Drag-reduction effectiveness defined

Therefore, in the case of turbulent flow, the drag reduction effect depends by the individual macromolecules stretching degree [1086]. By photographing J.W. Hoyt succeeded to visualise the elongated particles [1087]. The possible extrapolations and the limits of this effect have been defined by Hoyt starting from the friction velocity, u, caused by the friction to the pipe wall, which is expressed as ... 

Pharmacokinetics When EE was administered in combination with Drag XYZ, arithmetic mean 11/2 and Tmax values were comparable for both treatments. Geometric mean Cmax and AUCo-24values were approximately 20 % to 30 % lower, respectively, than when EE was administered with placebo. For AUCq-24, the lower and upper limit of the 90 % Cl were below the pre-defined 90% Cl of 0.8-1.25. Therefore, a pharmacokinetic interaction between Drug XYZ and EE can be concluded. The mechanism for this statistically significant reduction in systemic exposure to EE is unknown, however, since Drag XYZ is known to induce CYP 1A2 in man, and CYP 1A and phase II enzymes in animals, the observed effect could reflect a metabolic interaction between Drag XYZ and EE. 

These relationships are valid for isolated bubbles moving under laminar flow conditions. In the case of turbulent flow, the effect of turbulent eddies impinging on the bubble surface is to increase the drag forces. This is typically accounted for by introducing an effective fluid viscosity (rather than the molecular viscosity of the continuous phase, yUf) defined as pi.eff = Pi + C pts, where ef is the turbulence-dissipation rate in the fluid phase and Cl is a constant that is usually taken equal to 0.02. This effective viscosity, which is used for the calculation of the bubble/particle Reynolds number (Bakker van den Akker, 1994), accounts for the turbulent reduction of slip due to the increased momentum transport around the bubble, which is in turn related to the ratio of bubble size and turbulence length scale. However, the reader is reminded that the mesoscale model does not include macroscale turbulence and, hence, using an effective viscosity that is based on the macroscale turbulence is not appropriate. 

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