Interdisciplinary Applied Mathematics

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7.2.1    Near-Wall Potential Distribution………..261


7.3    Governing Equations………………….263


7.4    Electroosmotic Flows………………….266


7.4.1    Channel Flows…………………266


7.4.2    Time-Periodic and AC Flows………….272


7.4.3    EDL/Bulk Flow Interface Velocity


Matching Condition………………279


7.4.4    Slip Condition …………………280


7.4.5    A Model for Wall Drag Force………….281


7.4.6    Joule Heating………………….282


7.4.7    Applications ………………….283


7.5    Electrophoresis…………………….292


7.5.1    Governing Equations………………294


7.5.2    Classification………………….295


7.5.3    Taylor Dispersion………………..297


7.5.4    Charged Particle in a Pipe …………..302


7.6    Dielectrophoresis……………………302


7.6.1    Applications ………………….304


8    Surface Tension-Driven Flows    311


8.1    Basic Concepts…………………….312


8.2    General Form of Young’s Equation…………..317


8.3    Governing Equations for Thin Films………….319


8.4    Dynamics of Capillary Spreading……………321


8.5    Thermocapillary Pumping……………….324


8.6    Electrocapillary…………………….328


8.6.1    Generalized Young-Lippmann Equation…….333


8.6.2    Optoelectrowetting……………….335


8.7    Bubble Transport in Capillaries…………….337


9    Mixers and Chaotic Advection    343


9.1    The Need for Mixing at Microscales ………….344


9.2    Chaotic Advection…………………..346


9.3    Micromixers………………………349


9.4    Quantitative Characterization of Mixing………..357


10    Simple Fluids in Nanochannels    365


10.1    Atomistic Simulation of Simple Fluids…………366


10.2    Density Distribution………………….368


10.3    Diffusion Transport…………………..375


10.4    Validity of the Navier-Stokes Equations………..381


10.5    Boundary Conditions at Solid-Liquid Interfaces…….387


10.5.1    Experimental and Computational Results……387


10.5.2    Conceptual Models of Slip……………396


10.5.3    Reynolds-Vinogradova Theory for


Hydrophobic Surfaces……………..401


11    Water in Nanochannels    407


11.1    Definitions and Models…………………407


11.1.1    Atomistic Models………………..409


11.2    Static Behavior…………………….416


11.2.1    Density Distribution and Dipole Orientation …. 417


11.2.2    Hydrogen Bonding……………….422


11.2.3    Contact Angle …………………427

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