Hong Et Al. Reply to Walliser

We find it absurd that Walliser [1] essentially used the same analysis and obtained identical results as reported in [3], yet arrived at different conclusions. Namely, based on an incomplete theory and using erroneous arguments , he not only disputes the original results [2], but also claims them wrong. A more complete theory and much more detailed studies were published in [3], from which we concluded that such results support the mechanism of segregation introduced in ref. [2]. We want to make it clear that Walliser obtained partial results of ref. [3] and arrived at the opposite conclusion. In the following we discuss his comment and its relevance, but at the same time point out what went wrong with his arguments. First, the free energy functional used in refs. [1,3] is the granular gas/fluid free energy. The observation of either the Brazil-Nut or the reverse Brazil-Nut [2] was, however, discussed and connected to the condensation or crys-tallization of the material at the bottom of the container. In such very dense situations in the absence of convection, the geometrical size-segregation presumably overrides other segregation phenomena [4]. If the system density is nowhere close to the crystallization density, the fluid free energy description is appropriate for the granular gas. The other situations, where parts of the system are condensed/crystallized, cannot be explained qualitatively by a gas/fluid free energy-as attempted in the Comment [1] and cannot be understood by a gas/fluid based approach. The correct way of describing such crystallization is to go beyond a simple density functional approach [1,3], and use the weighted density functional approach, see ref. [5] and references therein. Also other attempts based on Enskog theory [6], and/or empirical predictions for a global equation of state [7] and numerical modeling, at least account for the crystallization and the corresponding change of material behavior. Such advanced methods clearly reveal the formation of crystals 1