The Scheil equation comes from assuming that solute mixes perfectly in the remaining liquid but never diffuses back into the solid once it has frozen in place. Under that assumption, every new sliver of solid that forms rejects nearly all its solute into the shrinking pool of liquid ahead of it, so the solute content locked into the solid keeps climbing as freezing proceeds. Tracking this build up along a growing dendrite arm from its core outward is precisely what the Scheil relation, \( C_s = k C_0 (1-f_s)^{k-1} \), describes. It says nothing about how fast a dendrite grows, how heat diffuses, or how the interface curves, so its role is describing solute distribution in the solid along a dendrite arm, option (D).