A Flow Model for the Settling Velocities of non Spherical Particles in Creeping Motion, Part II

This paper follows previous work regarding the settling velocity of non spherical particles in creeping motion. In the previous work it was found that the shear stress in the fluid is opposed the mass of the fluid. The challenge of the shear stress by the mass imply a pressure gradient by default, i.e. the transfer of the shear stress to the mass is in the form of a surface stress (Pa/m), perpendicular to the shear stress, controlled by the mechanics of viscosity. The dynamics are triggered by the wall shear of the particle. Examination using measured settling velocities shows that the pressure gradient is a unique value for the fluid properties, so that the computed shear stress equal to the viscosity when the velocity gradient is equal to unit and the velocity is satisfied simultaneously, hence, defining the size of the expansion about the shear stress. We learned that application of the viscosity principle demand simultaneous consideration of the volumetric nature of the pressure gradient and the geometry dependence of the velocity gradient. We here undertake an examination to find how the pressure gradient is controlled by the fluid properties and a solution is reached. The solution is in good agreement with published experimental data. In addition we pursued further improvement of the relationships derived previously with further simplification.