Soft Matter and Complex Systems Seminar
sala 2.08, ul. Pasteura 5
2014-10-10 (09:30) 
Paweł Kondratiuk (IFT UW)
Invariantly propagating parabolic dissolution fingers
The mechanism of mineral dissolution is ubiquitous in nature. For instance, it is responsible for the development of one of the most picturesque types of landscape on the Earth - the karst landscape. The reason why the dissolution of the rock may create such a complicated morphologies as the karst, lies in the coupling between the rock morphology and the flow of groundwater carrying the solvents. A locally increased dissolution makes this region of the rock more porous and more permeable, eventually increasing there the groundwater flow. Such a positive feedback leads to the creation of highly localized flow paths, called "wormholes". The described mechanism is referred to in the literature as the "reactive-infiltration instability".
The initial stages of the wormholes development due to the breakup of the initially planar reaction front have been extensively studied and are now quite well understood. However, the complete description of the dynamics in the fully nonlinear regime is still lacking. In this paper we aim to challenge this problem and investigate the matrix dissolution system long after the initial reaction front breakup. We study the flow-transport-reaction system analytically, checking the possibility of formation of single, invariantly propagating finger-shaped wormholes. It turns out that such forms can indeed develop. To be exactly stationary, they (in 2D) need to have parabolic shape. The velocity of propagation of such a dissolution finger should depend on its tip radius of curvature. Similar results can be obtained for the complementary case - dissolution of a piece of permeable matrix by surrounding flow transporting reactants.
The initial stages of the wormholes development due to the breakup of the initially planar reaction front have been extensively studied and are now quite well understood. However, the complete description of the dynamics in the fully nonlinear regime is still lacking. In this paper we aim to challenge this problem and investigate the matrix dissolution system long after the initial reaction front breakup. We study the flow-transport-reaction system analytically, checking the possibility of formation of single, invariantly propagating finger-shaped wormholes. It turns out that such forms can indeed develop. To be exactly stationary, they (in 2D) need to have parabolic shape. The velocity of propagation of such a dissolution finger should depend on its tip radius of curvature. Similar results can be obtained for the complementary case - dissolution of a piece of permeable matrix by surrounding flow transporting reactants.
The mechanism of mineral dissolution is ubiquitous in nature. For instance, it is responsible for the development of one of the most picturesque types of landscape on the Earth - the karst landscape. The reason why the dissolution of the rock may create such a complicated morphologies as the karst, lies in the coupling between the rock morphology and the flow of groundwater carrying the solvents. A locally increased dissolution makes this region of the rock more porous and more permeable, eventually increasing there the groundwater flow. Such a positive feedback leads to the creation of highly localized flow paths, called "wormholes". The described mechanism is referred to in the literature as the "reactive-infiltration instability".
The initial stages of the wormholes development due to the breakup of the initially planar reaction front have been extensively studied and are now quite well understood. However, the complete description of the dynamics in the fully nonlinear regime is still lacking. In this paper we aim to challenge this problem and investigate the matrix dissolution system long after the initial reaction front breakup. We study the flow-transport-reaction system analytically, checking the possibility of formation of single, invariantly propagating finger-shaped wormholes. It turns out that such forms can indeed develop. To be exactly stationary, they (in 2D) need to have parabolic shape. The velocity of propagation of such a dissolution finger should depend on its tip radius of curvature. Similar results can be obtained for the complementary case - dissolution of a piece of permeable matrix by surrounding flow transporting reactants.
The initial stages of the wormholes development due to the breakup of the initially planar reaction front have been extensively studied and are now quite well understood. However, the complete description of the dynamics in the fully nonlinear regime is still lacking. In this paper we aim to challenge this problem and investigate the matrix dissolution system long after the initial reaction front breakup. We study the flow-transport-reaction system analytically, checking the possibility of formation of single, invariantly propagating finger-shaped wormholes. It turns out that such forms can indeed develop. To be exactly stationary, they (in 2D) need to have parabolic shape. The velocity of propagation of such a dissolution finger should depend on its tip radius of curvature. Similar results can be obtained for the complementary case - dissolution of a piece of permeable matrix by surrounding flow transporting reactants.