Article
Mechanics
John C. Grenfell-Shaw, Edward M. Hinton, Andrew W. Woods
Summary: This study investigates the stability of the interface between two immiscible fluids flowing in a thin cell with vertically varying gap width. It reveals that stability is mainly determined by the density difference, the effect of surface tension in different directions, and the varying channel width.
JOURNAL OF FLUID MECHANICS
(2021)
Article
Chemistry, Physical
Gongtian Gu, Jin Huang, Wenhu Han, Cheng Wang
Summary: Experimental investigation was conducted on flame propagation in Hele-Shaw cells with a micro-sized gap. Different regimes of flame propagation were identified based on gap size, leading to various flame front morphologies and speeds. The non-accelerating flame in narrow gaps exhibited distinct behaviors compared to the self-accelerating flame in wider gaps, influenced by hydrodynamic instabilities.
INTERNATIONAL JOURNAL OF HYDROGEN ENERGY
(2021)
Article
Mechanics
Sourojeet Chakraborty, Arun Ramachandran
Summary: A depth-averaged, convection-dispersion equation is derived for the particle volume fraction distribution in the pressure-driven flow of a concentrated suspension of neutrally buoyant, non-colloidal particles. The Taylor-dispersion coefficient scales with characteristic velocity, channel depth and particle radius. Shear-induced migration causes particle redistribution perpendicular to flow. The linear stability analysis shows growth rate and wavenumber scaling with velocity and particle size in the flow direction.
JOURNAL OF FLUID MECHANICS
(2021)
Article
Mechanics
Min Chan Kim, Lopamudra Palodhi, Joung Sook Hong, Manoranjan Mishra
Summary: The coupled effects of thermodynamic and hydrodynamic instabilities during viscous fingering (VF) are studied using a modified Cahn-Hilliard phase-field model. The temporal evolution of spatial inhomogeneities is investigated by describing the free energy using a modified Flory-Huggins model. The governing equations are solved using COMSOL multiphysics software, and the results are in agreement with experimental and numerical results obtained using classical models. The effects of the Margules parameter and gradient parameter on VF are systematically studied, showing asymmetric features and a stronger thermodynamic effect with increasing phase separation and droplet formation.
JOURNAL OF FLUID MECHANICS
(2023)
Article
Mechanics
D. A. Bratsun, A. Mizev, E. A. Mosheva
Summary: Theoretical study of buoyancy-driven chemoconvection induced by a neutralization reaction in a system of nitric acid and sodium hydroxide solutions reveals richer possible instabilities than previously thought. The formation of patterns depends on a single parameter, the reaction-induced buoyancy number, leading to insights necessary for a full understanding of the observed phenomena. The mathematical model developed includes reaction-diffusion-advection equations coupled with Navier-Stokes equations, with a focus on transient linear stability analysis and numerical simulations to examine system dynamics.
JOURNAL OF FLUID MECHANICS
(2021)
Article
Physics, Multidisciplinary
Jianwei Guo, Farid Laouafa, Michel Quintard
Summary: This paper focuses on the dissolution problems occurring in laterally large 3D systems with very small dimensions along the third coordinate, such as fractures or Hele-Shaw cells. The study applies upscaling to the 3D pore-scale model using volume averaging method to develop 2D averaged equations. The influence of momentum equations on the accuracy of the 2D Hele-Shaw model is discussed, and it is shown that the results obtained using Darcy-Brinkman equations are better due to the consideration of the viscous boundary layer. The validity and accuracy of the resulting 2D model are assessed based on comparisons with full 3D solutions.
SCIENCE CHINA-PHYSICS MECHANICS & ASTRONOMY
(2023)
Article
Mechanics
C. A. Klettner, T. D. Dang, F. T. Smith
Summary: In this study, the effect of vertical confinement and inertia on the flow past thin ellipses in a Hele-Shaw cell was investigated using asymptotic methods and numerical simulations. The results showed the presence of a Stokes region at the ellipse vertices, and the aspect ratio of the ellipse had an impact on the flow. Two flow conditions at an angle of attack were examined, and predictions of the drag and lift coefficients were made using a modified Bernoulli equation and the Kutta-Joukowski theorem.
JOURNAL OF FLUID MECHANICS
(2023)
Article
Mathematics, Applied
Amlan K. Barua
Summary: This article presents a spectrally accurate boundary integral method to investigate the evolution of a Hele Shaw blob in a rotating, radial cell with time dependent gap. The method of complex moments is used to characterize the solution of the moving boundary problem and linear analysis is conducted to investigate the morphology. The results suggest a destabilizing influence of rotation. Numerical simulations using a boundary integral technique reveal that rotation causes a more complex pattern on the fluid interface, with the formation of narrow fingers and more splitting. A method for controlling viscous fingering is also proposed and validated through simulations.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2022)
Article
Mechanics
Priya Verma, Vandita Sharma, Manoranjan Mishra
Summary: This study provides numerical insights into the radial displacement of two viscously stable reactants undergoing an infinitely fast chemical reaction, expanding the numerical knowledge of the interaction between chemical reaction and hydrodynamic instability. By calculating the onset time of instability and dividing the time domain into stable and unstable zones, the characteristics of reactants in terms of flow stability can be characterized. The dependence of the onset time of instability on the mobility ratio and the Peclet number is obtained, and the length of the fingers in the unstable zone is found to be dependent on the sign of the mobility ratio.
JOURNAL OF FLUID MECHANICS
(2022)
Article
Mechanics
Shoji Seya, Ryuta X. Suzuki, Yuichiro Nagatsu, Takahiko Ban, Manoranjan Mishra
Summary: We developed coupled evolution equations for viscous fingering and phase separation, and demonstrated the transition of VF pattern into droplet formation pattern by spinodal decomposition effect. The experimental results matched the theoretical predictions.
JOURNAL OF FLUID MECHANICS
(2022)
Article
Mechanics
Vandita Sharma, Hamirul Bin Othman, Yuichiro Nagatsu, Manoranjan Mishra
Summary: Through numerical computations and experimental studies, miscible viscous fingering (VF) in an annulus is examined, showing contrast to classical radial VF and instability of a straight displaced slice. The persistence of VF in a miscible annular ring is observed, with variance as a non-monotonic function indicating interaction of two fronts, pressure fingers growing faster than concentration fingers. The variation of finger length with flow rate depends on the amount of more viscous fluid in the annulus, with critical parameters for instability related to viscosity contrast and sample amount.
JOURNAL OF FLUID MECHANICS
(2021)
Article
Water Resources
Didi Li, Yuhui Zhong, Xi Jiang
Summary: This study conducted a series of experiments in Hele-Shaw cells to compare and analyze the effects of common impurities (N2, O2, and/or Ar) on density-driven convective mixing process. The results showed that the presence of these impurities delayed the onset of convection, but had different effects on the subsequent fingering development depending on their species and compositions. The study provides insights into the effects of multiple impurities in impure CO2 geological sequestration.
ADVANCES IN WATER RESOURCES
(2023)
Article
Mechanics
Ricardo Arturo Lopez de la Cruz, Christian Diddens, Xuehua Zhang, Detlef Lohse
Summary: The study investigates the instability at the liquid-gas interface of an ethanol-water solution under heating conditions, observing the growth of convective cells and changes in the velocity field to draw conclusions that align closely with numerical simulation results.
JOURNAL OF FLUID MECHANICS
(2021)
Article
Mechanics
Rafael M. Oliveira, Behbood Abedi, Larissa F. Santos, Pedro S. Camara, Paulo R. de Souza Mendes
Summary: We performed nonlinear simulations to study the radial growth of viscous fingers in a Hele-Shaw cell, varying two dimensionless parameters: the viscosity contrast (A) and the effective surface tension (B). Higher surface tension led to slower and fewer fingering growth patterns. Higher surface tension also resulted in the formation of similar fingering patterns with larger sizes and longer development times. Comparison between the calculated interfacial shapes and experimental measurements showed a close resemblance with a few discrepancies. Changes to the initial nearly circular interface affected both the morphology of viscous fingers and the timescale for pattern formation.
Article
Energy & Fuels
Hamid Ait Abderrahmane, Shahid Rabbani, Mohamed Sassi
Summary: This study demonstrates that inertia plays a stabilizing role in fingering instability and enhances displacement efficiency at high mobility-viscosity ratios. Additionally, under certain conditions, inertia can slightly reduce finger-splitting and the mixing between the two fluids.
Article
Chemistry, Physical
A. Vreme, B. Pouligny, F. Nadal, G. Liger-Belair
JOURNAL OF COLLOID AND INTERFACE SCIENCE
(2015)