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Drag reduction phenomenon with special emphasis on homogeneous polymer solutions

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

Abstract

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.

Keywords

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.

Abbreviations

Latin Symbols

a

Mark-Houwink exponent

A2

second virial coefficient

AAm

acrylamide

c

concentration

COP

poly(acrylamide-co-acrylate)

d

diameter

De

Deborah number

DR

drag reduction

f

friction factor (Darcy-Weisbach)

f′

friction factor (Fanning)

k

Boltzmann constant

KH

Huggins constant

kη

constant of the Mark-Houwink relationship

kθ

optical constant

l

length

LALLS

low-angle-laser light scattering

lc−c

length of one monomer bond

LDA

laser-doppler anemometry

LK

eddy size

Lmax

chain length of the extended polymer

lmon

length of one monomer unit

Lp

chain length

LS

light scattering

M

molecular weight

m0

weight of one monomer unit

Mw/Mn

molecular weight distribution

n

constant of mixture distance

Δp

pressure loss due to friction

P

degree of polymerization

PAAm

poly(acrylamide)

PS

polystyrene

Re

Reynolds number

RG

radius of gyration

〈Rg2

mean square radius of gyration

RH

effective hydrodynamic radius

RI

refractive index

Rθ

Rayleigh ratio

Q

flow rate

SEC

size-exclusion chromatography

t

time

T

temperature

tk

eddy life time

tp

relaxation time

um

mean velocity in pipe

u+

dimensionless velocity

v

volume

y+

dimensionless wall coordinate

Greek Symbols

\(\dot \gamma\)

shear rate

δ

bond angle

ε

rate of elongation

η

shear viscosity

[η]

intrinsic viscosity

η0

zero-shear viscosity

ηsp

specific viscosity

λ0

wave length

ϱ

liquid density

τ

relaxation time

τw

wall shear stress

v

kinematic viscosity

χ

mixing-way constant

Indices

a

additive

cr

critical

deg

degradation

equ
LS

light scattering

max

maximum

n

number average

p

polymer

s

solvent

t

time

w

weight average

ϑ

angle

η

viscosity average

*

critical

+

dimensionless

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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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