Kalinay Pavol
Institute of Physics, Slovak Academy of Sciences, Dúbravská cesta 9, 84511, Bratislava, Slovakia.
Phys Rev E. 2020 Oct;102(4-1):042606. doi: 10.1103/PhysRevE.102.042606.
Diffusion of particles carried by Poiseuille flow of the surrounding solvent in a three-dimensional (3D) tube of varying diameter is considered. We revisit our mapping technique [F. Slanina and P. Kalinay, Phys. Rev. E 100, 032606 (2019)2470-004510.1103/PhysRevE.100.032606], projecting the corresponding 3D advection-diffusion equation onto the longitudinal coordinate and generating an effective one-dimensional modified Fick-Jacobs (or Smoluchowski) equation. A different scaling of the transverse forces by a small auxiliary parameter ε is used here. It results in a recurrence scheme enabling us to derive the corrections of the effective diffusion coefficient and the averaged driving force up to higher orders in ε. The new scaling also preserves symmetries of the stationary solution in any order of ε. Finally we show that Reguera-Rubí's formula, widely applied for description of diffusion in corrugated tubes, can be systematically corrected by the strength of the flow Q; we give here the first two terms in the form of closed analytic formulas.
考虑了在直径变化的三维（3D）管中，由周围溶剂的泊肃叶流携带的粒子扩散。我们重新审视我们的映射技术[F. 斯拉尼纳和P. 卡利奈，《物理评论E》100, 032606 (2019)2470 - 004510.1103/PhysRevE.100.032606]，将相应的三维平流 - 扩散方程投影到纵向坐标上，并生成一个有效的一维修正菲克 - 雅各布斯（或斯莫卢霍夫斯基）方程。这里使用一个小的辅助参数ε对横向力进行不同的缩放。这导致了一个递推方案，使我们能够推导出有效扩散系数和平均驱动力在ε的高阶项上的修正。新的缩放还在ε的任何阶次上保持了定态解的对称性。最后我们表明，广泛应用于描述波纹管中扩散的雷格拉 - 鲁比公式，可以通过流强Q进行系统修正；我们在此以封闭解析公式的形式给出前两项。
