Viscous fingering in a wedge

The selection of self-similar fingers growing in a wedge is examined numerically both in the convergent and divergent flow regime. For divergent flows, a bifurcation occurs in the spectrum of the relative finger width {λ} versus {σ}, the effective surface tension parameter, when it is very small ({σ}0.005). By comparison with experimental data, we show that it can explain the tip-splitting instability usual to any radial growth process. At finite surface tension ({σ}>0.005), a universal selection law is revealed numerically for any sector value, in both growth regimes.