Anomalous diffusion in viscosity landscapes
Markus Burgis, Volker Schaller, Martin Gl\"assl, Benjamin Kaiser,, Werner K\"ohler, Alexei Krekhov, Walter Zimmermann
TL;DR
This paper investigates how Brownian particles diffuse in inhomogeneous viscosity landscapes, revealing conditions for anomalous diffusion types through scaling, simulations, and analytical solutions, and proposing experimental substances.
Contribution
It introduces a comprehensive analysis of anomalous diffusion in viscosity landscapes using scaling, simulations, and analytical solutions, highlighting new diffusion behaviors.
Findings
Subdiffusive motion at viscosity minima
Superdiffusive motion at viscosity maxima
Superdiffusion in monotonic viscosity profiles
Abstract
Anomalous diffusion is predicted for Brownian particles in inhomogeneous viscosity landscapes by means of scaling arguments, which are substantiated through numerical simulations. Analytical solutions of the related Fokker-Planck equation in limiting cases confirm our results. For an ensemble of particles starting at a spatial minimum (maximum) of the viscous damping we find subdiffusive (superdiffusive) motion. Superdiffusion occurs also for a monotonically varying viscosity profile. We suggest different substances for related experimental investigations.
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