what is the initial and boundary condition of miscible viscous fingering?
When one less viscous fluid displace another one more viscous fluid.
The miscible viscous fingering is a hydrodynamic instability that occurs when a low viscosity fluid displaces a high viscosity fluid in a porous medium. The initial and boundary conditions for this phenomenon are:
- Initial condition: The two fluids are separated by a flat interface, and they are in a state of static equilibrium. The interface between the two fluids is assumed to be perfectly flat and parallel to the direction of flow.
- Boundary condition: The two fluids are injected into the porous medium through two parallel channels or pipes. The injection rate of the low viscosity fluid is higher than the injection rate of the high viscosity fluid. The injection rates can be constant or variable with time. The two fluids are assumed to be fully miscible and have similar densities.
As the low viscosity fluid displaces the high viscosity fluid, the interface between the two fluids becomes unstable and develops into a pattern of finger-like structures. The fingers grow and coalesce, eventually leading to a fully mixed state of the two fluids.
Miscible viscous fingering is an example of hydrodynamic instability, which refers to the spontaneous development of patterns and structures in fluid flows due to the presence of small perturbations or fluctuations in the flow. Other examples of hydrodynamic instability include Rayleigh-Bénard convection, Taylor-Couette flow, and Kelvin-Helmholtz instability.
Hydrodynamic instability is an important area of research in fluid dynamics, with many practical applications in engineering, physics, and biology.
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