$2.$ Describe the concept and importance of three$-$phase flow in engineering applications.

a$.$ Outline the dynamics involved in gas$-$solid$-$liquid contactors, focusing on agitated vessels and packed beds, and explain how these dynamics influence the design and operation of these systems.

b$.$ Discuss the challenges in modeling and scaling$-$up three$-$phase reactors for industrial applications, including flow regime identification and the estimation of pressure drops and volume fractions.

c$.$ Evaluate different techniques used for flow regime identification in three$-$phase systems and their impact on reactor design and process optimization.