Scaling of fractal flow

For fractal, two-phase flow, we show that the standard Darcy's law treatment is incorrect. We present a scaling theory for the saturation of injected fluid and for its current, commonly called fractional flow. These scaling predictions are verified using a standard model of two-phase flow in two dimensions with a viscosity ratio large enough such that the flow is fractal for the size of the systems considered. Our scaling theory follows closely the critical point scaling approach pioneered by Michael Fisher and others.