The method of moments (MOM) may be used to determine the evolution of the lower-order moments of an unknown aerosol distribution. Previous applications of the method have been limited by the requirement that the equations governing the evolution of the lower-order moments be in closed form. Here a new approach, the quadrature method of moments (QMOM), is described. The dynamical equations for moment evolution are replaced by a quadrature-based approximate set that satisfies closure under a much broader range of conditions without requiring that the size distribution or growth law maintain any special mathematical form. The conventional MOM is recovered as a special case of the QMOM under those conditions, e.g., free-molecular growth, for which conventional closure is satisfied. The QMOM is illustrated for the growth of sulfuric acid-water aerosols and simulations of diffusion-controlled cloud droplet growth are presented.

https://www.tandfonline.com/doi/pdf/10.1080/02786829708965471

Description of Aerosol Dynamics by the Quadrature Method of Moments

Description of interaction processes in agitated liquid-liquid dispersions

Preface Acknowledgements 1. Introduction 2. Atmospheric structure, composition and thermodynamics 3. The continuity and thermodynamic energy equations 4. The momentum equation in Cartesian and spherical coordinates 5. Vertical-coordinate conversions 6. Numerical solutions to partial differential equations 7. Finite-differencing the equations of atmospheric dynamics 8. Boundary-layer and surface processes 9. Radiative energy transfer 10. Gas-phase species, chemical reactions and reaction rates 11. Urban, free-tropospheric and stratospheric chemistry 12. Methods of solving chemical ordinary differential equations 13. Particle components, size distributions and size structures 14. Aerosol emission and nucleation 15. Coagulation 16. Condensation, evaporation, deposition and sublimation 17. Chemical equilibrium and dissolution processes 18. Cloud thermodynamics and dynamics 19. Irreversible aqueous chemistry 20. Sedimentation, dry deposition and air-sea exchange 21. Model design, application and testing Appendix A. Conversions and constants Appendix B. Tables References Index.

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Fundamentals of atmospheric modeling

Solution of population balance equations using the direct quadrature method of moments

The lithium-ion battery is an ideal candidate for a wide variety of applications due to its high energy/power density and operating voltage. Some limitations of existing lithium-ion battery technology include underutilization, stress-induced material damage, capacity fade, and the potential for thermal runaway. This paper reviews efforts in the modeling and simulation of lithium-ion batteries and their use in the design of better batteries. Likely future directions in battery modeling and design including promising research opportunities are outlined.

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H.M. Hulburt

Papers

Some problems in particle technology: A statistical mechanical formulation