Drag force on a single rigid sphere in laminar flow

1 Drag force on a single rigid sphere in laminar flow 

Stokes showed in 1851 that for very low Reynolds numbers (Rep 1) the drag force can be found by theoretical analysis [142]  

Due to its great importance in reactor simulations, a brief survey of the main steps involved in Stokes solution of the Navier-Stokes equation for creeping motion about a smooth immersed rigid sphere is provided. The details of the derivation is not repeated in this book as this task is explained very well in many textbooks [169, 14, 103, 15]. 

In most papers the contribution from the normal viscous stresses is assumed negligible compared to the pressure contribution [169, 22, 14, 15]. Nevertheless, Middleman [103] kept the normal viscous stress contributions and after a lengthy exercise in calculus he shows that the the above mentioned simplification is valid. Actually, for any kind of flow pattern the normal viscous stresses are zero at fluid-solid boundaries for Newtonian fluids with constant density (i.e., in which the continuity equation reduces to V v = 0) as a consequence of the no-slip boundary condition [15]. 

Likewise, the viscous shear component (Tre(rp, 0) x sin 0) can be integrated to give a viscous force acting in the direction of the external flow. 

1 Drag Force on a Single Rigid Sphere in Laminar Flow 

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