Reynolds number, Rer

Where Ro is the lumen radius, I if the fiber length, u is the longitudinal convective velocity, P is pressure, X is the dimensionless axial space coordinate, R is the dimensionless radial coordinate. In writing Equation 14.24 it was assumed that flow is laminar and that entrance effects can be ignored. In addition, the axial stress terms have been neglected since the aspect ratio of the hollow fiber (Ro/L) is typically less than 0.01. The inertial terms have been neglected also, which is valid if the radial Reynolds number (ReR— puRo/fi) is much less than 1 [11], The boundary conditions for the solution ... 

The parameter n correlates with the terminal particle Reynolds number Rer. it acquires constant values in both the creeping flow and inertial flow regimes ( 4.8 and 2.4 respectively), changing progressively with Ret in the intermediate regime between these limiting values. The following convenient relation (Khan and Richardson, 1989) enables n to be... 

R Overall electric resistance of the membrane stack (O) Re Reynolds number (defined in Table III dimensionless) RErs Electric resistance of electrode rinsing solution (O)... 

Slatter [4] defined Rer as the roughness Reynolds number for yield pseudoplastic slurry... 

The authors then establish a plot (see Figure 5.3) in the plane (Rer, Gr), where Gr is the Grashof number and Rer is the total Reynolds number, equal to the sum of the viscous Reynolds number and a magnetic Reynolds number. Hence, we have the following definitions ... 

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