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RESEARCH PAPERS: Non-Newtonian Behavior and Rheology

Modeling and Measurement of the Dynamic Surface Tension of Surfactant Solutions

[+] Author and Article Information
Tomiichi Hasegawa

Faculty of Engineering, Niigata University, 8050, Ikarashi-2, Nishi-ku, Niigata-shi 950-2181, Japanhasegawa@eng.niigata-u.ac.jp

Masahiro Karasawa

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

Takatsune Narumi

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

J. Fluids Eng 130(8), 081505 (Jul 29, 2008) (8 pages) doi:10.1115/1.2956597 History: Received May 04, 2007; Revised February 17, 2008; Published July 29, 2008

Surfactant solutions are usually used under conditions accompanied by transient dynamic surfaces, and therefore the dynamic surface tension (DST) is important in many industrial processes. Theories regarding DST have been developed exclusively on the adsorption theory that molecules are transported from bulk solution to the interface. However, the adsorption theory is not closed and requires another relationship between the interfacial concentration of the adsorbing molecules and the bulk concentration of molecules near and at the surface, which at present is based on assumptions. In addition, DST obtained by the adsorption theory contains several parameters that must be determined beforehand, and it is not simple to use for practical purposes. Here, we propose a new model based on the concept that surfactant molecules rotate during the process reaching the equilibrium surface state, which is different from the conventional adsorption theory, and we obtained a simple expression of DST as a function of the surface age. In addition, an experiment was carried out to determine DST by measuring the period and weight of droplets falling from a capillary. The expression by the proposed model was compared with the results of this experiment and with those reported previously by several other authors, and good agreement was obtained. Furthermore, the characteristic time in the model was shown to be correlated with the concentrations of solutions regardless of the type of solutions examined.

Copyright © 2008 by American Society of Mechanical Engineers
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Figures

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Figure 2

Schematic representation of the present modeling

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Figure 3

Image of a rotating surfactant molecule

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Figure 4

Schematic representation of a droplet

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Figure 5

Experimental apparatus

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Figure 6

Equilibrium surface tension σs plotted against concentrations of AE: Pure water (27°C), tap water (27°C), and AE(23) (22°C), AE(10) (24°C), AE(20) (16°C), and AE(100) (17°C) aqueous solutions

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Figure 7

DST σ of AE(23) in pure water (30°C) and tap water (27°C) plotted against surface age t

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Figure 11

σθ against t; experimental data for AE(23) (symbols) and model predictions (lines). K (s) was chosen for best fit of the model prediction to the experimental data at each concentration. (a) 10–80ppm. (b) 100–10,000ppm.

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Figure 12

Comparison of the data (symbols) of (a) Triton X-100 and (b) Triton X-405 measured by the FFD method (13) and the model prediction (lines). K (s) was chosen for the best fit.

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Figure 13

Comparison of the data (symbols) of C10E8 measured by video-enhanced pendant bubble tensiometry (14) with the model prediction (lines). K (s) was chosen for the best fit.

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Figure 14

Comparison of the data of C10E5 measured by the maximum bubble pressure (MBP) method (open symbols) and the drop shape technique (solid symbols) (15) with the model prediction (lines). K (s) was chosen for the best fit.

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Figure 1

Schematic representation of the adsorption theory for surfactant solutions

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Figure 8

Normalized DST σθ plotted against the surface age t; 10ppm(13°C), 20ppm(15°C), 40ppm(16°C), 50ppm(14°C), 80ppm(12°C), 100ppm(14°C), 200ppm(13°C), 1000ppm(19°C), and 10,000ppm(19°C) AE(23) solutions in water. Inner diameter is 0.27mm

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Figure 9

σθ measured by the maximum bubble method (MBP) (25°C) and the present drop weight method (14–16°C)

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Figure 10

σθ against t for different AEs at the same molar concentration. (a) AE(10) (27°C) and AE(23) (17°C) for 5×10−7mol∕cm3 and AE(10) (20°C) and AE(23) (20°C) for 5×10−8mol∕cm3. (b) AE(20) (25°C) and AE(100) (29°C) for 1×10−7mol∕cm3, and AE(20) (30°C) and AE(100) (31°C) for 1×10−8mol∕cm3.

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Figure 15

K (s) plotted against concentration C (mol∕cm3 or ppm) for all solutions listed. (a) K (s) against molar concentration C(mol∕cm3). (b) K (s) against weight concentration C (ppm). The line in shows the relationship K=185C−1.2 between K (s) and C (ppm).

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