The subject of this book is the physics of vortices. A detailed analysis of the dynamics of vortices will be presented. The important topics of vorticity and molecular spin will be dealt with, including the electromagnetic analogy and quantization in superfluids. The effect of molecular spin on the dynamics of molecular nano-confined fluids using the extended Navier-Stokes equations will also be covered –especially important to the theory and applicability of nanofluidics and associated devices. The nanoscale boundary layer and nanoscale vortex core are regions of intense vorticity (molecular spin). It will be shown, based on molecular kinetic theory and thermodynamics, that the macroscopic (solid body) rotation must be accompanied by internal rotation of the molecules. Electric polarization of the internal molecular rotations about the local rotation axis –the Barnett effect – occurs. In such a spin aligned system, major changes in the physical properties of the fluid result.
About the Author
Professor McCormack has made significant contributions to the US space program, as an Engineering Science professor at Dartmouth, and later as Chief of Operational Medicine at NASA. He subsequently served as Chief of Aerospace Medicine Research at the Naval Air Warfare Center. He received a US Navy Commendation Medal in 1998, and the German Navy Cross of Honor in 2000. A member of the UIC Bioengineering faculty since 2001, Professor McCormack serves on the Advisory Council for the National Institute for Biomedical Imaging and Bioengineering (NIBIB), and gives frequent invited talks on nanobiology and radiation damage.
Table of ContentsThe Vortex.- Brief History.- Kinematics.- Definition of a Vortex.- Vorticity and Circulation.- Plane Circular Vortex.- Rankine Vortex.- Curved Vortex Lines, Tubes and Vortex Rings.- Translational Velocity of the Inviscid Vortex Ring.- Velocity of a Viscous Vortex Ring.- Hydrodynamic Impulse and Vortex Ring Generation.- The Spectral Range of Vortex Size.- Forces(Lift, Drag, Thrust, Torque) on Moving Submerged Bodies Due to Vortex Formation.- Aerodynamic Lift and Drag.- Analytical Derivation of Lift and Drag on a Cylinder.- Axial Thrust, Torque and Helical Vortices.- Some Other Kinds of Simple Vortices.- Intake and Inlet Vortices.- Clearance Vortices.- Multiple Point Vortices and Their Motion.- Quantum Vortices and the Hydrodynamics of Superfluids.- Concluding Remarks on Chapter 1.- Vorticity(Molecular Spin).- Introduction.- Generation of Vorticity.- Generation by Shock Waves.- Generation by Free Convective Flow and Buoyancy.- Generation by Baroclinic Effects.- The General Vorticity Equation.- Viscous Diffusion of Vorticity.- Viscous Diffusion at a Wall.- Subsequent Motion of Wall-generated Vorticity.- Vorticity Increase by Vortex Stretching.- Hill’s Spherical Vortex(refs.2.13,2.14).- Vorticity in Rotating Frames of Reference.- Atmospheric Fluid Motion and Vorticity.- Dissipation Function, Vorticity Function and Curvature Function(eddy or vortex motion).- Generation of Vorticity in a Viscous Boundary Layer – Precursor to Turbulence.- Typical Vorticity Distributions.- Vorticity in a Compressible Fluid.- Vorticity and the Electromagnetic Analogy.- Quantization of Circulation and Vorticity.- Quantized Vortices in He II.- The NanoBoundary Layer and NanoVortex Core.- Introduction.- Kinetic Theory of the Vortex Core Gas.- Effect of Local (Macroscopic) Rotation of the Gas.- Transport and Optical properties of the Core Gas.- Electric(Barnett) Polarisation in the Boundary Layer.- Electric Charge –Dipole Interaction.- Concluding Remarks.- Nanoduct Fluid Flow.- Introduction.- Kinetic Theory for Fluid Transport Parameters.- Molecular Dynamics and Monte Carlo Simulation(MCS).- Diffusion in Nanochannels.- Electrokinetics in Nanochannels.- Slip Flow in Nanoducts.- Water Flow in Nanochannels.- Molecular Spin in Nanoduct Fluid Flow.- Nanoscale Forces.- Theoretical Analyses.- Overview of Phenomena Occurring at the Nanoscale.- Surface-energy-related Phenomena.- Shear-related Phenomena.- Electric Double-Layer-related Phenomena.- Entropy-related Phenomena.- Molecular-structure-related Phenomena.- The Field of Nanofluidics.