A phase-field approach is presented for the numerical simulation of two fluid forced flow in channels. The difference in physical properties of the two components is handled following a quasi-incompressible approach (J. Lowengrub and L. Truskinovsky, Proc. R. Soc. Lond. A, 1998). The axisymmetric form of the Navier-Stokes and Cahn-Hilliard equations system is solved, and the numerical results presented here consider a narrow pipe of radius R = 1mm, where buoyancy effects are neglected.Results of three simulations for the evolution of spherical and elongated hexane bubbles in water for Re = 220 and We = 96 are reported