This paper describes the development of a new topology optimization framework that controls, captures, isolates, switches, or separates particles depending on their material properties and initial locations. Controlling the trajectories of particles in laminar fluid has several potential applications. The fluid drag force, which depends on the fluid and particle velocities and the material properties of particles, acts on the surfaces of the particles, thereby affecting the trajectories of the particles whose deformability can be neglected. By changing the drag or inertia force, particles can be controlled and sorted depending on their properties and initial locations. In several engineering applications, the transient motion of particles can be controlled and optimized by changing the velocity of the fluid. This paper presents topology optimization schemes to determine optimal pseudo rigid domains in fluid to control the motion of particles depending on their properties, locations, and geometric constraints. The transient sensitivity analysis of the positions of particles can be derived with respect to the spatial distributed design variables in topology optimization. The current optimization formulations are evaluated for effectiveness based on different conditions. The experimental results indicate that the formulations can determine optimal fluid layouts to control the trajectories of multiple particles.