Consider a dendrite with a tip radius r, forming in the solidification of a pure metal with supercooling T (see Fig. 4.18 in the textbook). The critical radius of a nucleus associated with the given supercooling T is given by r*.

(1) Derive the maximal tip growth velocity v_max as a function of r*, assuming the latent heat Lv, liquid thermal conductivity KL are known (hint: this was discussed in class, you need to consider both the temperature gradient at the tip as well as the Gibbs-Thomson effect).

(2) Discuss how v_max varies as a function of the supercooling T (hint: how r* depends on T, assuming the interface energy sL is known).topic name : Solidification in Pure Systems