Particle-fluid mixtures occur in many process engineering systems, such as drying and crystallization. The focus of this work is the subgroup of transport-dominated systems, which are characterized by a predominantly one-dimensional fluid flow. In a first step, a modeling approach based on partial differential equations is developed and applied to two example systems, namely the rotary dryer and the DTB crystallizer. This is followed by a system analysis on equilibria and their stability behavior. In a final step, a control system is designed for one of the example systems, focusing on energy flexibility.