Water desalination becomes an increasingly important approach for clean water supply to meet the rapidly growing demand of population boost, industrialization, and urbanization. The main challenge in current desalination technologies lies in the reduction of energy consumption and economic costs. Here, we propose to use charged nanopores drilled in a graphene sheet as ion exchange membranes to promote the efficiency and capacity of desalination systems. Using molecular dynamics simulations, we investigate the selective ion transport behavior of electric-field-driven KCl electrolyte solution through charge modified graphene nanopores. Our results reveal that the presence of negative charges at the edge of graphene nanopore can remarkably impede the passage of Cl(-) while enhance the transport of K(+), which is an indication of ion selectivity for electrolytes. We further demonstrate that this selectivity is dependent on the pore size and total charge number assigned at the nanopore edge. By adjusting the nanopore diameter and electric charge on the graphene nanopore, a nearly complete rejection of Cl(-) can be realized. The electrical resistance of nanoporous graphene, which is a key parameter to evaluate the performance of ion exchange membranes, is found two orders of magnitude lower than commercially used membranes. Our results thus suggest that graphene nanopores are promising candidates to be used in electrodialysis technology for water desalinations with a high permselectivity.

From the viewpoint of nonlinear dynamics, the stability and bifurcation of the rotor dynamical system supported in gas bearings are investigated. First, the dynamical model of gas bearing-Jeffcott rotor system is given, and the finite element method is used to approach the unsteady Reynolds equation in order to obtain gas film forces. Then, the method for stability analysis of the unbalance response of the rotor system is developed in combination with the Newmark-based direct integral method and Floquet theory. Finally, a numerical example is presented, and the complex behaviors of the nonlinear dynamical system are simulated numerically, including the trajectory of the journal and phase portrait. In particular, the stabilities of the system’s equilibrium position and unbalance responses are studied via the orbit diagram, phase space, Poincaré mapping, bifurcation diagram, and power spectrum. The results show that the numerical method for solving the unsteady Reynolds equation is efficient, and there exist a rich variety of nonlinear phenomena in the system. The half-speed whirl encountered in practice is the result from Hopf bifurcation of equilibrium, and the numerical method presented is available for the stability and bifurcation analysis of the complicated gas film-rotor dynamic system.

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The unsteady flow separation of airfoil with a local flexible structure (LFS) is studied numerically in Lagrangian frames in detail, in order to investigate the nature of its high aerodynamic performance. For such aeroelastic system, the characteristic-based split (CBS) scheme combined with arbitrary Lagrangian-Eulerian (ALE) framework is developed firstly for the numerical analysis of unsteady flow, and Galerkin method is used to approach the flexible structure. The local flexible skin of airfoil, which can lead to self-induced oscillations, is considered as unsteady perturbation to the flow. Then, the ensuing high aerodynamic performances and complex unsteady flow separation at low Reynolds number are studied by Lagrangian coherent structures (LCSs). The results show that the LFS has a significant influence on the unsteady flow separation, which is the key point for the lift enhancement. Specifically, the oscillations of the LFS can induce the generations of moving separation and vortex, which can enhance the kinetic energy transport from main flow to the boundary layer. The results could give a deep understand of the dynamics in unsteady flow separation and flow control for the flow over airfoil.

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