Gap size effects for the Kelvin-Helmholtz instability in a Hele-Shaw cell

Gravity-driven controls on fluid and carbonate precipitation distributions in fractures

Many challenges related to carbon-dioxide ([Formula: see text]) sequestration in subsurface rock are linked to the injection of fluids through induced or existing fracture networks and how these fluids are altered through geochemical interactions. Here, we demonstrate that fluid mixing and carbonate mineral distributions in fractures are controlled by gravity-driven chemical dynamics. Using optical imaging and numerical simulations, we show that a density contrast between two miscible fluids causes the formation of a low-density fluid runlet that increases in areal extent as the fracture inclination decreases from 90[Formula: see text] (vertical fracture plane) to 30[Formula: see text]. The runlet is sustained over time and the stability of the runlet is controlled by the gravity-driven formation of 3D vortices that arise in a laminar flow regime. When homogeneous precipitation was induced, calcium carbonate covered the entire surface for horizontal fractures (0[Formula: see text]). However, for fracture inclinations greater than 10[Formula: see text], the runlet formation limited the areal extent of the precipitation to less than 15% of the fracture surface. These insights suggest that the ability to sequester [Formula: see text] through mineralization along fractures will depend on the fracture orientation relative to gravity, with horizontal fractures more likely to seal uniformly.

Stability of the fluid interface in a Hele-Shaw cell subjected to horizontal vibrations

The stability of the horizontal interface of two immiscible viscous fluids in a Hele-Shaw cell subject to gravity and horizontal vibrations is studied. The problem is reduced to the generalized Hill equation, which is solved analytically by the multiple scale method and numerically. The long-wave instability, the resonance (parametric resonance) excitation of waves at finite frequencies of vibrations (for the first three resonances), and the limit of high-frequency vibrations are studied analytically under the assumption of small amplitudes of vibrations and small viscosity. For finite amplitudes of vibrations, finite wave numbers, and finite viscosity, the study is performed numerically. The influence of the specific natural control parameters and physical parameters of the system on its instability threshold is discussed. The results provide extension to other results [J. Bouchgl, S. Aniss, and M. Souhar, Phys. Rev. E 88, 023027 (2013)10.1103/PhysRevE.88.023027], where the authors considered a similar problem but took into account viscosity in the basic state and did not consider it in the equations for perturbations.

Subcritical Kelvin-Helmholtz instability in a Hele-Shaw cell

We investigate experimentally the subcritical behavior of the Kelvin-Helmholtz instability for a gas-liquid shearing flow in a Hele-Shaw cell. The subcritical curve separating the solutions of a stable plane interface and a fully saturated nonlinear wave train is determined. Experimental results are fitted by a fifth order complex Ginzburg-Landau equation whose linear coefficients are compared to theoretical ones.

Analytical approach to viscous fingering in a cylindrical Hele-Shaw cell

We report analytical results for the development of the viscous fingering instability in a cylindrical Hele-Shaw cell of radius a and thickness b. We derive a generalized version of Darcy's law in such cylindrical background, and find it recovers the usual Darcy's law for flow in flat, rectangular cells, with corrections of higher order in b/a. We focus our interest on the influence of the cell's radius of curvature on the instability characteristics. Linear and slightly nonlinear flow regimes are studied through a mode-coupling analysis. Our analytical results reveal that linear growth rates and finger competition are inhibited for an increasingly larger radius of curvature. The absence of tip-splitting events in cylindrical cells is also discussed.