A numerical study of the rise of a Taylor bubble through a sudden/gradual expansion in Newtonian and shear-thinning liquids

In the present work, the rise of a single elongated gas bubble in a vertical tube filled with Newtonian or shear-thinning (CarboxyMethyl Cellulose or CMC) liquid is numerically studied in the presence of a sudden/gradual area expansion. The shear-thinning rheology was modeled using the well-known Carreau-Yasuda viscosity function. Governing equations are discretized using the finite volume approach and the gas/liquid interface was captured using the volume of fluid method. Numerical results are carefully validated against experimental data and a thorough parametric study was undertaken to delineate the effect of shear-thinning behavior on the Taylor bubble splitting process across the sudden/gradual expansion. It is shown that the structure of flow field and relevant length scales of the bubble are affected by the CMC content of the aquatic solution and the strength of non-Newtonian fluid rheology. For instance, the equivalent diameter of the upper daughter bubble decreases by increasing the CMC concentration and expansion angle, and the sensitivity of this length scale to the CMC content is higher at smaller expansion angles. Finally, the shear-thinning behavior slightly reduces the splitting length while significantly decreasing the pressure drop across the necking region.