Department of Chemical Engineering, Faculty of Chemistry, Sofia University, Sofia 1164, Bulgaria.
J Colloid Interface Sci. 2012 Feb 15;368(1):342-55. doi: 10.1016/j.jcis.2011.11.031. Epub 2011 Nov 25.
Here we present the exact solution of two approaching spherical droplets problem, at small Reynolds and Peclet numbers, taking into account surface shear and dilatational viscosities, Gibbs elasticity, surface and bulk diffusivities due to the presence of surfactant in both disperse and continuous phases. For large interparticle distances, the drag force coefficient, f, increases only about 50% from fully mobile to tangentially immobile interfaces, while at small distances, f can differ several orders of magnitude. There is significant influence of the degree of surface coverage, θ, on hydrodynamic resistance β for insoluble surfactant monolayers. When the surfactant is soluble only in the continuous phase the bulk diffusion suppresses the Marangoni effect only for very low values of θ, while in reverse situation, the bulk diffusion from the drop phase is more efficient and the hydrodynamic resistance is lower. Surfactants with low value of the critical micelle concentration (CMC) make the interfaces tangentially immobile, while large CMC surfactants cannot suppress interfacial mobility, which lowers the hydrodynamic resistance between drops. For micron-sized droplets the interfacial viscosities practically block the surface mobility and they approach each other as solid spheres with high values of the drag coefficient.
我们在这里给出了两个接近的球形液滴问题的精确解，在小雷诺数和 Peclet 数的情况下，考虑了表面剪切和拉伸黏度、Gibbs 弹性、由于分散相和连续相中的表面活性剂的存在而引起的表面和体扩散系数。对于较大的颗粒间距离，阻力系数 f 仅从完全可动到切向不可动界面增加约 50%，而在较小的距离，f 可以相差几个数量级。表面覆盖率θ对不可溶性表面活性剂单层的流体动力阻力β有显著影响。当表面活性剂仅在连续相中可溶时，体扩散仅在θ非常低的值时抑制了 Marangoni 效应，而在相反的情况下，从液滴相的体扩散更有效，流体动力阻力更低。具有低临界胶束浓度（CMC）的表面活性剂使界面切向不可动，而大 CMC 表面活性剂不能抑制界面流动性，从而降低了液滴之间的流体动力阻力。对于微米级大小的液滴，界面黏度实际上阻止了表面的流动性，它们彼此接近，阻力系数很大，类似于固体球体。
