Why is a longer ingot useful when an impurity has a distribution coefficient close to one?

In zone refining, the effectiveness of the purification process depends on the distribution coefficient, which represents the ratio of an impurity's concentration in the solid phase to its concentration in the liquid phase.

When an impurity has a distribution coefficient close to unity, the separation process becomes less efficient because the impurity concentration in the solid and liquid phases is nearly identical. To compensate for this and achieve the desired level of purity, the ratio of the ingot length to the zone length must be increased. By using a longer ingot relative to the molten zone, the process can effectively redistribute the impurities over a greater distance, allowing for successful purification even when the distribution coefficient is not particularly favorable.1