Particle deposition and transport in human airways is frequently modeled numerically by the Lagrangian approach. Current formulations of such models always require some ad hoc assumptions, and they are computationally expensive. A new drift-flux model is developed and incorporated into a commercial finite volume code. Because it is Eulerian in nature, the model is able to simulate particle deposition patterns, distribution and transport both spatially and temporally. Brownian diffusion, gravitational settling, and electrostatic force are three major particle deposition mechanisms in human airways. The model is validated against analytical results for three deposition mechanisms in a straight tube prior to applying the method to a single bifurcation G3-G4. Two laminar flows with Reynolds numbers 500 and 2000 are simulated. Particle concentration contour, deposition pattern, and enhancement factor are evaluated. To demonstrate how the diffusion and settling influence the deposition and transport along the bifurcation, particle sizes from are studied. Different deposition mechanisms can be combined into the mass conversation equation. Combined deposition efficiency for the three mechanisms simultaneously was evaluated and compared with two commonly used empirical expressions.