Investigation of bubble formation and its detachment in shear-thinning liquids at low capillary and Bond numbers

Abstract

In the present paper, the formation of an air bubble in a shear-thinning non-Newtonian fluid was investigated numerically. For modeling, an algebraic volume of fluid (VOF) solver of $$\hbox {OpenFOAM}^\circledR $$ was improved by applying a Laplacian filter and was evaluated using the experimental results from the literature. The enhanced solver could compute the surface tension force more accurately, and it was important especially at low capillary and Bond numbers due to the dominance of surface tension force relative to the other forces. The adiabatic bubble growth was simulated in an axisymmetric domain for $$\hbox {Bo}=0.05,0.1,0.5$$ and $$\hbox {Ca}=10^{-1},10^{-2},10^{-3},10^{-4}$$ , and the bubble detachment time and volume were examined. According to the results, for Newtonian fluids, there is a critical capillary number for a given Bond number, and for lower values of this critical number, no difference is observed between the bubble detachment volumes and also bubble detachment times. Similarly, the results indicated that for non-Newtonian fluids, if apparent capillary number (obtained by apparent viscosity) is less than the critical capillary number, the detachment volume is the same as the corresponding Newtonian case. The velocity of the bubble during its formation in Newtonian and shear-thinning fluids was also studied. Moreover, the bubble formation and detachment characteristics such as instantaneous contact angle and necking radius were investigated for Newtonian and non-Newtonian liquids, and the shear-thinning effect was examined as well. The results indicated that changing the ambient fluid to a non-Newtonian liquid has no effect on the trend of the contact angle; however, the minimum contact angle has a higher value when the shear-thinning effect increases. Also, the variation of neck radius with the time until detachment was presented by the power relation $${R}_{\mathrm{n}} =\left( {{t}_{\mathrm {det}} -{t}} \right) ^{{\eta }}$$ , and the effect of shear thinning on its exponent $${\eta }$$ was investigated.