Creeping motion of spheres through shear-thinning elastic fluids described by the Carreau viscosity equation

A numerical study of the motion of a spherical drop rising in shear-thinning fluid systems

“…It is fair to say that the drop motion for the CMC systems is very close to that of a rising drop in Newtonian fluids. Here, we shall compare our results with the theory for creeping motion developed by Chhabra and Uhlherr [57]. Chhabra and Uhlherr [57] presented a theoretical formulation for the drag force on a solid sphere in creeping motion through a Carreau model fluid.…”

“…Here, we shall compare our results with the theory for creeping motion developed by Chhabra and Uhlherr [57]. Chhabra and Uhlherr [57] presented a theoretical formulation for the drag force on a solid sphere in creeping motion through a Carreau model fluid. The predictions of Chhabra and Uhlherr [57] were verified by numerical analysis using the boundary element method by Bush and Phan-Thien [58].…”

“…Chhabra and Uhlherr [57] presented a theoretical formulation for the drag force on a solid sphere in creeping motion through a Carreau model fluid. The predictions of Chhabra and Uhlherr [57] were verified by numerical analysis using the boundary element method by Bush and Phan-Thien [58]. Strictly, we cannot easily compare a liquid-liquid (or gas-liquid) system with a solid-liquid system even if Re is very small (Re 1), because the existence of circulating flow depending on the viscosity ratio of a dispersed and continuous phase inside a drop (bubble) has much effect on the rising velocity.…”

Approximate solutions for drag coefficient of bubbles moving in shear-thinning elastic fluids

“…As well as the results obtained using the Ellis model, the drag decreases with an increase of 2* and its effect becomes more pronounced as the shearthinning anomaly increases. For comparison, theoretical results and experimental data for solid spheres obtained by Chhabra and Uhlherr [14] are included in figure 2. The present results for bubbles with immobile interface show good agreement with the solutions derived using variational principle when the parameter in the Carreau model t/is close to 1 but the predictions of this work lie somewhat above the solutions from the variational principle in the highly shear-thinning region.…”

“…In the work of Chhabra etal. [14][15][16][17], the motion of solid spheres moving in shearthinning elastic fluids was discussed using an Ellis and a Carreau model which are capable of predicting fluid elasticity. It should be noted that these models are applicable to viscous non-Newton[an and elastic fluids (shear-thinning elastic fluids) but not to viscous Newton[an and elastic fluids (purely elastic fluids).…”