Fall of spherical particles through an Allen-Uhlherr model fluid

In this work, the numerical solution of Hill's variational principles is presented for the estimation of upper and lower bounds to the drag coefficient correction function necessary for the determination of terminal velocity of spherical particles falling in purely viscous fluids obeying the four-parameter Allen-Uhlherr viscosity model. The calculated data of the drag coeficient correction functions are compared with the available experimental data. In the experiments, terminal falling velocities of spheres in aqueous solutions of polyalkylene glycol Emkarox HV 45 with small addition (0.06.and 0.08% wt) of polyacrylamide Praestol 2935 were measured. At the same time, viscosity function measurements and oscillation dynamic tests of liquids were performed using rheometer RS 150 (Haake). It was found that due to the liquid elasticity the experimental values Xexp of the drag coefficient correction function are beyond the calculated interval of upper and lower bounds and are higher than the upper bounds Xu However, terminal velocities of spheres falling in fluids of the similar type as the test ones can be roughly estimated using the upper bound Xufor determination of a sphere drag coefficient