us, Immiscible fluids Bubbles Numerical simulation

) me the the om ble increasing yield stress and decreasing surface tension. These oscillations are accompanied by the alter-s that licatio ing an terials tical va shear-thinning (or thickening). According to this model the mate-rial can be in two possible states; it can be either yielded or unyiel-ded, depending on the level of stress it experiences. As the common boundary of the two distinct regions the so-called yield surface is approached, the exact Bingham model becomes singular. stic mater ubble shap velocities in Carbopol solutions. They observed that curves ble velocity vs bubble volume for viscoplastic liquids had an change in slope at a critical value of bubble volume that dep on the concentration of Carbopol in the solution, i.e. the yield stress of the material. Many years later, Terasaka and Tsuge [17] used xanthan gum and Carbopol solutions to examine the formation of bubbles at a nozzle and derived an approximate model for bubble growth. Dubash and Frigaard [18] also performed experiments with Carbopol solutions and were able to comfirm the observations of Astarita and Apuzzo [16] on the existence of a critical bubble q Dedicated to Prof Ken Walters FRS on the occasion of his 80th Birthday