REGULATION OF RAMIFIED ELECTROCHEMICAL GROWTH BY A DIFFUSIVE WAVE

The role of ion transport during ramified growth in a dilute, binary e lectrolyte is investigated by obtaining a wave solution to effective e quations derived by asymptotic analysis of the Nernst transport equati ons. The concentration profile exhibits a diffusion layer ahead of the growing tips, in agreement with experiment and theory. The non-laplac ian electric field is stronger in the diffusion layer than in the bulk , and cations are accelerated through the layer toward the tips. The w ell-known growth speed of the aggregate envelope, roughly equal to the speed of migrating anions in the bulk emerges as the characteristic w ave speed of our equations. The ''copper ratio'' is also predicted and is linked to the regulation of growth by the diffusive wave. Finally, an estimate of the induction time for ramified growth is derived, bas ed on the idea that a critical diffusion layer width must be attained.