Do partial differential equations have a lot to do with electrochemistry?
Partial differential equation, namely, Fick's second law is the basis for the treatment of most time-dependent diffusion problem in Electrochemistry.
The symmetry of the phenomena on the electrodes can be described by partial differential equations with diffusion. See i.e. book entitled "Chemical Waves and Patterns" - there's a lot of maths in chemical patterns formation, including the phenomena on the electrodes (simplified approach due to the "just" 2D systems).
Thank you Wojciech. Can you tell in what application we need to maintain or describe the symmetry of the phenomena of the electrodes?
Hi, for example when we have nanoporous anodic oxides. These are Turing's patterns described by whole sets of differential equations.
Partial differential equation, namely, Fick's second law is the basis for the treatment of most time-dependent diffusion problem in Electrochemistry.
It is interesting to know that they are applied with the nanoporous anodic oxides. Yes, the differential equations were utilized quite often to describe diffusion and transport, like Fick's second law and those associated to Boltzmann equations.
Thanks!
In heat conduction problems, we use Fourier’s law I think in a similar way as we analyse diffusion problem using Fick's law. This give rise to what we call parabolic partial differential equation. In heat conduction we have this anomaly of infinite heat propagation velocity with regard to parabolic heat conduction. Some researchers modified the equation and consider instead hyperbolic heat conduction model. Is there such a concept as non Fick diffusion model in electrochemistry? Hyperbolic material diffusion model?
The diffusion toward electrodes with different geometries is a fundamental problem in electrochemistry. Diffusion to fractal or microarray surfaces problems are under investigation currently
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