Hysteresis and phase transition in many-particle storage systems

Dreyer, Wolfgang; Guhlke, Clemens; Herrmann, Michael
May 2011
Continuum Mechanics & Thermodynamics;May2011, Vol. 23 Issue 3, p211
Academic Journal
We study the behavior of systems that can be described as ensembles of interconnected storage particles. Our examples concern the storage of lithium in many-particle electrodes of rechargeable lithium-ion batteries and the storage of air in a system of interconnected rubber balloons. We are particularly interested in those storage systems whose constituents exhibit non-monotone material behavior leading to transitions between two coexisting phases and to hysteresis. In the current study, we consider the case that the time to approach equilibrium of a single storage particle is much smaller than the time for full charging of the ensemble. In this regime, the evolution of the probability to find a particle of the ensemble in a certain state may be described by a non-local conservation law of Fokker-Planck type. The resulting equation contains two parameter which control whether the ensemble transits the 2-phase region along a Maxwell line or along a hysteresis path, or whether the ensemble shows the same non-monotone behavior as its constituents.


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