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Miscible viscous fingering is a hydrodynamic instability that occurs when a less viscous fluid displaces a more viscous, fully miscible fluid, giving rise to complex interfacial patterns that strongly influence mixing and transport in confined flows and porous media. Laboratory experiments are performed in a Hele–Shaw cell under controlled conditions, where a low-viscosity fluid (water) displaces a more viscous resident fluid (glycerol). The experiments are conducted at high Peclet numbers to ensure advection-dominated transport, allowing clear visualization of finger initiation, linear growth, and subsequent nonlinear interactions. Time-resolved concentration images capture the evolution of fingering patterns from onset to the fully nonlinear regime, including finger splitting, shielding, and merging.
Despite extensive experimental and numerical studies, achieving a rigorous quantitative comparison between simulations and experiments remains challenging due to the diffuse nature of miscible interfaces and the multiscale evolution of finger structures. In this work, miscible viscous fingering is investigated through a combined experimental and numerical approach, with validation conducted using Fast Fourier Transform (FFT)–based spectral analysis of the mode. The mathematical model is based on solving the coupled Darcy flow and species transport equation, considering a concentration dependent viscosity affecting the relative mobility of the two phases. The simulations reproduce the principal qualitative features of the experimental fingering dynamics, including the formation, elongation, and interaction of fingers.
For quantitative comparison, discrete FFT analysis is applied to both experimental and the computational output. Fourier transforms of transverse concentration profiles are used to compute amplitude and power spectra at successive time instants. The spectral analysis identifies the dominant mode and corresponding amplitude, providing a quantitative measure of characteristic finger spacing and growth. The experimentally measured dominant mode and amplitude show close agreement with numerical predictions, indicating that the numerical framework accurately capture the primary instability mechanisms and mode selection processes.
The mode analysis further reveal spectral broadening and a gradual shift toward lower modes at later times, reflecting nonlinear finger interactions and merging. The combined experimental, numerical, and spectral approach offers deeper insight into instability dynamics, mode selection, and nonlinear evolution, and provides a methodology that can be extended to other miscible displacement and transport problems in confined and porous flow systems related to CO2 geo-sequestration and CO2 enhanced oil recovery applications.
| Country | India |
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