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Updated: Jun 21, 2026
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Measurement of Particle Size Distribution in Turbid Solutions by Dynamic Light Scattering Microscopy
Published on: January 9, 2017
Anomalous diffusion in a field of randomly distributed scatterers.
1Institute for Theoretical Physics, University of Münster, Wilhelm-Klemm-Str. 9, D-48149 Münster, Germany.
Summary
Particles scattered by random obstacles exhibit anomalous diffusion. A scale-free obstacle distribution leads to a time-fractional master equation, revealing power-law diffusion coefficients in multi-dimensional systems.
Area of Science:
- Physics
- Statistical Mechanics
- Complex Systems
Background:
- Particle motion in disordered media is fundamental to many physical phenomena.
- Anomalous diffusion describes non-standard particle transport, deviating from Brownian motion.
- Previous models often simplify obstacle interactions or particle dynamics.
Purpose of the Study:
- To investigate particle motion with uniform movement between random scattering events.
- To derive a governing master equation for this system.
- To analyze the emergence of anomalous diffusion under specific scattering conditions.
Main Methods:
- Mapping the scattering problem to a known master equation for inertial anomalous diffusion.
- Deriving a time-fractional master equation for a scale-free distance distribution of scatterers.
- Solving the resulting diffusion equation in d dimensions using the method of subordination.
Main Results:
- A time-fractional master equation accurately describes the particle motion.
- The diffusion coefficient exhibits a power-law dependence on time.
- The solution in d dimensions is obtained via subordination.
Conclusions:
- Scale-free distributions of obstacles lead to time-fractional anomalous diffusion.
- The derived model provides a framework for understanding complex transport phenomena.
- The method of subordination offers a powerful tool for solving such diffusion equations.
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