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Pseudo-laminarization effect of several types of surfactant solutions in small-sized pipe flows

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Abstract

Fluid mechanics at a very small scale, particularly micro-flows and nano-flows, have many technical applications, and the elastic properties of small-scale flows are strongly expressed even for dilute aqueous solutions of non-Newtonian fluids. We have investigated the flow properties of water and several types of surfactant solutions with spherical or rod-like micelles. Before the flow property investigations, Newtonian and non-Newtonian viscosities for the test fluids were observed by using a capillary viscosity meter. Pressure drops were experimentally measured, and the frictional coefficient of the pipe was estimated in flows through capillaries ranging from 133 \(\upmu \)m to 2.87 mm in diameter. For water flow, good agreement was obtained between the experimental results and the predictions for Hagen–Poiseuille flow and the Blasius expression. The flow properties of the spherical micelle surfactant solutions agreed with those of water. However, the rod-like micelle surfactant solutions maintained laminar flows in the transition regions. Thus, a pseudo-laminarization effect for surfactant solutions with rod-like micelles is indicated. A relationship between these experimental results and estimated first normal stress differences is also strongly suggested.

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Abbreviations

C :

Molar concentration (mol/L)

\(C_{m}\) :

Mass concentration (wt%)

D :

Diameter of capillary (mm, \(\upmu \)m)

DR :

Drag reduction rate (\(-\))

k :

Gradient in plotting log (\(T_{M} - T_{m}\)) against log \(SR_{w}\) (\(-\))

L :

Capillary length (mm)

m :

Dilatant viscosity (Pa s\(^{n}\))

n :

Power law index (\(-\))

\(N_{1}\) :

First normal stress difference (Pa)

Q :

Flow rate (m\(^{3}\)/s)

Re :

Reynolds number (\(-\))

\(Re^{*}\) :

Generalized Reynolds number (\(-\))

\(Re_{c}\) :

Critical Reynolds number (\(-\))

\(SR_{c}\) :

Critical shear rate on wall (s\(^{-1}\))

\(SR_{w}\) :

Shear rate on wall (s\(^{-1}\))

T :

Temperature (\({}^\circ \mathrm {C}\))

\(T_{M}\) :

Theoretical outlet momentum (N)

\(T_{m}\) :

Jet thrust (N)

\(\varDelta p\) :

Pressure drop (Pa)

\(\uplambda \) :

Frictional coefficient of pipe (\(-\))

\(\mu \) :

Newtonian viscosity (Pa s)

\(\rho \) :

Density (kg/m\(^{3}\))

\(\sigma _{i}\) :

Interfacial tension (mN/m)

\(\tau _{w}\) :

Wall shear stress (Pa)

\(\varphi \) :

Molar concentration ratio (\(-\))

a :

Arquad (surfactant)

\({ exp}.\) :

Experimental value

e :

Ethoquad (surfactant)

n :

NaSal (counterion)

\({ pre}.\) :

Predicted value

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Authors and Affiliations

  1. Faculty of Engineering, Niigata University, 8050-2 Ikarashi, Nishi-ku, Niigata-shi, Niigata, 950-2181, Japan

    Akiomi Ushida & Takatsune Narumi

  2. Graduate School of Science and Technology, Niigata University, 8050-2 Ikarashi, Nishi-ku, Niigata-shi, Niigata, 950-2181, Japan

    Akira Ichijo

  3. The Institute of Education and Student Affairs, Niigata University, 8050-2 Ikarashi, Nishi-ku, Niigata-shi, Niigata, 950-2181, Japan

    Taisuke Sato

  4. Niigata College of Technology, 5-13-7 Kamishinei-cho, Nishi-ku, Niigata-shi, Niigata, 950-2076, Japan

    Tomiichi Hasegawa

Authors
  1. Akiomi Ushida
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  2. Akira Ichijo
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  4. Tomiichi Hasegawa
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Correspondence to Akiomi Ushida.

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Ushida, A., Ichijo, A., Sato, T. et al. Pseudo-laminarization effect of several types of surfactant solutions in small-sized pipe flows. Acta Mech 227, 2061–2074 (2016). https://doi.org/10.1007/s00707-016-1616-3

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