Identifying the Operating Regime for Viscous Blending

Two methods have been used to identify the boundary between transitional and laminar blending, and they give similar results for the value of Reynolds number at the boundary. Wichterle and Wein (1981) made visualization studies of the flow in vessels agitated by Rushton and pitched blade turbines. They deflned two Reynolds numbers the value when motion first appears and the value when all stagnant zones disappear. The second definition is used here  

for example, a pitched blade turbine with a power number of 1.8 and diameter equal to T/2 will have a value of Rert of 62. 

Hoogendoom and den Hartog (1967) measured blend times for a variety of impellers. They found that when the dimensionless blend time data were plotted, the exponent on Reynolds number changed from —1 to —10 at a value of Reynolds number of 170 for a Rushton turbine (i.e., the blend time became highly sensitive to the value of viscosity for Re 170). Johnson (1967) found that the exponent was —13. 

Hoogendoom and den Hartog proposed that the boundary between the laminar and transitional regimes could be estimated for all impellers by 

This agrees well with the conclusions of Zlokamik (1967), who concluded that the boundary occurs at a value of 0.25. Substituting the value of 1/Fo from eq. (9-45) into (9-6) and rearranging gives 

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