Understanding the dynamics of DNA solutions in simple and complex microfluidic channels is critical for devices that manipulate DNA molecules for analysis and chemical reaction applications. Recent simulation and experimental work have shown that hydrodynamic interactions between DNA segments can lead to DNA migration towards the channel center, thus enabling passive separation of DNA molecules by flow. In this work, we investigate the dynamics of DNA chains in channels of dimensions comparable to the chain radius of gyration by employing the lattice Boltzmann method (LBM). Prior comparisons to Brownian dynamics and experiments have shown that LBM is able to capture DNA relaxation and diffusion in confined systems. The present work investigates how inter-chain interactions affect the chain conformation and chain migration by varying the molecule concentration up to the dilute-semidilute crossover. We also extend this approach to study the dynamics of DNA – nanoparticle mixtures in the microchannels, and how the addition of nanoparticles affects the DNA conformation and migration dynamics.