"How does the process of distillation contribute to the separation of components in chemical engineering? Discuss the basic principles involved, including vapor$-$liquid equilibrium and fractional distillation. Explain the significance of boiling point differences in the separation process and how it enables the purification of substances. Furthermore, explore the applications of distillation in various industries and its role in producing high$-$purity products. Lastly, elaborate on any challenges or limitations associated with distillation techniques."