5. Concluding remarks

In this chapter, we investigated diffusion phenomenon as an irreversible process. By thermodynamic laws, entropy always increases as a system of interest evolves in a non-equilibrium state. The entropy-increasing rate per unit volume is a measure of how fast the system changes from the current to a more disordered state. Entropy concept is explained from the basic mathematics using several examples. Diffusion phenomenon is explained using (phenomenological) Fick's law, and more fundamental theories were summarized, which theoretically derive the diffusion coefficient and the convection-diffusion equation. Finally, the dissipation rate, i.e., entropy-changing rate per volume, is revisited and obtained in detail. The coupled, irreversible transport equation in steady state is applied to solute diffusion in an isothermal-isobaric process and heat transfer that is consisting of the conductive and convective transport due to the temperature gradient and fluid flow, respectively. As engineering processes are mostly open in the steady state, the theoretical approaches discussed in this chapter may be a starting point of the future development in irreversible thermodynamics and statistical mechanics.

Non-Equilibrium Particle Dynamics

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