Influence of the Hamaker Constant on the Value of the Critical Thickness of Foam Films
Abstract
:1. Introduction
- Experimental data of the critical thickness (in the place of the black spot formation) for films stabilized by nonionic surfactant n-dodecyl-β-D-maltoside (C12G2) and cationic surfactant n-dodecyl trimethylammonium bromide (C12ТАВ) in the presence of 0.1M NaBr;
- Values of the Hamaker constant calculated by means of different equations for film thicknesses from 15 to 70 nm;
- Values of critical thickness calculated by Vrij approach and Radoev-Scheludko-Manev (RShM) formula, using the measured drainage coefficients and the calculated values of the Hamaker constant.
2. Materials and Methods
2.1. Materials
2.2. Experimental Conditions
2.3. Methods
Interferometric Method for Thin Liquid Films Investigation
2.4. Calculations
2.4.1. Film Drainage
2.4.2. Critical Thickness
2.4.3. Hamaker Constant
3. Results and Discussion
3.1. Hamaker Constant
- Vassilieff’s values of the Hamaker constant are very close to the values of Aeff (h) (introduced by Coons et al.);
- The calculated values of the Hamaker constant by Nguyen are the lowest, probably because the authors model an expression for the bubble–particle system and introduce fitting coefficients for this system;
- There is no significant difference between the calculated values of A(h) at the two ionic strengths.
3.2. Comparison between Measured and Calculated Critical Thickness Values for Foam Films Stabilized by Nonionic n-Dodecyl-β-D-maltoside (C12G2) and by Cationic Surfactant n-Dodecyl Trimethyl Ammonium Bromide (C12TAB)
4. Conclusions
Funding
Acknowledgments
Conflicts of Interest
Appendix A
h, nm | AH Retarded × 1020, J | |||
---|---|---|---|---|
Vassilieff’s A(h) | Aret(h) (by Equation (17)) | Aeff (h) (by Equation (19) + (17)) | A(h) by Nguyen et al. (Equation (20)) | |
70.0 | 0.73 | 0.59 | 0.79 | 0.36 |
67.5 | 0.75 | 0.62 | 0.82 | 0.37 |
65.0 | 0.78 | 0.64 | 0.85 | 0.38 |
62.5 | 0.80 | 0.66 | 0.88 | 0.40 |
60.0 | 0.84 | 0.68 | 0.91 | 0.41 |
55.0 | 0.91 | 0.74 | 0.99 | 0.45 |
50.0 | 1.00 | 0.80 | 1.07 | 0.49 |
47.5 | 1.05 | 0.84 | 1.12 | 0.51 |
45.0 | 1.10 | 0.88 | 1.18 | 0.54 |
42.5 | 1.16 | 0.93 | 1.24 | 0.57 |
40.0 | 1.22 | 0.98 | 1.30 | 0.60 |
37.5 | 1.31 | 1.03 | 1.38 | 0.64 |
35.0 | 1.38 | 1.09 | 1.46 | 0.68 |
32.5 | 1.48 | 1.16 | 1.55 | 0.72 |
30.0 | 1.56 | 1.23 | 1.65 | 0.78 |
27.5 | 1.71 | 1.32 | 1.76 | 0.84 |
25.0 | 1.86 | 1.42 | 1.89 | 0.91 |
22.5 | 2.00 | 1.53 | 2.04 | 1.00 |
20.0 | 2.17 | 1.65 | 2.20 | 1.10 |
17.5 | 2.40 | 1.80 | 2.40 | 1.22 |
15.0 | 2.76 | 1.97 | 2.62 | 1.38 |
Appendix B
1.5 × 10-4 M C12G2 + 0.1 M NaBr | 4.2 × 10−3 M C12TAB + 0.1 M NaBr | ||
---|---|---|---|
Radius, mm | α, s−1 | Radius, mm | α, s−1 |
0.036 | 0.0430 | 0.034 | 0.0390 |
0.048 | 0.0320 | 0.042 | 0.0334 |
0.082 | 0.0200 | 0.077 | 0.0199 |
0.094 | 0.0180 | 0.090 | 0.0171 |
0.151 | 0.0113 | 0.152 | 0.0140 |
Appendix C
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Ivanova-Stancheva, D. Influence of the Hamaker Constant on the Value of the Critical Thickness of Foam Films. Coatings 2019, 9, 576. https://doi.org/10.3390/coatings9090576
Ivanova-Stancheva D. Influence of the Hamaker Constant on the Value of the Critical Thickness of Foam Films. Coatings. 2019; 9(9):576. https://doi.org/10.3390/coatings9090576
Chicago/Turabian StyleIvanova-Stancheva, Dilyana. 2019. "Influence of the Hamaker Constant on the Value of the Critical Thickness of Foam Films" Coatings 9, no. 9: 576. https://doi.org/10.3390/coatings9090576