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| Content Provider | Springer Nature Link |
|---|---|
| Author | Bevilacqua, L. Jiang, M. Silva Neto, A. Galeão, A. C. R. N. |
| Copyright Year | 2015 |
| Abstract | In previous papers, we presented a new theory of bi-flux diffusion processes. The bi-flux consists of the simultaneous flux of two sets of particles scattering with two distinct velocities. The first set obeys the classical Fick’s law, it is the primary flux. The complementary set follows a new law, it is the secondary flux. The primary and secondary fluxes are excited into two distinct energy states. The fundamental energy source for the primary flux is the translational energy or active energy. For the secondary flux, linear and angular momentum, both, contribute to the excitation state. Two cases are analyzed. The first one refers to an isolated system in a particular phase state S$_{1}$ where active energy decreases continuously. The system tends to an energy state where active energy is absent. In the second case, the system is in a different phase state S$_{2}$ where active energy increases continuously. The system recovers active energy and tends to a pure Fickian diffusion process. In both processes, the fractions representing the density distribution functions for the primary and secondary fluxes vary with time. It is remarkable that the fourth order equation provides a consistent approach to take into account the rotational energy which otherwise would not be possible with the classical theory. A particular law for the variation of the fraction of particles following Fick’s law is derived. A notion of entropy related to the particular energy states is introduced. Selected examples are presented showing the concentration profile evolution for different rates of energy transfer. |
| Starting Page | 1421 |
| Ending Page | 1432 |
| Page Count | 12 |
| File Format | |
| ISSN | 16785878 |
| Journal | Journal of the Brazilian Society of Mechanical Sciences and Engineering |
| Volume Number | 38 |
| Issue Number | 5 |
| e-ISSN | 18063691 |
| Language | English |
| Publisher | Springer Berlin Heidelberg |
| Publisher Date | 2015-12-31 |
| Publisher Place | Berlin, Heidelberg |
| Access Restriction | One Nation One Subscription (ONOS) |
| Subject Keyword | Anomalous diffusion Energy states Fourth order PDE Mechanical Engineering Bi-flux Time-dependent parameters |
| Content Type | Text |
| Resource Type | Article |
| Subject | Applied Mathematics Industrial and Manufacturing Engineering Automotive Engineering Mechanical Engineering Aerospace Engineering |
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