Danov Krassimir D, Kralchevsky Peter A, Ananthapadmanabhan Kavssery P, Lips Alex
Laboratory of Chemical Physics and Engineering, Faculty of Chemistry, University of Sofia, 1164 Sofia, Bulgaria.
J Colloid Interface Sci. 2006 Nov 1;303(1):56-68. doi: 10.1016/j.jcis.2006.07.045. Epub 2006 Jul 25.
Here, we derive analytical asymptotic expressions for the dynamic surface tension of ionic surfactant solutions in the general case of nonstationary interfacial expansion. Because the diffusion layer is much wider than the electric double layer, the equations contain a small parameter. The resulting perturbation problem is singular and it is solved by means of the method of matched asymptotic expansions. The derived general expression for the dynamic surface tension is simplified for the special case of immobile interface and for the maximum bubble pressure method (MBPM). The case of stationary interfacial expansion is also considered. The effective diffusivity of the ionic surfactant essentially depends on the concentrations of surfactant and nonamphiphilic salt. To test the theory, the derived equations are applied to calculate the surfactant adsorption from MBPM experimental data. The results excellently agree with the adsorption determined independently from equilibrium surface-tension isotherms. The derived theoretical expressions could find application for interpreting data obtained by MBPM and other experimental methods for investigating interfacial dynamics.
在此，我们推导了在非稳态界面扩张的一般情况下离子表面活性剂溶液动态表面张力的解析渐近表达式。由于扩散层比双电层宽得多，这些方程包含一个小参数。由此产生的摄动问题是奇异的，通过匹配渐近展开法求解。对于固定界面的特殊情况和最大气泡压力法（MBPM），简化了推导得到的动态表面张力的一般表达式。还考虑了稳态界面扩张的情况。离子表面活性剂的有效扩散率主要取决于表面活性剂和非两亲性盐的浓度。为了检验该理论，将推导得到的方程应用于根据MBPM实验数据计算表面活性剂吸附量。结果与通过平衡表面张力等温线独立测定的吸附量非常吻合。推导得到的理论表达式可用于解释通过MBPM和其他研究界面动力学的实验方法获得的数据。
