The dimensionless variables used in the simulations are the Reynolds number ([Re.sup.*]), the Bingham number ([Bn.sup.*]), the Stokes drag coefficient ([[C.sub.s].sup.*]), and the dimensionless yield stress ([[[Tau].sub.y].sup.*]) .
Each figure shows the extent of the fluid (white) and solid (shaded) regions as the sphere slows down within the fluid, indicated by the increase in Bingham number. Also provided with each figure are the values of the dimensionless yield stress, which also increase as the sphere slows down, indicating that the yield forces are slowly dominating over the externally applied force.
It can be visualized that the main vortex shrinks and approaching to the upper lid with an increase in the value of Bingham number Bn indicating that as the yield limit increases, the dead region increases and it occupies more of the cavity and the shear region is moved to be close to the moving lid.
Effect of Bingham number Bn on velocity profile is shown in Figure 3 which also confirms that at higher values of Bingham number Bn the velocity is nonzero only in the region close to the upper moving lid.
The horizontal segment with u = 0 from y = 0 up to a certain height corresponds to unyielded zone due to increase in Bingham number. The velocity is extremely low throughout the lower portion of the cavity for higher Bn numbers.
The dimensionless viscosity as a function of Bingham number Bn is displayed in Figure 5.
It is also noted that an increase in Bingham number results in the decrease of kinetic energy due to the enhanced plasticity effect producing unyielded regions.
We close this section by showing the dependence of the maximum nonlinear iterations on Bingham number in Table 6.
Caption: Figure 2: Stream function contours for different values of Bingham number Bn.
Caption: Figure 4: Vertical cut-lines at x = 0.5 for u velocity and v velocity for different values of Bingham number.
Caption: Figure 6: Stream function contours for double lid driven cavity at different values of Bingham number Bn.