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Effective Diffusivity for Transport with Fluctuating Drift Velocity.

Alexander M Berezhkovskii1, Attila Szabo2

  • 1Mathematical and Statistical Computing Laboratory, Office of Intramural Research, Center for Information Technology, National Institutes of Health, Bethesda, Maryland 20892, United States.

The Journal of Physical Chemistry. B
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This summary is machine-generated.

Particle drift velocity fluctuations, whether from state transitions or confined fluid diffusion, impact transport dynamics. Effective diffusivity is the sum of intrinsic diffusivity and velocity correlation, unifying transport theories.

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Area of Science:

  • Physics
  • Physical Chemistry
  • Biophysics

Background:

  • Particle transport is often influenced by fluctuating drift velocities.
  • Understanding these fluctuations is key to modeling complex systems like molecular motors and fluid dynamics.

Purpose of the Study:

  • To develop a unified analytical framework for particle transport with fluctuating drift velocities.
  • To show that effective diffusivity can be expressed as a sum of intrinsic diffusivity and a velocity correlation integral.

Main Methods:

  • Analyzing particle dynamics under two fluctuation models: discrete state transitions and diffusion in a confined moving fluid.
  • Deriving analytical expressions for effective diffusivity by integrating velocity correlation functions.

Main Results:

  • Effective diffusivity is shown to be the sum of average intrinsic diffusivity and the time integral of the velocity correlation function.
  • Closed-form solutions for the time integral are obtained for nearest-neighbor transitions and 1D diffusion.
  • The derived expressions reconcile Taylor dispersion and molecular motor transport models.

Conclusions:

  • A general theory for particle transport with fluctuating velocities is presented.
  • The framework unifies seemingly disparate transport phenomena.
  • Provides a basis for further studies in complex particle dynamics.