Steady-profile fingering flows in Marangoni driven thin films.
We present experimental and computational results indicating the existence of finite-amplitude fingering solutions in a flow of a thin film of a viscous fluid driven by thermally induced Marangoni stresses. Using carefully controlled experiments, spatially periodic perturbations to the contact line of an initially uniform thin film flow are shown to lead to the development of steady-profile two-dimensional traveling wave fingers. Using an infrared laser and scanning mirror, we impose thermal perturbations with a known wavelength to an initially uniform advancing fluid front. As the front advances in the experiment, we observe convergence to fingers with the initially prescribed wavelength. Experiments and numerical computations show that this family of solutions arises from a subcritical bifurcation.