Diffusion

Abstract: A derivation is given of the effect of a time‐dependent magnetic field gradient on the spin‐echo experiment, particularly in the presence of spin diffusion. There are several reasons for preferring certain kinds of time‐dependent magnetic field gradients to the more usual steady gradient. If the gradient is reduced during the rf pulses, H1 need not be particularly large; if the gradient is small at the time of the echo, the echo will be broad and its amplitude easy to measure. Both of these relaxations of restrictions on the measurement of diffusion coefficients by the spin‐echo technique serve to extend its range of applicability. Furthermore, a pulsed gradient can be recommended when it is critical to define the precise time period over which diffusion is being measured.The theoretical expression derived has been verified experimentally for several choices of time dependent magnetic field gradient. An apparatus is described suitable for the production of pulsed gradients with amplitudes as large as 100 ...

Abstract: Since to form a hole the size of a molecule in a liquid requires almost the same increase in free energy as to vaporize a molecule, the concentration of vapor above the liquid is a measure of such ``molecular'' holes in the liquid. This provides an explanation of the law of rectilinear diameters of Cailletet and Mathias. The theory of reaction rates yields an equation for absolute viscosity applicable to cases involving activation energies where the usual theory of energy transfer does not apply. This equation reduces to a number of the successful empirical equations under the appropriate limiting conditions. The increase of viscosity with shearing stress is explained. The same theory yields an equation for the diffusion coefficient which when combined with the viscosity and applied to the results of Orr and Butler for the diffusion of heavy into light water gives a satisfactory and suggestive interpretation. The usual theories for diffusion coefficients and absolute electrical conductance should be replaced by those developed here when ion and solvent molecule are of about the same size.

Abstract: Foreword Introduction 1. Vectors and tensors 2. Properties of a gas: definitions and theorems 3. The equations of Boltzmann and Maxwell 4. Boltzmann's H-theorem and the Maxwellian velocity-distribution 5. The free path, the collision-frequency and persistence of velocities 6. Elementary theories of the transport phenomena 7. The non-uniform state for a simple gas 8. The non-uniform state for a binary gas-mixture 9. Viscosity, thermal conduction, and diffusion: general expressions 10. Viscosity, thermal conduction, and diffusion: theoretical formulae for special molecular models 11. Molecules with internal energy 12 Viscosity: comparison of theory with experiment 13. Thermal conductivity: comparison of theory with experiment 14. Diffusion: comparison of theory with experiment 15. The third approximation to the velocity-distribution function 16. Dense gases 17. Quantum theory and the transport phenomena 18. Multiple gas mixtures 19. Electromagnetic phenomena in ionized gases Historical summary Name index Subject index References to numerical data for particular gases (simple and mixed).