Abstract
A new dynamic equation of aerosol in air is derived, using a model-in-model, by equilibrium of buoyancy, gravity and pressure, together with conservation laws of mass, momentum and energy via Reynolds transport theorem and supplemented by corresponding scientific laws for related properties of air and aerosols. This new dynamic equation of aerosol in air is a set of non-linear partial differential equations involved six unknown functions of mass densities, pressure, air and aerosol speeds and temperature. It has features: 1, it belongs to certain type; 2, it emphases the effect of buoyancy in equilibrium and potential energy, and the Archimedes principle of buoyancy is firstly extended to lateral directions based on logical deduction, the phenomenon of stirring a glass of oil-water mixture and the recorded of Hurricane Isabel (2003) from space station. The later shows the evidence of existence of lateral buoyancy; 3, the mass densities of air and aerosol of a point in our model are varied in different directions due to traction and are treated as vectors, and they have been used in the calculation of lateral buoyancy.
Highlights
IntroductionVarious types of aerosol, such as dust, fume, smoke, cloud, fog, haze, air pollutants, PM 2.5, PM 10, etc., have various physical and chemical properties related to corresponding scientific laws
An aerosol includes solid particles or liquid droplets in suspending air
A new dynamic equation of aerosol in air is derived, using a model-in-model, by equilibrium of buoyancy, gravity and pressure, together with conservation laws of mass, momentum and energy via Reynolds transport theorem and supplemented by corresponding scientific laws for related properties of air and aerosols. This new dynamic equation of aerosol in air is a set of non-linear partial differential equations involved six unknown functions of mass densities, pressure, air and aerosol speeds and temperature. It has features: 1, it belongs to certain type; 2, it emphases the effect of buoyancy in equilibrium and potential energy, and the Archimedes principle of buoyancy is firstly extended to lateral directions based on logical deduction, the phenomenon of stirring a glass of oil-water mixture and the recorded of Hurricane Isabel (2003) from space station
Summary
Various types of aerosol, such as dust, fume, smoke, cloud, fog, haze, air pollutants, PM 2.5, PM 10, etc., have various physical and chemical properties related to corresponding scientific laws Their motion in air can be described by a general governing dynamic equation of aerosol in air with certain type The above governing dynamic equation has at least three lacks in perfect: it involves random factor, e.g., the Brownian motion assumption, and leads to an uncertain type results; it neglects buoyancy effect as usually the calculation of terminal velocity of a particle in a fluid [4]; it complicates the effect of distribution of number of particles, size, and shapes on suspension motion. A model-in-model is used to set up a new dynamic equation for the two-phased motion problem of aerosol in air
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