具体描述
Covering all aspects of transport phenomena on the nano- and micro-scale, this encyclopedia features over 750 entries in three alphabetically-arranged volumes including the most up-to-date research, insights, and applied techniques across all areas. Coverage includes electrical double-layers, optofluidics, DNC lab-on-a-chip, nanosensors, and more.
Fluid Dynamics in Constrained Geometries: From Macro-Scale to the Molecular Limit A Comprehensive Text on Advanced Fluid Mechanics in Confined Spaces Book Overview This volume delves into the intricate world of fluid dynamics governed by spatial constraints, moving systematically from established continuum theories applicable at larger scales down to the fundamental molecular interactions that dictate flow behavior at the nanometer scale. It offers a rigorous theoretical framework integrated with practical methodologies necessary for understanding, modeling, and engineering systems where boundaries exert dominant control over fluid transport phenomena. This text is designed for advanced graduate students, researchers in physics, chemical engineering, mechanical engineering, and materials science seeking a deep, unified perspective on fluid behavior in highly confined geometries. Part I: Foundations of Continuum Flow in Channels and Porous Media This section establishes the classical governing equations of fluid motion, specifically tailored and adapted for situations involving significant boundary effects, where assumptions of bulk homogeneity break down. Chapter 1: Recalibrating the Navier-Stokes Equations for Confined Flow We begin by critically examining the standard Navier-Stokes equations, focusing on the implications of domain restriction. This chapter introduces modified boundary conditions necessary when surfaces are chemically active or exhibit significant slip/no-slip variations due to molecular layering or surface forces. Emphasis is placed on analyzing the transition from fully developed laminar flow in rectangular and circular ducts to transitional regimes influenced by surface roughness and thermal gradients imposed by closely spaced walls. Detailed analysis of pressure-driven flow in micro-channels, including non-Newtonian effects (e.g., shear-thinning in polymer solutions confined near surfaces), forms a core component. Chapter 2: Viscous Dissipation and Thermal Transport in Narrow Passages When the characteristic dimension of the flow channel approaches the thermal or viscous relaxation length scales of the fluid, viscous heating and non-isothermal effects become critical. This chapter develops models accounting for the interplay between viscous dissipation ($mu cdot (
abla u)^2$) and conductive/convective heat transfer across the narrow gap. We explore techniques for solving the coupled momentum and energy equations, focusing on scenarios like flow through micro-heat exchangers where surface-to-volume ratios maximize thermal interaction. Solutions for Graetz problems in confined rectangular ducts under constant wall temperature or heat flux conditions are derived, highlighting the significant impact of aspect ratio on Nusselt number predictions compared to traditional macro-scale correlations. Chapter 3: Flow in Porous and Packed Media: Beyond Darcy’s Law This part extends classical macroscopic models to address flow through complex, interconnected porous structures. While Darcy’s law remains a cornerstone for macroscopic filtration and groundwater modeling, this chapter critically evaluates its limitations when pore sizes decrease below the characteristic mean free path of the fluid or when fluid-solid interactions dominate. We introduce the Kozeny-Carman equation and its derivatives, discussing the critical role of tortuosity and connectivity. Advanced topics include Brinkman extension for modeling the transition zone near solid boundaries within the porous matrix and methods for characterizing effective permeability using computed tomography (CT) data from complex scaffolds. Part II: Interfacial Phenomena and Multiphase Systems in Confinement The presence of multiple fluid phases or interfaces within constrained spaces introduces complexities related to surface tension, wetting dynamics, and electrokinetic phenomena, often overshadowing inertial effects. Chapter 4: Wetting, Spreading, and Capillarity in Constrained Geometries Surface tension ($gamma$) dictates interface shape and movement when capillary forces dominate viscous and gravitational forces (low Bond number flows). This chapter provides a rigorous treatment of Young-Laplace equations adapted for complex geometries like corners, junctions, and three-phase contact lines in microstructures. Detailed analysis of receding and advancing contact angles under dynamic conditions (e.g., during droplet manipulation or spontaneous imbibition) is provided, integrating kinetic aspects of contact line motion via molecular kinetic theories. The mechanics of droplet formation and breakup in T-junctions and flow-focusing geometries are explored through dimensionless analysis. Chapter 5: Electrokinetics and Ion Transport Near Charged Surfaces In channels with characteristic dimensions comparable to the Debye screening length ($lambda_D$), the electrical double layer (EDL) occupies a significant portion of the fluid domain. This section focuses on the coupling between fluid flow and electrostatic potential, deriving the Poisson-Boltzmann equation and the Smoluchowski approximation. We analyze electro-osmotic flow (EOF) velocity profiles, demonstrating how the applied electric field generates bulk fluid motion independent of pressure gradients. The implications for separation science, including the resolution limits in capillary electrophoresis influenced by variations in surface charge density, are thoroughly investigated. Chapter 6: Dynamics of Colloids and Suspensions Under Confinement The motion of suspended particles (colloids, cells) within narrow channels is profoundly affected by hydrodynamic interactions with the walls and neighboring particles. This chapter reviews particle-wall lubrication forces and the resulting lift mechanisms (e.g., Segré-Silberberg effects) that cause particles to migrate towards specific equilibrium positions within a flow field. We analyze filtration efficiency in tortuous paths and address the mechanics of non-invasive particle focusing techniques utilizing inertial or viscoelastic effects in high-aspect-ratio channels. Part III: Bridging the Gap to Molecular Scales: Rarefied Gas and Liquid Behavior The final part addresses flow regimes where the continuum assumption fundamentally fails, requiring recourse to statistical mechanics or molecular simulation techniques. Chapter 7: Free Molecular Flow and the Knudsen Regime When the characteristic channel dimension ($L$) becomes significantly smaller than the molecular mean free path ($lambda$), the assumption of continuous fluid properties breaks down. This chapter introduces the Knudsen number ($Kn = lambda/L$) as the critical parameter. We analyze the transition from Navier-Stokes to slip-flow regimes ($0.01 < Kn < 0.1$) using modified macroscopic boundary conditions, followed by a deep dive into the free molecular regime ($Kn > 10$). Techniques for solving the Boltzmann equation using simplified kernels (e.g., BGK approximation) are introduced to predict mass flux in vacuum systems and ultra-low pressure gas handling components. Chapter 8: Molecular Dynamics Simulations of Confined Liquids Moving beyond analytical and macroscopic continuum approximations, this section focuses on computational methods essential for understanding fluid behavior at the atomic level. We detail the setup and execution of Molecular Dynamics (MD) simulations specifically tailored for liquid flow between parallel solid boundaries. Topics include force field selection (e.g., Lennard-Jones potentials), integration algorithms (e.g., Verlet), and statistical sampling techniques necessary to extract continuum-like observables (viscosity, diffusion coefficients) from discrete particle trajectories. Crucial attention is paid to boundary layer structure, liquid layering near solid interfaces, and the inherent difficulties in accurately measuring slip velocity from simulation data. Chapter 9: Thermal Fluctuations and Non-Equilibrium Effects at Interfaces The final chapter explores the limits of deterministic modeling. We examine how thermal noise (Brownian motion) affects the transport of nanoscale objects (e.g., molecular motors, fluctuating boundaries). Concepts from non-equilibrium statistical mechanics, such as fluctuating hydrodynamics, are introduced to describe transport processes where energy dissipation and thermal fluctuations are intrinsically linked within the confined system. This provides a theoretical underpinning for understanding active matter transport and the limits of precision in nanofluidic sensing devices influenced by inherent thermodynamic randomness.
