Bubbles rising in viscoelastic liquids may exhibit a jump discontinuity of the rise velocity as a critical bubble volume is exceeded. We carried out detailed experiments to investigate the occurrence of this discontinuity with single air bubble rising in various polymer solutions without influence of surfactants. The polymer solutions were characterized thoroughly by means of shear and elongational rheometry, as well as tensiometry. The experiments showed that a jump discontinuity can exist only if the non-dimensional group lambda(E)(g(3) rho(1)/sigma)(1/4), found by dimensional analysis, exceeds a critical value. A universal correlation of non-dimensional numbers for the non-dimensional critical bubble volume at the jump discontinuity was found. The non-dimensional numbers represent the relevant theological and dynamic liquid properties. This is the first time that the prediction of the critical bubble volume as well as the potential of the solution to exhibit a bubble rise velocity discontinuity becomes possible based on liquid properties only. In the correlation found, the relaxation time of the polymer solutions in elongational flow of the viscoelastic liquid was found to play a key role. (C) 2007 Elsevier B.V. All rights reserved.