Riva Simone, Banetta Luca, Zaccone Alessio
Department of Physics, A. Pontremoli, University of Milan, Via Celoria 16, 20133 Milan, Italy.
Department of Applied Science and Technology (DISAT), Politecnico of Turin, Italy.
Phys Rev E. 2022 May;105(5-1):054606. doi: 10.1103/PhysRevE.105.054606.
We developed an analytical theoretical method to determine the microscopical structure of weakly to moderately sheared colloidal suspensions in dilute conditions. The microstructure is described by the static structure factor, obtained by solving the stationary two-body Smoluchowski advection-diffusion equation. The singularly perturbed partial differential equation problem is solved by performing an angular averaging over the extensional and compressing sectors and by the rigorous application of boundary-layer theory (intermediate asymptotics). This allows us to expand the solution to a higher order in Péclet with respect to previous methods. The scheme is independent of the type of interaction potential. We apply it to the example of charge-stabilized colloidal particles interacting via the repulsive Yukawa potential and study the distortion of the structure factor. It is predicted that the distortion is larger at small wave vectors k and its dependence on Pe is a simple power law. At increasing Pe, the main peak of the structure factor displays a broadening and shift toward lower k in the extensional sectors, which indicates shear-induced spreading out of particle correlations and neighbor particles locally being dragged away from the reference one. In the compressing sectors, instead, a narrowing and shift toward high k is predicted, reflecting shear-induced ordering near contact and concomitant depletion in the medium range. An overall narrowing of the peak is also predicted for the structure factor averaged over the whole solid angle. Calculations are also performed for hard spheres, showing good overall agreement with experimental data. It is also shown that the shear-induced structure factor distortion is orders of magnitude larger for the Yukawa repulsion than for the hard spheres.
我们开发了一种分析理论方法，用于确定稀溶液中弱至中等剪切的胶体悬浮液的微观结构。微观结构由静态结构因子描述，该因子通过求解稳态两体斯莫卢霍夫斯基平流扩散方程获得。通过对拉伸和压缩扇区进行角度平均，并严格应用边界层理论（中间渐近性），解决了奇异摄动偏微分方程问题。这使我们能够相对于以前的方法将解在佩克莱特数上展开到更高阶。该方案与相互作用势的类型无关。我们将其应用于通过排斥性汤川势相互作用的电荷稳定胶体颗粒的示例，并研究结构因子的畸变。预计在小波矢k处畸变更大，并且其对佩克莱特数的依赖性是一个简单的幂律。随着佩克莱特数增加，结构因子的主峰在拉伸扇区显示出变宽并向较低的k移动，这表明剪切诱导的颗粒相关性扩展以及相邻颗粒局部地从参考颗粒被拖走。相反，在压缩扇区，预计会变窄并向高k移动，反映出近接触处的剪切诱导有序以及中程伴随的耗尽。对于在整个立体角上平均的结构因子，也预计主峰会整体变窄。还对硬球进行了计算，与实验数据总体上显示出良好的一致性。还表明，对于汤川排斥，剪切诱导的结构因子畸变比硬球大几个数量级。
