Numerical simulations of dispersion and deposition of particles in an axisymmetric turbulent pipe flow with sudden expansion are performed. The cases that particles of different sizes are released from point sources and/or are uniformly distributed are studied. The effects of turbulence diffusion, Brownian dispersion, lift force, and gravity are included in the computational model. A thermodynamically consistent, rate-dependent algebraic stress model is used to simulate the mean velocity and turbulent intensity fields. The instantaneous fluctuating velocity is simulated as a continuous Gaussian random vector field. The Brownian force is modeled as a Gaussian white noise random process. Ensembles of several thousand particle trajectories are evaluated and are statistically analyzed. The effects of particle source location, particle size, and gravity on dispersion and deposition are studied. The particle capture efficiency for an initially uniform distribution is also evaluated. The predicted particle and fluid velocities are compared with the available experimental data and reasonable agreement is observed.