Drag reduction phenomenon with special emphasis on homogeneous polymer solutions

  • W.-M. Kulicke
  • M. Kötter
  • H. Gräger
Conference paper
Part of the Advances in Polymer Science book series (POLYMER, volume 89)


A drastic reduction of drag in the turbulent flow of solutions in comparison to the pure solvent can be observed, even when only minute amounts of suitable additives are added. This report shows that a wide range of technical and biochemical applications exists but that these applications have so far only been realized in a few exceptional cases. the reason for this must surely lie in the fact that a precise explanation for the effectiveness of drag reducing agents is neither possible from mathematical theories nor from molecular modelling.

First of all a brief outline will be given of the currently well-known theories concerning this phenomenon; molecular theories will be emphasized.

Special attention will be paid to the polymeric additives in homogeneous solutions as they can be counted amongst the most effective flow enhancers. In this respect molecular parameters (e.g., molecular weight, molecular weight distribution, solvent quality, chemical nature of the polymer, coil volume) having an influence on drag reduction will be discussed. Here the water-soluble, non-ionic polymers and polyelectrolytes are especially noteworthy because of their increasing technological and pharmaceutical importance. As a result of this work into establishing the properties required of a good drag reducing agent in homogeneous solutions, one should ask for a high degree of polymerization and a high flexibility of the chain, avoid branched structures in preference to linear ones, reduce the molecular weight of the monomer unit, and increase the coil volume, for example, by introducing ionic side groups, to name but a few examples. In addition, it has been proved that single polymer coils are effective (c ≪ c*). Problems arising in the characterization and handling of water-soluble substances will also be discussed.

Drag reduction decreases with flow time — which is in most application undesirable — and is obviously caused by a degradation of the polymer chain. Degradation of polymeric additives in turbulent flow cannot be easily understood on the basis of present knowledge, i.e., predictions towards the onset of chain scission cannot yet be made. These difficulties can be attributed, on the one hand, to the complex fluid structure and, on the other hand, to the fact that both shear and tensile stresses act simultaneously in turbulent flows.


Polymer Solution Molecular Weight Distribution Polymer Molecule Elongational Viscosity Elongational Flow 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Latin Symbols


Mark-Houwink exponent


second virial coefficient










Deborah number


drag reduction


friction factor (Darcy-Weisbach)


friction factor (Fanning)


Boltzmann constant


Huggins constant


constant of the Mark-Houwink relationship


optical constant




low-angle-laser light scattering


length of one monomer bond


laser-doppler anemometry


eddy size


chain length of the extended polymer


length of one monomer unit


chain length


light scattering


molecular weight


weight of one monomer unit


molecular weight distribution


constant of mixture distance


pressure loss due to friction


degree of polymerization






Reynolds number


radius of gyration


mean square radius of gyration


effective hydrodynamic radius


refractive index


Rayleigh ratio


flow rate


size-exclusion chromatography






eddy life time


relaxation time


mean velocity in pipe


dimensionless velocity




dimensionless wall coordinate

Greek Symbols

\(\dot \gamma\)

shear rate


bond angle


rate of elongation


shear viscosity


intrinsic viscosity


zero-shear viscosity


specific viscosity


wave length


liquid density


relaxation time


wall shear stress


kinematic viscosity


mixing-way constant









light scattering




number average








weight average




viscosity average






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Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  • W.-M. Kulicke
    • 1
  • M. Kötter
    • 1
  • H. Gräger
    • 2
  1. 1.Institut für Technische und Makromolekulare ChemieUniversität HamburgHamburg 13Germany
  2. 2.Horstmann-SteinbergCelleGermany

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