SMALL AMPLITUDE CELLS IN DIRECTIONAL VISCOUS FINGERING

We study the small-amplitude steady-state cellular patterns which occu r in directional viscous fingering. We carry out a weakly nonlinear an alysis for a general gap profile and show that when the capillary numb er is above the threshold for instability of a straight contact line, there exists a continuum of possible small-amplitude cellular steady-s tates. We also discuss the relation between the response of the front to perturbations and the problem of wavelength selection. In particula r, we show how one might search for the preferred state by perturbing the front and examining its response.