Steady-State Saffman-Taylor Fingering in AN Anisotropic Hele-Shaw Cell

Selection of steady-state viscous fingers has been measured in Hele-Shaw cells perturbed by having rectangular and square lattices etched on one of their plates. The strength of the perturbation was varied by varying the cell gap, and over a wide range of observable tip-velocities this local perturbation was also made microscopic in the sense of having the capillary length of the flow large in comparison to the cell size of the underlying lattice. Flows at different orientations, theta, between the direction of flow and the lattice axes have been studied for both lattices. Above a threshold the microscopic perturbation results in selection of wider fingers than are selected in the unperturbed flow for all channel orientations in the experiment. All observed solutions are symmetric, centered in the channel and have the relation between tip-curvature and finger width expected of members of the Saffman-Taylor family of solutions. Selected solutions narrow again at tip-velocities where the perturbations can no longer be considered microscopic. Flows over both the square and rectangular lattice both give wide fingers, with little difference between flows over either lattice. There is some dependence of the width of the fingers on the orientation of the flow, for both lattices. For the rectangular lattice, fingers at 0^circ and 10 ^circ are wider than those found at 45^circ, although all the fingers were wider than corresponding unperturbed fingers. For the square lattice, the full range of dynamically interesting angles (theta = 0^ circ to 45^circ) was examined, with fingers at theta = 0^circ being the widest with respect to the unperturbed fingers, and fingers at 45^circ being the least wide, although again still wider than the unperturbed fingers.