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In this paper, the behaviors of single bubble in shear-thinning viscoelastic fluids were investigated using OpenFOAM. The volume-of-fluid method was used to capture the interface, and the Giesekus model was adopted for describing the rheological behaviors of shear-thinning viscoelastic fluids. The bubble cusp, negative wake, and velocity jump phenomenons in viscoelastic fluids were obtained, and the effects of wall effect, mobility factor α, and Weissenberg number (Wi) on bubble behaviors were investigated. The results showed that the viscoelastic stress is the main reason for the formation of bubble cusp, the relaxation of polymer macromolecules leads to the formation of negative wake, and the negative wake may be the main reason for the velocity jump. The open angle θ of the negative wake decreases and the distribution region in the vertical direction increases with the increasing Reynolds numbers (Re). In addition, the magnitude of the maximum negative velocity increases with Re and appears further away from the bubble cusp. Moreover, decreasing the wall effect can accelerate the formation of viscoelastic stress and make the bubble cusp appear earlier. As the mobility factor α increases, the viscosity and viscoelastic stress of the fluid near the bubble decrease; this causes the terminal velocity of the bubble to increase. As the Wi increases, both the maximum velocity and terminal velocity of the bubble increase, and the time lag occur. The viscoelastic stress τyy has a longer linear distribution at the tail of the bubble with the increase in Wi. [ABSTRACT FROM AUTHOR]