In this paper the time transient isothermal flow of lyotropic nematic liquid crystals (LC) between two eccentric cylinders was studied numerically by applying the Landau-de Gennes (LdG) theory. The start-up flow induced by the steady rotation of the inner cylinder was used to model the lubrication problem inside a journal bearing. The ability of liquid crystalline materials to form ordered boundary layers with good load-carrying capacity, outstanding lubricating properties, has been widely demonstrated. The LdG theory for the microstructure of the molecules along with continuity and momentum equations were solved simultaneously using General PDE and Laminar Flow packages of the COMSOL Multiphysics. Flow properties and structure were investigated as a function of simulation time, the Reynolds number and the Energy ratio, R. Interconnection and impact of the texture and defects formation/evolution on velocity profile and pressure distribution was observed; nucleation and evolution of disclination line and defect points were detected and pursued over the simulation time. For high Reynolds numbers, the flow reached quasi-stationary condition while the microstructure evolution was at unsteady state. The influence of the Energy ratio and the Reynolds number on the formation and evolution of polydomains was studied. Indeed, it was found that coupling the evolution of liquid crystalline microstructure with the hydrodynamics has a quantitative and qualitative impact on the macro-scale attributes of the flow and on the structure. The standard procedure to classify defects has been applied, oblate and isotropic defects have been identified. (C) 2014 Elsevier B.V. All rights reserved.