Correlation equations for average deposition rate coefficients of nanoparticles in a cylindrical pore

Nanoparticle deposition behavior observed at the Darcy scale represents an average of the processes occurring at the pore scale. Hence, the effect of various pore-scale parameters on nanoparticle deposition can be understood by studying nanoparticle transport at pore scale and upscaling the results to the Darcy scale. In this work, correlation equations for the deposition rate coefficients of nanoparticles in a cylindrical pore are developed as a function of nine pore-scale parameters: the pore radius, nanoparticle radius, mean flow velocity, solution ionic strength, viscosity, temperature, solution dielectric constant, and nanoparticle and collector surface potentials. Based on dominant processes, the pore space is divided into three different regions, namely, bulk, diffusion, and potential regions. Advection-diffusion equations for nanoparticle transport are prescribed for the bulk and diffusion regions, while the interaction between the diffusion and potential regions is included as a boundary condition. This interaction is modeled as a first-order reversible kinetic adsorption. The expressions for the mass transfer rate coefficients between the diffusion and the potential regions are derived in terms of the interaction energy profile. Among other effects, we account for nanoparticle-collector interaction forces on nanoparticle deposition. The resulting equations are solved numerically for a range of values of pore-scale parameters. The nanoparticle concentration profile obtained for the cylindrical pore is averaged over a moving averaging volume within the pore in order to get the 1-D concentration field. The latter is fitted to the 1-D advection-dispersion equation with an equilibrium or kinetic adsorption model to determine the values of the average deposition rate coefficients. In this study, pore-scale simulations are performed for three values of Peclet number, Pe = 0.05, 5, and 50. We find that under unfavorable conditions, the nanoparticle deposition at pore scale is best described by an equilibrium model at low Peclet numbers (Pe = 0.05) and by a kinetic model at high Peclet numbers (Pe = 50). But, at an intermediate Pe (e.g., near Pe = 5), both equilibrium and kinetic models fit the 1-D concentration field. Correlation equations for the pore-averaged nanoparticle deposition rate coefficients under unfavorable conditions are derived by performing a multiple-linear regression analysis between the estimated deposition rate coefficients for a single pore and various pore-scale parameters. The correlation equations, which follow a power law relation with nine pore-scale parameters, are found to be consistent with the column-scale and pore-scale experimental results, and qualitatively agree with the colloid filtration theory. These equations can be incorporated into pore network models to study the effect of pore-scale parameters on nanoparticle deposition at larger length scales such as Darcy scale.

Electrochemical deposition of manganese oxide-phosphate-reduced graphene oxide composite and electrocatalysis of the oxygen evolution reaction

A composite of manganese oxide and reduced graphene oxide (rGO) is prepared in a single step electrochemical reduction process in a phosphate buffer solution for studying as an electrocatalyst for the oxygen evolution reaction (OER). The novel composite catalyst, namely, MnOx-Pi-rGO, is electrodeposited from a suspension of graphene oxide (GO) in a neutral phosphate buffer solution containing KMnO4. The manganese oxide incorporates phosphate ions and deposits on the rGO sheet, which in turn is formed on the substrate electrode by electrochemical reduction of GO in the suspension. The OER is studied with the MnOx-Pi-rGO catalyst in a neutral phosphate electrolyte by linear sweep voltammetry. The results indicate a positive influence of rGO in the catalyst. By varying the ratio of KMnO4 and GO in the deposition medium and performing linear sweep voltammetry for the OER, the optimum composition of the deposition medium is obtained as 20 mM KMnO4 + 6.5% GO in 0.1 M phosphate buffer solution of pH 7. Under identical conditions, the MnOx-Pi-rGO catalyst exhibits 6.2 mA cm(-2) OER current against 2.9 mA cm(-2) by MnOx-Pi catalyst at 2.05 V in neutral phosphate solution. The Tafel slopes measured for OER at MnOx-Pi and MnOx-Pi-rGO are similar in magnitude at about 0.180 V decade(-1). The high Tafel slopes are attributed to partial dissolution of the catalyst during oxygen evolution. The O-2 evolved at the catalyst is measured by the water displacement method and the positive role of rGO on catalytic activity of MnOx-Pi is demonstrated.