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Development characteristics of drag-reducing surfactant solution flow in a duct

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Abstract

Development characteristics of dilute cationic surfactant solution flow have been studied through the measurements of the time characteristics of surfactant solution by birefringence experiments and of the streamwise mean velocity profiles of surfactant solution duct flow by a laser Doppler velocimetry system. For both experiments, the concentration of cationic surfactant (oleylbishydroxymethylethylammonium chloride: Ethoquad O/12) was kept constant at 1000 ppm and the molar ratio of the counter ion of sodium salicylate to the surfactants was at 1.5. From the birefringence experiments, dilute surfactant solution shows very long retardation time corresponding to micellar shear induced structure formation. This causes very slow flow development of surfactant solution in a duct. Even at the end of the test section with the distance of 112 times of hydraulic diameter form the inlet, the flow is not fully developed but still has the developing boundary layer characteristics on the duct wall. From the time characteristics and the boundary layer development, it is concluded that the entry length of 1000 to 2000 times hydraulic diameter is required for fully developed surfactant solution flow.

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Abbreviations

A1, A2 :

Coefficients for time constant fitting [-]

B:

Breadth of the test duct [m]

C1, C2 :

Coefficients for time constant fitting [-]

D:

Pipe diameter [m]

DH :

Hydraulic diameter [m]

g:

Impulse response function [Pa]

H:

Width of the test duct [m]

n:

Index of Bird-Carreau model [-]

Re:

Reynolds number (=UmDH/ν)

ReD :

Pipe Reynolds number (=UmD/ν)

Rex :

Streamwise distance Reynolds number (=U0x/ν)

T:

Absolute temperature [K]

t:

Time [s]

ta :

Retardation time [s]

tb :

Build-up time [s]

tx :

Relaxation time [s]

tx1, tx2 :

Relaxation time for double time constant fitting [s]

t′:

Time constant in Bird-Carreau model [s]

U:

Time mean velocity [m/s]

Um :

Bulk mean velocity [m/s]

Umax :

Maximum velocity in a pipe [m/s]

U0 :

Main flow velocity [m/s]

uτ :

Friction velocity [m/s]

x, y:

Coordinates [m]

\( \ifmmode\expandafter\dot\else\expandafter\.\fi{\gamma } \) :

Shear rate [s−1]

\( \ifmmode\expandafter\dot\else\expandafter\.\fi{\gamma }m \) :

Mean shear rate [s−1]

Δn′:

Birefringence [-]

δ:

99% boundary layer thickness [m]

η:

Solution viscosity [Pa·s]

ηP, ηS :

Surfactant and solvent viscosity [Pa·s]

η 0, η ∞ :

Zero and infinite viscosity of Bird-Carreau model [Pa·s]

λ:

Characteristic time in Maxwell model [s]

ν:

Water kinematic viscosity [m2/s]

ρ:

Density [kg/m3]

σ:

Solution shear stress [Pa]

σP, σS :

Surfactant and solvent shear stress [Pa]

τ:

Time in convolution [s]

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Acknowledgement

The authors acknowledge the partial support given through the Grant in Aid of Science Research of Japan Society for the Promotion of Science, No. 12650753. HS gratefully acknowledges funding received from the Venture Business Laboratory of Kobe University, to support a sabbatical stay at Stanford University. Thanks go to Dr. Willy Wiyatno for his assistance in initiating experiments.

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Authors and Affiliations

  1. Graduate School of Science and Technology, Kobe University, 1-1 Rokkodai-cho, Nada-ku, Kobe 657–8501, Japan

    Hiroshi Suzuki & Tomoe Nakayama

  2. Department of Chemical Engineering, Stanford University, 381 North-South Mall, Stanford, CA 94305, USA

    Gerald G. Fuller

  3. Department of Chemical Engineering and Science, Kobe University, 1-1 Rokkodai-cho, Nada-ku, Kobe 657-8501, Japan

    Hiromoto Usui

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  1. Hiroshi Suzuki
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  2. Gerald G. Fuller
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  3. Tomoe Nakayama
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  4. Hiromoto Usui
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Correspondence to Hiroshi Suzuki.

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Suzuki, H., Fuller, G.G., Nakayama, T. et al. Development characteristics of drag-reducing surfactant solution flow in a duct. Rheol Acta 43, 232–239 (2004). https://doi.org/10.1007/s00397-003-0335-6

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