Multidimensional viscous fingering is accurately simulated by an extension of the Hartley spectral methods to three dimensions. Two types of initial conditions were used in the rectilinear displacements−white noise and polygonal cells of the wave number of the mode of maximum instability identified by the linear theory. White noise initial conditions demonstrated that the mechanisms of nonlinear interaction of viscous fingers found in two‐dimensional (2‐D) simulations persist to three dimensions. Further, the long‐time rate of advance of viscous fingers remains unchanged from two dimensions, suggesting that 2‐D simulations are sufficient to capture essential features of nonlinear viscous fingering. Simulations with polygonal cellular symmetries, specifically square cells and hexagonal cells, illustrated that weak nonlinear theory cannot predict the shape selection of viscous fingers, as the mechanisms of finger interactions that dominate shape selection lack transverse symmetry and symmetry with respect to the displacement front.
Skip Nav Destination
Article navigation
September 1992
This content was originally published in
Physics of Fluids A: Fluid Dynamics
Research Article|
September 01 1992
Three‐dimensional viscous fingering: A numerical study
W. B. Zimmerman;
W. B. Zimmerman
Chemical Engineering Department, Stanford University, Stanford, California 94305
Search for other works by this author on:
G. M. Homsy
G. M. Homsy
Chemical Engineering Department, Stanford University, Stanford, California 94305
Search for other works by this author on:
Phys. Fluids 4, 1901–1914 (1992)
Article history
Received:
October 25 1991
Accepted:
April 16 1992
Citation
W. B. Zimmerman, G. M. Homsy; Three‐dimensional viscous fingering: A numerical study. Phys. Fluids 1 September 1992; 4 (9): 1901–1914. https://doi.org/10.1063/1.858361
Download citation file:
Sign in
Don't already have an account? Register
Sign In
You could not be signed in. Please check your credentials and make sure you have an active account and try again.
Pay-Per-View Access
$40.00
Citing articles via
On Oreology, the fracture and flow of “milk's favorite cookie®”
Crystal E. Owens, Max R. Fan (范瑞), et al.
Fluid–structure interaction on vibrating square prisms considering interference effects
Zengshun Chen (陈增顺), 陈增顺, et al.
A unified theory for bubble dynamics
A-Man Zhang (张阿漫), 张阿漫, et al.
Related Content
Viscous fingering in miscible displacements: Unification of effects of viscosity contrast, anisotropic dispersion, and velocity dependence of dispersion on nonlinear finger propagation
Physics of Fluids A: Fluid Dynamics (November 1992)
A numerical study on miscible viscous fingering instability in anisotropic porous media
Physics of Fluids (August 2014)
Simulation of nonlinear viscous fingering in miscible displacement
Phys. Fluids (June 1988)
Nonlinear simulation and linear stability analysis of viscous fingering instability of viscoelastic liquids
Physics of Fluids (March 2017)