An analysis of the entropy of mixing for granular materials

作者：Gu Zongyu^*; Chen J J J

来源：Powder Technology, 2014, 266: 90-95.

DOI：10.1016/j.powtec.2014.06.029

• Granular materials
• Particle processing
• Mixing
• Entropy of mixing
• Shannon entropy
• Phase space

Many existing definitions of the entropy of mixing for granular materials involve a %26quot;total entropy%26quot; that is calculated from the %26quot;local entropies%26quot; of all cells in the domain of the mixture. The total entropy has been used as a measure of mixedness by many authors, but they have virtually never presented the values of the individual local entropies. For comparison purposes, we introduced a parallel definition of the entropy of mixing by considering an alternative %26quot;total entropy%26quot; that is based on the %26quot;per-species entropies%26quot; of all types of particles in the mixture. Using a simple mixing model in continuous variables, we showed that the contributions of the individual %26quot;local entropies%26quot; and the %26quot;per-species entropies%26quot; to their respective totals show different trends during a specific, idealised mixing process: while the total entropy constantly increases following either definition, only the local entropies show non-monotonic changes; on the other hand, only the per-species entropies reach the maximum possible value of the Shannon entropy at the steady state of mixing. We rationalised these differences by considering the changes in the probabilities associated with each individual entropic term, in the context of the properties of the Shannon entropy, and confirmed these ideas by studying the two-dimensional phase-space trajectories of the individual entropic terms for the mixing process considered.

• 出版日期2014-11