Interdisciplinary Applied Mathematics

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11.2.4    Dielectric Constant……………….429


11.3    Dynamic Behavior…………………..430


11.3.1    Basic Concepts…………………430


11.3.2    Diffusion Transport ………………435


11.3.3    Filling and Emptying Kinetics …………437


12    Electroosmotic Flow in Nanochannels    447


12.1    The Need for Atomistic Simulation…………..447


12.2    Ion Concentrations…………………..452


12.2.1    Modified Poisson-Boltzmann Equation……..455


12.3    Velocity Profiles ……………………457


12.4    Slip Condition …………………….461


12.5    Charge Inversion and Flow Reversal………….464


13    Functional Fluids and Functionalized Nanotubes    471


13.1    Colloidal Particles and Self-Assembly………….472


13.1.1    Magnetorheological (MR) Fluids………..475


13.1.2 Electrophoretic Deposition …………..486


13.2 Electrolyte Transport Through Carbon Nanotubes…..490


13.2.1    Carbon Nanotubes……………….491


13.2.2    Ion Channels in Biological Membranes……..493


13.2.3    Transport Through Unmodified Nanotubes…..495


13.2.4    Transport Through Nanotubes with Charges at


the Ends ……………………497


13.2.5    Transport Through Functionalized Nanotubes …. 498


13.2.6    Anomalous Behavior………………499


14    Numerical Methods for


Continuum Simulation    509


14.1    Spectral Element Method: The p,Flow Program…….510


14.1.1    Incompressible Flows………………514


14.1.2    Compressible Flows ………………517


14.1.3    Verification Example: Resolution of the Electric


Double Layer………………….524


14.1.4    Moving Domains………………..525


14.2    Meshless Methods …………………..531


14.2.1    Domain Simulation……………….532


14.2.2    Boundary-Only Simulation …………..537


14.3    Particulate Microflows…………………542


14.3.1    Hydrodynamic Forces on Spheres………..543


14.3.2    The Force Coupling Method (FCM)………547


15    Multiscale Modeling of Gas Flows    559


15.1    Direct Simulation Monte Carlo (DSMC) Method……560


15.1.1    Limitations and Errors in DSMC………..562


15.1.2    DSMC for Unsteady Flows …………..567


15.1.3    DSMC: Information-Preservation Method……569


15.2    DSM: Continuum Coupling………………572


15.2.1    The Schwarz Algorithm…………….575

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