosity

2006 ◽  
Vol 84 (4) ◽  
pp. 273-287 ◽  
Author(s):  
Kristi E Holloway ◽  
John R Bruyn
Keyword(s):  
Growth Rate ◽  
Numerical Simulations ◽  
Viscosity Ratio ◽  
Temperature Dependent ◽  
Temperature Dependent Viscosity ◽  
Cell Width ◽  
Inlet Velocity ◽  
Fingering Instability ◽  
Dependent Viscosity ◽  
Hele Shaw Cell

We have performed numerical simulations of the flow of hot glycerine as it displaces colder, more viscous glycerine in a radial Hele–Shaw cell. We find that fingering occurs for sufficiently high inlet velocities and viscosity ratios. The wavelength of the instability is independent of inlet velocity and viscosity ratio, but depends weakly on cell width. The growth rate of the fingers is found to increase with inlet velocity and decrease with the cell width. We compare our results with those from experiments.PACS No.: 47.54.–r

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