When a less viscous fluid (water) displaces a more viscous one (oil) in a Hele-Shaw cell (thin gap between plates), the interface is unstable. Perturbations grow into branching "fingers." The growth is governed by Darcy's law: v = −(b²/12μ)∇P. Finger width scales as 1/√(Ca) where Ca is the capillary number — surface tension selects the finger width.