Theoretical and numerical studies on the interface movement and the onset of gravitational instability during the carbon dioxide dissolution into oil

In consideration of the interface movement and the viscosity lowering due to the CO2 dissolution, the onset of gravitational instabilities in a horizontal fluid layer is analyzed theoretically and numerically. Under the linear stability theory, new stability equations are derived in the semi-infinite τ,ζ-domain. We proved that the normal mode stability analysis is possible for the deep-pool case—where the lower boundary plays little role in the spatiotemporal evolution of the concentration field. Moreover, we obtained critical conditions for the onset of convection by solving the normal mode stability equations. In addition, the effect of the swelling and the viscosity lowering on the stability, temporal evolution concentration field, and pattern formation on the dissolving interface is analyzed by solving the fully nonlinear governing equations of the flow and the concentration fields. The present linear and nonlinear analyses show consistently that both interface movement and viscosity lowering accelerate the onset of instability and enhance the dissolution of CO2. Finally, we visualize the pattern formation on the dissolving interface through the three-dimensional numerical simulations.