Abstract
We present fluorescence microscopy observations of growing two-dimensional solid domains in alcohol monolayers spread on a subphase containing a soluble fatty acid (pKa = 4.5). The morphologies are highly branched when pH > pKa, and almost compact in the opposite case. For pH > pKathe 2D growth is limited by the 2D diffusion of fluorescent impurities, whereas for pH < pKa the growth is limited by fatty acid "impurities" diffusing in the subphase as well. A theoretical analysis shows that, unlike the traditional similarity solution where a planar front advances like (t)1/2, bulk diffusion leads to the existence of a planar front moving at a constant velocity, governed by the residence time of soluble impurities at the surface. An exact solution for this planar front and its stability is provided analytically. We also show numerical results bearing resemblence with the experimental patterns.