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Time dependent diffusion in a disordered medium with partially absorbing walls: a perturbative approach.

Jiang Qian1, Pabitra N Sen

  • 1Lyman Laboratory of Physics, Harvard University, Cambridge, Massachusetts 02138, USA. jqian@physics.harvard.edu

The Journal of Chemical Physics
|November 30, 2006
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This study analyzes the time-dependent diffusion coefficient in sphere suspensions with partial absorption. We derived a formula for diffusion coefficient D(t) accurate to first order in sphere volume fraction.

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Area of Science:

  • Physics
  • Physical Chemistry
  • Colloid Science

Background:

  • Understanding diffusion in suspensions is crucial for various physical and chemical processes.
  • Particle interactions and boundary conditions significantly influence diffusion dynamics.

Purpose of the Study:

  • To analytically determine the time-dependent diffusion coefficient in a dilute suspension of spheres.
  • To investigate the effect of partially absorbing boundary conditions on diffusion.

Main Methods:

  • Utilized a perturbative expansion based on the volume fraction of spheres.
  • Employed the exact single-particle t-operator for partially absorbing boundaries.
  • Derived a closed-form expression for the time-dependent diffusion coefficient, D(t).

Main Results:

  • Obtained D(t) accurate to first order in volume fraction (f).
  • Validated short-time limits against known results for absorbing and reflecting boundaries.
  • Derived a specific long-time diffusion coefficient for fully absorbing boundaries: D(t) = 5a^2 / (12fD(0)t) + O((D(0)t/a^2)^-2).

Conclusions:

  • The derived perturbative result provides an accurate first-order approximation for D(t).
  • The study highlights the importance of boundary conditions in suspension diffusion.
  • Further discussion on the validity and applicability of the perturbative approach is provided.