Experimental verification of our previous numerical simulation of wall effects on the terminal falling velocity of spherical particles moving slowly along the axis of a cylindrical vessel filled with a Carreau model fluid is presented. Dependences of the wall correction factor F W on the sphere to tube ratio d/D and on the dimensionless Carreau model parameters m, Λ, and η r were obtained using a finite element method. Calculated data of the wall correction factor were compared with the results of our new falling sphere experiments. The experiments were carried out in six types of cylindrical Perspex columns (16 mm, 21 mm, 26 mm, 34 mm, 40 mm, and 90 mm in diameter) filled with aqueous solutions of polymers exhibiting different degrees of shear thinning and elasticity. Seventeen types of spherical particles (1–8 mm in diameter) made of glass, ceramics, steel, lead, and tungsten carbide were used for the drop tests. Measurements of the liquid flow curves, primary normal stress differences, oscillatory, creep and recovery, stress relaxation, and stress growth tests were carried out on the rheometer Haake MARS (Thermo Scientific). A good agreement between numerically and experimentally obtained F W data was found.

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Results of numerical calculations of dynamic shape and wall correction factors for the flow of a Newtonian fluid over a vertically oriented cylindrical particle in a cylindrical tube are reported. Mathematical model of the flow was solved using the finite element method by means of the COMSOL Multiphysics software. Dependences of the shape factor on the cylinder aspect ratio and of the wall correction factor, F W, on the ratio of the cylindrical particle diameter to the tube diameter, and on the aspect ratio were obtained. Numerical dependences were approximated by simple relationships suitable for dynamic shape and wall correction factors prediction.

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