SIMILARITY LAWS IN EUTECTIC GROWTH

We show that the full boundary integral equation reduces, for small Peclet numbers, to a nonlinear similarity equation which contains only two dimensionless parameters, sigma = d0l/lambda-2 and chi = l/l(T), where d0, l, and l(T) are the capillary, diffusion, and thermal lengths and lambda is the wavelength of the pattern. All physical quantities should depend on sigma and chi only. This is confirmed by numerically integrating the original equations. The selected wavelength should scale as lambda approximately V-1/2f(l/l(T)) (V is the velocity). Our results suggest that lambda approximately V-alpha), where alpha congruent-to 1/2 for large V and alpha less-than 1/2 for small V. Our results agree with experiments and we propose further experimental tests.