Figure 1: Densely branched growth in quasi-2D electrochemical deposition. (a) Radial geometry. Zinc deposited from 0.05M at 10V, with mm and R=4.2 cm. (b) Flat geometry. Copper deposited from 0.1M at 5V with R=4 mm.
Figure 2: Dimensionless growth rate of the th harmonic in the three-dimensional radial geometry. Conductivity anisotropy = 0.01, , and . Lines are plotted for . As the branches become increasingly resistive, the critical mode number below which all modes are stable increases. The dependence on R is very weak provided .
Figure 3: Plot of the critical perturbation harmonic as a function of the amount of dissipation and degree of anisotropy in the three-dimensional radial geometry model, with , and . Dissipation and anisotropy both help stabilize the DBM.
Figure 4: Plot of the critical perturbation harmonic as a function of the size of the pattern, , in the three-dimensional radial geometry model, with and . Lines are plotted for , , , and . Predictions for the size-dependent crossover to stable growth in the anisotropic limit given by Eq. (18), , 8, 10.5, and 13 for the four values respectively, agree well with the jump in for the full solution.