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A unit-cube geometry model is proposed to characterize the internal structure of porous carbon foam. The unit-cube model is based on interconnected sphere-centered cubes, where the interconnected spheres represent the fluid or void phase. The unit-cube model is used to derive all of the geometric parameters required to calculate the heat transfer and flow through the porous foam. An expression for the effective thermal conductivity is derived based on the unit-cube geometry. Validations show that the conductivity model gives excellent predictions of the effective conductivity as a function of porosity. When combined with existing expressions for the pore-level Nusselt number, the proposed model also yields reasonable predictions of the internal convective heat transfer, but estimates could be improved if a Nusselt number expression for a spherical void phase material were available. Estimates of the fluid pressure drop are shown to be well-described using the Darcy-Forchhiemer law, however, further exploration is required to understand how the permeability and Forchhiemer coefficients vary as a function of porosity and pore diameter.

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12The comparative studies of the carbon xerogel (CX) and commercial activated carbon (AC) on the 13 textural properties demonstrated that CX has higher total pore volume and pore diameter, whereas 14 its adsorption capacity on Pb(II) ions in aqueous solution is lower. Herein, the purpose of the present 15 study is to improve the adsorption performance by the introduction of N into the CX matrix in the 16 basis of the extraordinary textural property. Accordingly, the surface chemistry, porous texture, and 17 morphology of the obtained N-doped CX (NCX) were modified. The removal efficiencies of Pb, Zn 18 and Cu by NCX were 1.97, 1.67, and 1.64 times of those by CX, respectively. It was found that the 19 surface density of adsorbed metal ions to per unit specific surface area of NCX increased as a 20 linear function with the increase in the N content. The adsorption process of Pb(II) ions followed 21 the pseudo-second-order kinetics and Langmuir model with the maximum adsorption capacity of 22 83.8 mg/g, indicating that NCX would be a promising adsorbent for removal of heavy metal ions 23 from water. 24

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