The objective of this study was to simulate the flow of graphene oxide (GO) dispersions, a discotic nematic liquid crystal (DNLC), using the Ericksen-Leslie (EL) theory. GO aqueous suspension, as a lubricant, effectively reduces the friction between solid surfaces. The geometry considered in this study was two cylinders with a small gap size, which is the preliminary geometry for journal bearings. The Leslie viscosity coefficients calculated in our previous study were used to calculate the stress tensor in the EL theory. The behavior of GO dispersions in the concentration range of 15 mg/mL to 30 mg/mL, shown in our recent experiments to be in the nematic phase, was investigated to obtain the orientation and the viscosity profile. The viscosities of GO dispersions obtained from numerical simulations were compared with those from our recent experimental study, and we observed that the values are within the range of experimental uncertainty. In addition, the alignment angles of GO dispersions at different concentrations were calculated numerically using EL theory and compared with the respective theoretical values, which were within 1% error. The anchoring angles corresponding to viscosity values closest to the experimental results were between 114 and 118 degrees. Moreover, a sensitivity analysis was performed to determine the effects of different ratios of the elasticity coefficients in EL theory. Using this procedure, the same study could be extended for other DNLCs in different geometries.

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