Scaling law of stable single cells in density fingering of chemical fronts

Stable single fingers evolving in a thin layer of hydrodynamically unstable reactive solution are investigated in moderately wide Hele-Shaw cells. The mixing length associated with the final pattern is shown to be proportional to the width of the container. The scaling law, which is best illustrated by the overlay of temporal average front profiles, is demonstrated for two chemical compositions and boundaries of different thermal conductances. The observed single finger is found to be independent of the orientation of the reaction vessel for a wide range of tilt angles.