Academia.eduAcademia.edu

Figure 4 – uploaded by Nguyễn Thế Anh

See full PDFdownloadDownload figure
Fig. 3. Gibbs elasticity, E=—(d0/dln I”), for mixtures of SDS and dodecanol at 100:1 mass ratio, as predicted using the data shown in Fig. 2.

Figure 3 Gibbs elasticity, E=—(d0/dln I”), for mixtures of SDS and dodecanol at 100:1 mass ratio, as predicted using the data shown in Fig. 2.

Related Figures (15)

Fig. 1. Schematic of the micro-interferometric apparatus with an Scheludko cell, a metallurgical inverted microscope, and a high-speed video camera system.
Fig. 1. Schematic of the micro-interferometric apparatus with an Scheludko cell, a metallurgical inverted microscope, and a high-speed video camera system.
The experimental results for surface tension of the mixtures of sodium dodecyl sulphate and dodecanol at 100:1 mass ratio are shown in Fig. 2. The surface tension has a minimum in the vicinity of the critical micelle concentration (CMC), which is at about 8 mmol/L (mM) for SDS and is characteristic for the mixed SDS and dodecanol adsorption layers. The parameters of the surfactant adsorption can be obtained from the experi- mental data by employing appropriate adsorption models. The adsorption of the mixtures was modelled following the available approach [36]. Briefly, the surface tension was calculated using the Gibbs adsorption equation. The correlations between the sur- factant surface excess and the bulk concentration were predicted using the van der waals isotherms. The counter ion binding was accounted for by employing the Stern layer model. The distri- butions of the SDS surfactant and counter ions were determined from the Poisson—Boltzmann equation. The difference between the experimental data and model for surface tension was min- imised using the non-linear regression analysis by changing the model parameters which included the adsorption constants, adsorption energies, and molecular interaction constants. The agreement between the experimental data and the model pre- diction (solid line) for surface tension is shown in Fig. 2. The Gibbs elasticity and the adsorption length determined by the model and the experimental data for surface tension are shown in Figs. 3 and 4. Fig. 2. Experimental (points) and theoretical (line) results for surface tension versus sodium dodecyl] sulphate (SDS) concentration for mixtures of SDS and dodecanol at 100:1 mass ratio.
The experimental results for surface tension of the mixtures of sodium dodecyl sulphate and dodecanol at 100:1 mass ratio are shown in Fig. 2. The surface tension has a minimum in the vicinity of the critical micelle concentration (CMC), which is at about 8 mmol/L (mM) for SDS and is characteristic for the mixed SDS and dodecanol adsorption layers. The parameters of the surfactant adsorption can be obtained from the experi- mental data by employing appropriate adsorption models. The adsorption of the mixtures was modelled following the available approach [36]. Briefly, the surface tension was calculated using the Gibbs adsorption equation. The correlations between the sur- factant surface excess and the bulk concentration were predicted using the van der waals isotherms. The counter ion binding was accounted for by employing the Stern layer model. The distri- butions of the SDS surfactant and counter ions were determined from the Poisson—Boltzmann equation. The difference between the experimental data and model for surface tension was min- imised using the non-linear regression analysis by changing the model parameters which included the adsorption constants, adsorption energies, and molecular interaction constants. The agreement between the experimental data and the model pre- diction (solid line) for surface tension is shown in Fig. 2. The Gibbs elasticity and the adsorption length determined by the model and the experimental data for surface tension are shown in Figs. 3 and 4. Fig. 2. Experimental (points) and theoretical (line) results for surface tension versus sodium dodecyl] sulphate (SDS) concentration for mixtures of SDS and dodecanol at 100:1 mass ratio.
Fig. 5. Experimental data (points) for the zeta potential of micro air bubbles in mixtures of SDS and dodecanol at 100:1 mass ratio. The maximum standard deviation is about 12 mV. The solid line presents a polynomial regression. The experimental results for the zeta potential of micro air bubbles in the mixtures of SDS and dodecanol are shown in Fig. 5. The zeta potential has a minimum at the concentra- tion (~5.5 mmol/L) corresponding to the point of the saturation adsorption density. It is assumed that the zeta potentials are not
Fig. 5. Experimental data (points) for the zeta potential of micro air bubbles in mixtures of SDS and dodecanol at 100:1 mass ratio. The maximum standard deviation is about 12 mV. The solid line presents a polynomial regression. The experimental results for the zeta potential of micro air bubbles in the mixtures of SDS and dodecanol are shown in Fig. 5. The zeta potential has a minimum at the concentra- tion (~5.5 mmol/L) corresponding to the point of the saturation adsorption density. It is assumed that the zeta potentials are not
Fig. 4. Adsorption length, @ = dI/dC, for mixtures of SDS and dodecanol at 100:1 mass ratio, as predicted using the data shown in Fig. 2.
Fig. 4. Adsorption length, @ = dI/dC, for mixtures of SDS and dodecanol at 100:1 mass ratio, as predicted using the data shown in Fig. 2.
Fig. 6. Comparison between experiment (points) and theory (lines) for transien thickness of a foam film containing 3.5 mM SDS + 10 mg/L dodecanol (us = 0.1! surface poise and R=0.075 mm). The line shows the drainage models describes by Eqs. (2), (4) and (5). The DLVO disjoining pressures described by Eqs. (6 and (8) are used in the model predictions.
Fig. 6. Comparison between experiment (points) and theory (lines) for transien thickness of a foam film containing 3.5 mM SDS + 10 mg/L dodecanol (us = 0.1! surface poise and R=0.075 mm). The line shows the drainage models describes by Eqs. (2), (4) and (5). The DLVO disjoining pressures described by Eqs. (6 and (8) are used in the model predictions.
Fig. 8. Transient images of a small foam film confirming the uniform film thickness during drainage (3.5 mM SDS + 10 mg/L dodecanol, R =0.075 mm, and times 0, 10, 20 and 30 ms). ity obtained by a deep channel viscometer is about 0.18 s.p. (0.18 x 1073 kg/s) (Fig. 7). Only the DLVO disjoining pressures as described by Eqs. (6) and (8) are used in the model predictions shown in Fig. 6. The drainage equations are described by the dif- ferential equations of the first-order for thickness, h, versus time, t. The differential equations were numerically solved using the fourth-step Runge-Kutta algorithm. A macro was written using the Visual Basic for Application (VBA) programming language available in Microsoft Excel. The inputs for the numerical inte- gration included the capillary pressure, P,, and the Marangoni Shown in Fig. 6 is a comparison between the experi- mental results and theoretical predictions for the film thick- ness versus time, obtained for a foam film containing 3.5mM SDS+10mg/L dodecanol. The surface shear viscos-
Fig. 8. Transient images of a small foam film confirming the uniform film thickness during drainage (3.5 mM SDS + 10 mg/L dodecanol, R =0.075 mm, and times 0, 10, 20 and 30 ms). ity obtained by a deep channel viscometer is about 0.18 s.p. (0.18 x 1073 kg/s) (Fig. 7). Only the DLVO disjoining pressures as described by Eqs. (6) and (8) are used in the model predictions shown in Fig. 6. The drainage equations are described by the dif- ferential equations of the first-order for thickness, h, versus time, t. The differential equations were numerically solved using the fourth-step Runge-Kutta algorithm. A macro was written using the Visual Basic for Application (VBA) programming language available in Microsoft Excel. The inputs for the numerical inte- gration included the capillary pressure, P,, and the Marangoni Shown in Fig. 6 is a comparison between the experi- mental results and theoretical predictions for the film thick- ness versus time, obtained for a foam film containing 3.5mM SDS+10mg/L dodecanol. The surface shear viscos-
Fig. 7. Surface shear viscosity of mixtures of SDS and dodecanol at 100:1 mass ratio as determined by a deep channel surface shear viscometer [34,39].
Fig. 7. Surface shear viscosity of mixtures of SDS and dodecanol at 100:1 mass ratio as determined by a deep channel surface shear viscometer [34,39].
Parameters for hydrophobic interaction obtained by best fit using Eqs. (5) anc (10) Table 1
Parameters for hydrophobic interaction obtained by best fit using Eqs. (5) anc (10) Table 1
Fig. 9. Comparison between experiment (points) and predictions (lines) by DLVO theory for transient thickness of a foam film containing 7mM SDS+20mg/L dodecanol (uw; =0.09s.p. and R=0.075mm) and 8.75mM SDS +25 mg/L dodecanol (us =0.03 s.p. and R=0.075 mm). The lines show the drainage models described by Eqs. (2), (4) and (5). The DLVO disjoining pressures are described by Eqs. (6) and (8) or (9).
Fig. 9. Comparison between experiment (points) and predictions (lines) by DLVO theory for transient thickness of a foam film containing 7mM SDS+20mg/L dodecanol (uw; =0.09s.p. and R=0.075mm) and 8.75mM SDS +25 mg/L dodecanol (us =0.03 s.p. and R=0.075 mm). The lines show the drainage models described by Eqs. (2), (4) and (5). The DLVO disjoining pressures are described by Eqs. (6) and (8) or (9).
Adsorption parameters and dimensionless numbers obtained for the surfactant mixtures (assuming D=4 x 107!° m?/s and D, =4 x 10~? m?/s)
Adsorption parameters and dimensionless numbers obtained for the surfactant mixtures (assuming D=4 x 107!° m?/s and D, =4 x 10~? m?/s)
Fig. 10. Comparison between experimental data (points) for transient thickness of the foam films and predictions (lines) by the extended DLVO theory with the inclusion of the hydrophobic disjoining pressure described by Eq. (10). The numerical values for K and 4 were obtained by the best fit using the drainage Eq. (5) and Eqs. (6), (8), and (10).
Fig. 10. Comparison between experimental data (points) for transient thickness of the foam films and predictions (lines) by the extended DLVO theory with the inclusion of the hydrophobic disjoining pressure described by Eq. (10). The numerical values for K and 4 were obtained by the best fit using the drainage Eq. (5) and Eqs. (6), (8), and (10).
Fig. 12. Effect of surface diffusion, Ds, on the drainage mobility, V/Vpe, of a foam film containing 8.75 mM and 25 mg dodecanol (j1s = 0.03 s.p.). Thick and thin lines describe Eqs. (5) and (4), respectively. For D,=4 x 10~° m?/s, Ma=7.43 x 10° and N=375. For D,=4 x 1078 m/s, Ma=7.43 x 10* and N=38. For both cases, Bo=400. are incorporated into the new drainage theory described by Eq. (5). The magnitudes of the dimensionless numbers obtained for the foam films produced using the mixtures of SDS and dode- canol are shown in Table 2. At present, the assessment of the >ffect of the parameters on foam film drainage is difficult because the coefficient of the surface diffusion is not precisely known and is often indirectly inferred from the film drainage experiments [11,65]. Some available data for the coefficient of surface dif- fusion have been obtained for common and Newton black films [67-69], where the surface mobility of adsorbed molecules is Jecreased due to high adsorption density. Indeed, it has been suggested that the coefficient of surface diffusion depends on the surface excess of adsorbed surfactants. The coefficient of surface diffusion can be higher than 4 x 107° m?/s chosen in the modelling shown in Figs. 6-9. If De=4 x 1078 m2/s is chosen
Fig. 12. Effect of surface diffusion, Ds, on the drainage mobility, V/Vpe, of a foam film containing 8.75 mM and 25 mg dodecanol (j1s = 0.03 s.p.). Thick and thin lines describe Eqs. (5) and (4), respectively. For D,=4 x 10~° m?/s, Ma=7.43 x 10° and N=375. For D,=4 x 1078 m/s, Ma=7.43 x 10* and N=38. For both cases, Bo=400. are incorporated into the new drainage theory described by Eq. (5). The magnitudes of the dimensionless numbers obtained for the foam films produced using the mixtures of SDS and dode- canol are shown in Table 2. At present, the assessment of the >ffect of the parameters on foam film drainage is difficult because the coefficient of the surface diffusion is not precisely known and is often indirectly inferred from the film drainage experiments [11,65]. Some available data for the coefficient of surface dif- fusion have been obtained for common and Newton black films [67-69], where the surface mobility of adsorbed molecules is Jecreased due to high adsorption density. Indeed, it has been suggested that the coefficient of surface diffusion depends on the surface excess of adsorbed surfactants. The coefficient of surface diffusion can be higher than 4 x 107° m?/s chosen in the modelling shown in Figs. 6-9. If De=4 x 1078 m2/s is chosen
Fig. 11. Agreement between the experimental data (points) for transient thick- ness of a SDS film and prediction (line) with the classical DLVO theory (R=0.077 mm).
Fig. 11. Agreement between the experimental data (points) for transient thick- ness of a SDS film and prediction (line) with the classical DLVO theory (R=0.077 mm).
Fig. 13. Experimental and modelled results for transient thickness for a foam film containing 8.75 mM and 25 mg dodecanol. The model prediction is based on the same equations and parameters used to produce Fig. 10, except for the coefficient of surface diffusion.
Fig. 13. Experimental and modelled results for transient thickness for a foam film containing 8.75 mM and 25 mg dodecanol. The model prediction is based on the same equations and parameters used to produce Fig. 10, except for the coefficient of surface diffusion.
Fig. 14. Schematic of foam film in the Scheludko cell. Appendix A. Drainage model with surface shear viscosity
Fig. 14. Schematic of foam film in the Scheludko cell. Appendix A. Drainage model with surface shear viscosity
Related topics:
EngineeringChemistryPhysical ChemistryThermodynamics of Electrolyte SolutionsThin Liquid FilmsSuper-Hydrophobic SurfacesPotential Energy SurfaceSodium Dodecyl SulphateAqueous electrolyte
580 California St., Suite 400
San Francisco, CA, 94104
© 2025 Academia. All rights reserved