$14.$ Explore the concept of three$-$phase flow, detailing the mechanisms of interaction between gas, liquid, and solid phases in various engineering applications.

a$.$ Analyze the role and dynamics of gas$-$solid liquid contactors, including agitated vessels and packed beds, in facilitating efficient mass transfer and reaction kinetics.

b$.$ Identify the challenges and strategies in flow regime identification for three$-$phase systems, with a focus on the importance of accurate regime identification for design and optimization of industrial processes.

c$.$ Examine the methods for estimating pressure drop and volume fraction in three$-$phase flow systems, including both theoretical approaches and empirical correlations.