At the static state，worm-like micellar structures can beformed in most of thesurfactant drag reducer solutions.Exerted withshear stress，the worm-like micellarstructures are apt to align withthe flow direction，resulting in the occurrence ofturbulentdrag-reducing effect and a larger critical shear stress or criticalReynoldsnumber（the turbulent DR rate increases with the increase ofthe flow Reynolds numberat first and reaches the maximum level atthe critical Reynolds number; after that，theDR rate decreases withthe further increase of the fiow Reynolds number until itreacheszero）.Surfactant drag reducer solutions with inner worm-likemicellarstructures usually display obvious theologicalproperties，such as relatively largezero-shear viscosity，shearthinning properties（the shear viscosity decreases with theincreaseof shear rate），large viscoelasticity，a rapid rebounding phenomenonafter thecease of rotation driving，a large ratio of extensionalviscosity to shear viscosity（normally larger than 100），and soon.
　　In some turbulent drag-reducing fluid systems，worm-like micellarstructures withbranches，that is，worm-like structures with threebranches joined together，can beformed.When the energy necessary forforming the semispherical head of a micellarstructure becomes highenough to form a saddle-shaped branch joint，the branchstructure canthus be generated.Comparing this with the former case，the numberofends of the worm-like micellar microstructures in the solutiondecreases.It has beenobserved from experiments that the joints ofbranches can freely move along the axialdirection of the worm-likemicellar structure.Hence，when exerted by shear，the shearstress canbe immediately released，and so the shear viscosity ofsolutiondecreases [281.The turbulent drag-reducing effect is alsoobvious for the surfactantsolution fiow with branchedmicrostructures.But its maximum DR rate is smallercompared withthat of nonbranched microstructures，while its criticalReynoldsnumber is larger.Moreover，the complicated behavior of thefree movement of thebranch joints along the axial direction ofmicellar structures also induces much morecomplex theologicalproperties for such surfactant solutions.
　　There are also some kinds of surfactant solutions in whichvesicular or crystalstructures can be formed at the static state.Inturbulent fiows，when the exerted shearrate exceeds the criticalvalue，these structures can change to worm-like micellarstructuresand make the surfactant solution fiow display the turbulent DRphenom-enon.This transition process of surfactant solution，from astate without drag-reducingeffect to one with drag-reducingeffect，is analogous to the inception process of DR in aturbulentflow of surfactant solution.The difference is that the inception ofDR cannotbe observed when the critical shear rate for the change ofmicrostructures in surfactantsolution is smaller than the criticalwall shear for the laminar-to-turbulent transition.For the normaltheology measurements，if the applied shear rate by theometerisusually not large enough to reach the critical shear rate for thechange of micro-structures in surfactant solution，the measuredsolution may display Newtonian fluidproperties，that is，a relativelysmall shear viscosity，no generation of SIS，the firstnormal stressdifference is O，a relatively small ratio of extensional viscosityto shearviscosity，and so on.
　　1.3.2 Explanations of the Turbulent DR Mechanism from theViewpoint of the Physics of Turbulence
　　Several typical theories for turbulent DR published up to thepresent are summarizedbelow.
　　1.3.2.1 Pseudo-plasticity
　　Early on，Toms proposed that polymer solutions havepseudo-plasticity.The largerthe shear rate is，the smaller theapparent viscosity of a polymer solution becomes.Hence，when asolution flows in a pipe，its apparent viscosity decreases withproximityto the wall due to the local large shear rate，and so thefiow resistance is decreased.From then on，through a large amount ofexperimental and theoretical studies，it hasbeen shown that themechanisms of turbulent DR by polymer additives are muchmorecomplicated，and this theory is currently denied.
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