The present paper reports a study of the motion of air bubbles in both non-Newtonian fluids and fluid-solid (laponite) suspensions. Quantitative information concerning the bubble rise velocity was obtained. In particular, the acceleration mechanism of the rise velocity in fluids was investigated by both a modern tehnique -Particle Image Velocimetry and a classical method - birefringence visualization. An analytical modeling is proposed to compute the rise velocity of a bubble train with the memory effects. Finally, the visualization demonstrates that the bubble shape and rise velocity in a suspension are very complicated due to the displacement of solid particles by bubbles.