Hele-Shaw scaling properties of low-contrast Saffman-Taylor flows

We have measured variations of Saffman-Taylor flows by changing dimensionless surface tension B alone and by changing B in conjunction with changes in dimensionless viscosity contrast A. Our low-aspect-ratio cell permits close study of the linear- and early nonlinear-flow regimes. Our critical binary-liquid sample allows study of very low values of A. The predictions of linear stability analysis work well for predicting which length scales are important, but discrepancies are observed for growth rates. We observe an empirical scaling law for growth of the Fourier modes of the patterns in the linear regime. The observed front propagation velocity for side-wall disturbances is constantly 2±{}1 in dimensionless units, a value consistent with the predictions of Langer and of van Saarloos. Patterns in both the linear and nonlinear regimes collapse impressively under the scaling suggested by the Hele-Shaw equations. Violations of scaling due to wetting phenomena are not evident here, presumably because the wetting properties of the two phases of the critical binary liquid are so similar; thus direct comparison with large-scale Hele-Shaw simulations should be meaningful.