A. Rogerson et E. Meiburg, NUMERICAL-SIMULATION OF MISCIBLE DISPLACEMENT PROCESSES IN POROUS-MEDIA FLOWS UNDER GRAVITY, Physics of fluids. A, Fluid dynamics, 5(11), 1993, pp. 2644-2660
The nonlinear evolution of the interface between two miscible fluids o
f different densities and viscosities is simulated numerically for flo
w in a two-dimensional porous medium in which gravity is directed at v
arious angles to the interface. Global velocities tangential to the in
terface are included in the analysis in addition to a normal displacin
g velocity. In unstable configurations, the viscous fingers that resul
t translate as they amplify when nonzero tangential velocities are pre
sent. The increased stabilization by tangential shearing velocities re
ported in [A. Rogerson and E. Meiburg, Phys. Fluids A 5, 1344 (1993)]
affects the growth and wavelength selection of the emerging fingers. T
angential shearing also breaks the symmetry in the shape and concentra
tion distribution of emerging fingers. In addition to the fingering me
chanisms reported in previous studies, new mechanisms of diagonal fing
ering, trailing-lobe detachment, and secondary side-finger instability
, resulting from the presence of gravity and tangential velocities, ha
ve been identified. These phenomena are reflected in one-dimensional a
veraged profiles of the concentration field. Also, how different densi
ty-concentration relations influence the interfacial evolution is inve
stigated. When the dependence of viscosity and density on the concentr
ation has different functional forms, the region of instability may be
localized. The nature of the interfacial development is altered by va
rying the density relation and thereby changing the region of instabil
ity, suggesting that careful modeling of the density and viscosity rel
ations is warranted.