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"Investigate the principles and applications of distillation in chemical engineering. Explain the concept of distillation, including the separation mechanism based on differences in volatility, and the fundamental stages of the distillation process. Explore the factors influencing distillation efficiency, such as temperature, pressure, reflux ratio, and tray or packing design. Discuss the various types of distillation configurations, including simple distillation, fractional distillation, and extractive distillation, along with their respective advantages and limitations in industrial applications. Additionally, analyze the role of azeotropic and non$-$azeotropic mixtures in distillation, and the strategies employed to overcome separation challenges posed by these mixtures. Highlight the key considerations for optimizing distillation processes in chemical engineering operations."