Drag Reduction Effect of Rod-Like Polymer Solutions. I. Influences of Polymer Concentration and Rigidity of Skeltal Back Bone

Drag reduction behaviors of xanthan polysacharide and scizophyllum polysacharide solutions are presented. The friction factor relation of \(1/√f=4.0·log (Re·√f)-0.4+δ\) is observed for solutions of polymers having long persistent lengths, where f · R e and δ are a Fanning friction factor, a Reynolds number and a constant, respectively. On the other hand, the relation of \(1/√f=(4.0+D)·log (Re·√f+A\) is observed for solutions of polymers having short persistent lengths, where D and A are constants. From concentration dependencies of these relations, the following relations are found; S + ∝ C p 0.75 for the former case and S + ∝ C p 0.75 ·ln (γ v /γ v * ) for the latter case, where S + , C p , γ v and γ v * are a normalized slipping velocity between a viscous sublayer and a Newtonian plug zone, a polymer concentration, a shear rate in the viscous sublayer and an onset γ v for the drag reduction, respectively. The γ v * is found to be a monotonically decreasing function of the persistent length. Theoretical comments on the experimental results are also presented.