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In the phenomenological approach, diffusion is the movement of a substance from a region of high concentration to a region of low concentration without bulk motion. According to Fick's laws, the diffusion flux is proportional to the negative gradient of concentrations. It goes from regions of higher concentration to regions of lower concentration.
There are some notable similarities in equations for momentum, energy, and mass transfer [7] which can all be transported by diffusion, as illustrated by the following examples: Mass: the spreading and dissipation of odors in air is an example of mass diffusion. Energy: the conduction of heat in a solid material is an example of heat diffusion.
The diffusion equation can be obtained easily from this when combined with the phenomenological Fick's first law, which states that the flux of the diffusing material in any part of the system is proportional to the local density gradient: = (,) (,).
Phenomenology is commonly applied to the field of particle physics, where it forms a bridge between the mathematical models of theoretical physics (such as quantum field theories and theories of the structure of space-time) and the results of the high-energy particle experiments.
Multicomponent diffusion is diffusion in mixtures, and diffusiophoresis is the special case where we are interested in the movement of one species that is usually a colloidal particle, in a gradient of a much smaller species, such as dissolved salt such as sodium chloride in water. or a miscible liquid, such as ethanol in water.
Three examples of Turing patterns Six stable states from Turing equations, the last one forms Turing patterns. The Turing pattern is a concept introduced by English mathematician Alan Turing in a 1952 paper titled "The Chemical Basis of Morphogenesis" which describes how patterns in nature, such as stripes and spots, can arise naturally and autonomously from a homogeneous, uniform state.
The rate of entropy production for the above simple example uses only two entropic forces, and a 2×2 Onsager phenomenological matrix. The expression for the linear approximation to the fluxes and the rate of entropy production can very often be expressed in an analogous way for many more general and complicated systems.
Reaction–diffusion systems are mathematical models that correspond to several physical phenomena. The most common is the change in space and time of the concentration of one or more chemical substances: local chemical reactions in which the substances are transformed into each other, and diffusion which causes the substances to spread out ...