Hele-Shaw Cell

Physics: Hele-Shaw flow between closely-spaced plates obeys ∇²P = 0, making it mathematically identical to 2D potential flow. The gap-averaged velocity u = -h²/(12μ) · ∇P, where h is plate separation. Flow around a cylinder: ψ = U·r·sinθ·(1 - R²/r²) (stream function). The Saffman-Taylor instability occurs when a less-viscous fluid displaces a more-viscous one: fingers form with wavelength λ* = πh/√(12·Ca), where Ca = μU/γ is the capillary number. Used extensively in microfluidics research.