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首页> 美国卫生研究院文献>The Journal of Chemical Physics >One-dimensional description of diffusion in a tube of abruptly changing diameter: Boundary homogenization based approach
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One-dimensional description of diffusion in a tube of abruptly changing diameter: Boundary homogenization based approach

机译：直径突然变化的管中扩散的一维描述：基于边界均匀化的方法

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摘要

Reduction of three-dimensional (3D) description of diffusion in a tube of variable cross section to an approximate one-dimensional (1D) description has been studied in detail previously only in tubes of slowly varying diameter. Here we discuss an effective 1D description in the opposite limiting case when the tube diameter changes abruptly, i.e., in a tube composed of any number of cylindrical sections of different diameters. The key step of our approach is an approximate description of the particle transitions between the wide and narrow parts of the tube as trapping by partially absorbing boundaries with appropriately chosen trapping rates. Boundary homogenization is used to determine the trapping rate for transitions from the wide part of the tube to the narrow one. This trapping rate is then used in combination with the condition of detailed balance to find the trapping rate for transitions in the opposite direction, from the narrow part of the tube to the wide one. Comparison with numerical solution of the 3D diffusion equation allows us to test the approximate 1D description and to establish the conditions of its applicability. We find that suggested 1D description works quite well when the wide part of the tube is not too short, whereas the length of the narrow part can be arbitrary. Taking advantage of this description in the problem of escape of diffusing particle from a cylindrical cavity through a cylindrical tunnel we can lift restricting assumptions accepted in earlier theories: We can consider the particle motion in the tunnel and in the cavity on an equal footing, i.e., we can relax the assumption of fast intracavity relaxation used in all earlier theories. As a consequence, the dependence of the escape kinetics on the particle initial position in the system can be analyzed. Moreover, using the 1D description we can analyze the escape kinetics at an arbitrary tunnel radius, whereas all earlier theories are based on the assumption that the tunnel is narrow.
机译：先前仅在直径缓慢变化的管中详细研究了将可变截面管中的扩散的三维描述（3D）简化为近似一维（1D）描述。在这里，我们讨论了在相反的极限情况下，当管子直径突然变化时（即，在由任意数量的不同直径的圆柱部分组成的管子中）的有效一维描述。我们方法的关键步骤是通过适当地选择捕集速率部分吸收边界来捕集在管的宽和窄部分之间的粒子过渡的近似描述。边界均匀化用于确定从管的较宽部分到较窄的部分的捕获率。然后，将该捕获率与详细平衡的条件结合使用，以找到从相反方向（从管的较窄部分到较宽的部分）的捕获率。通过与3D扩散方程的数值解进行比较，可以测试近似的1D描述并确定其适用条件。我们发现，当管的较宽部分不太短时，建议的1D描述效果很好，而较窄部分的长度可以是任意的。利用这一描述，可以解决粒子从圆柱腔通过圆柱隧道逃逸的问题，我们可以提出较早理论中接受的限制性假设：我们可以考虑在隧道和空腔中以相同的立足点进行粒子运动，即，我们可以放宽所有早期理论中使用的腔内快速弛豫的假设。结果，可以分析逃逸动力学对系统中粒子初始位置的依赖性。此外，使用一维描述，我们可以分析任意隧道半径下的逃逸动力学，而所有较早的理论均基于隧道狭窄的假设。

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