In a tapered Hele-Shaw cell with small gap gradient α, the dimensionless finger width satisfies Λ − 1/2 ∼ f(α) Ca_m^{2/3} as Ca_m → 0 with |α| ≪ 1, where f(α) is linear and recovers the parallel-cell value at α = 0.
Numerical investigation of viscous fingering in hele-shaw cell with spatially periodic variation of depth.Applied Mathematics and Mechanics, 37(1):45–58, 2016
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On the selection of Saffman-Taylor fingers in a tapered Hele-Shaw cell
In a tapered Hele-Shaw cell with small gap gradient α, the dimensionless finger width satisfies Λ − 1/2 ∼ f(α) Ca_m^{2/3} as Ca_m → 0 with |α| ≪ 1, where f(α) is linear and recovers the parallel-cell value at α = 0.