Time Evolution Of Number Density Research Articles

Ice Multiplication by Fragmentation during Quasi-Spherical Freezing of Raindrops: A Theoretical Investigation

AbstractIce multiplication by fragmentation during collision–freezing of supercooled rain or drizzle is investigated. A zero-dimensional dynamical system describes the time evolution of number densities of supercooled drops and ice crystals in a mixed-phase cloud. The characteristic time scale for this collision–freezing ice fragmentation is controlled by the collision efficiency, the number of ice fragments per freezing event, and the available number concentration of supercooled drops. The rate of the process is proportional to the number of supercooled drops available. Thus, ice may multiply extensively, even when the fragmentation number per freezing event is relatively small. The ratio of total numbers of ice particles to those from the first ice, namely, the “ice-enhancement factor,” is controlled both by the number of fragments per freezing event and by the available number concentration of supercooled drops in a similar manner. Especially, when ice fragmentation by freezing of supercooled drops is considered in isolation, the number of originally existing supercooled drops multiplied by the fragmentation number per freezing event yields the eventual number of ice crystals. When supercooled drops are continuously generated by coalescence, ice crystals from freezing fragmentation also continuously increase asymptotically at a rate equal to the generation rate of supercooled drops multiplied by the fragmentation number per freezing event. All these results are expressed by simple analytical forms, thanks to the simplicity of the theoretical model. These parameters can practically be used as a means for characterizing observed mixed-phase clouds.

Zero-dimensional numerical simulation of dry reforming of methane in atmospheric pressure non-equilibrium plasma

Recently, atmospheric non-equilibrium plasma has been proposed as a potential and novel type of “reaction carrier” for the activation and conversion of greenhouse gases (methane and carbon dioxide) into value-added chemicals, due to its unique non-equilibrium characteristics. In this paper, a zero-dimensional plasma chemical reaction kinetic model in CH<sub>4</sub>/CO<sub>2</sub> gas mixture is constructed, with an emphasis on reaction mechanism for plasma dry reforming of methane to syngas and oxygenates. Especially, the effect of the CH<sub>4</sub> molar fraction (5%–95%) on plasma dry reforming of methane is investigated. First, the time evolution of electron temperature and density with initial methane content is presented, and the results show that both the electron temperature and electron density vary periodically with the applied triangular power density pulse, and the higher initial methane content in gas mixture is favored for a larger electron temperature and density. Subsequently, the time evolution of number densities of free radicals, ions and molecules at different CH<sub>4</sub>/CO<sub>2</sub> molar fraction are given. The higher the initial methane content, the greater the number densities of H, H<sup>–</sup>, H<sub>2</sub>, and CH<sub>3</sub>, leading to insufficient oxygen atoms to participate in the reaction for oxygenates synthesis. The conversions of inlet gases, the selectivities of syngas and important oxygenates are also calculated. The conversion rate of carbon dioxide increases with the increasing methane content, but the conversion rate of methane is insensitive to the variation of methane content. As methane mole fraction is increased from 5% to 95%, the selectivities of important oxygenates (CH<sub>3</sub>OH and CH<sub>2</sub>O) are relatively low (<5%), and the selectivity of H<sub>2</sub> gradually increases from 13.0% to 24.6%, while the selectivity of CO significantly decreases from 58.9% to 9.7%. Moreover, the dominant reaction pathways governing production and destruction of H<sub>2</sub>, CO, CH<sub>2</sub>O and CH<sub>3</sub>OH are determined, and CH<sub>3</sub> and OH radicals are found to be the key intermediate for the production of valuable oxygenates. Finally, a schematic overview of the transformation relationship between dominant plasma species is summarized and shown to clearly reveal intrinsic reaction mechanism of dry reforming of methane in atmospheric non-equilibrium plasma.

Time variation of particle and antiparticle asymmetry in an expanding universe

Particle number violating interactions wash out the primordial asymmetry of particle number density generated by some interaction satisfying Sakharov conditions for baryogenesis. In this paper, we study how the primordial asymmetry evolves in time under the presence of particle number violating interactions and in the environment of expanding universe. We introduce a complex scalar model with particle number violating mass terms and calculate the time evolution of the particle number density with non-equilibrium quantum field theory. We show how the time evolution of the number density depends on parameters, including the chemical potential related with the particle number, temperature, size of the particle number violating mass terms, and the expansion rate of the universe. Depending upon whether the chemical potential is larger or smaller than the rest mass of the scalar particle, behaviors of the number density are very different to each other. When the chemical potential is smaller than the mass, the interference among the contribution of oscillators with various momenta reduces the number density in addition to the dilution due to the expansion of universe. In opposite case, the oscillation of the particle number density lasts for a long time and the cancellation due to the interference does not occur.

Condensation on Surface Energy Gradient Shifts Drop Size Distribution toward Small Drops

During dropwise condensation from vapor onto a cooled surface, distributions of drops evolve by nucleation, growth, and coalescence. Drop surface coverage dictates the heat transfer characteristics and depends on both drop size and number of drops present on the surface at any given time. Thus, manipulating drop distributions is crucial to maximizing heat transfer. On earth, manipulation is achieved with gravity. However, in applications with small length scales or in low gravity environments, other methods of removal, such as a surface energy gradient, are required. This study examines how chemical modification of a cooled surface affects drop growth and coalescence, which in turn influences how a population of drops evolves. Steam is condensed onto a horizontally oriented surface that has been treated by silanization to deliver either a spatially uniform contact angle (hydrophilic, hydrophobic) or a continuous radial gradient of contact angles (hydrophobic to hydrophilic). The time evolution of number density and associated drop size distributions are measured. For a uniform surface, the shape of the drop size distribution is unique and can be used to identify the progress of condensation. In contrast, the drop size distribution for a gradient surface, relative to a uniform surface, shifts toward a population of small drops. The frequent sweeping of drops truncates maturation of the first generation of large drops and locks the distribution shape at the initial distribution. The absence of a shape change indicates that dropwise condensation has reached a steady state. Previous reports of heat transfer enhancement on chemical gradient surfaces can be explained by this shift toward smaller drops, from which the high heat transfer coefficients in dropwise condensation are attributed to. Terrestrial applications using gravity as the primary removal mechanism also stand to benefit from inclusion of gradient surfaces because the critical threshold size required for drop movement is reduced.

Nonequilibrium dynamics of coupled quantum systems

The nonequilibrium dynamics of coupled quantum oscillators subject to different time-dependent quenches are analyzed in the context of the Liouville–von Neumann approach. We consider models of quantum oscillators in interaction that are exactly soluble in the cases of both sudden and smooth quenches. The time evolution of number densities, the final equilibration temperature and equilibration time for the problem of a quantum oscillator coupled to an infinity set of other oscillators (a bath) are explicitly worked out.