Particle size correlations and the effects of limited mixing on agglomerating particulate systems
Abstract Population balance equations for particulate systems are derived based on two basic but tacit assumptions. The first is that a local volume of thorough particle mixing exists over which a more detailed balance equation may be averaged to obtain the population balance equation. The second is that there is a large enough population in the mixing volume that particle correlation effects do not become important. Both the foregoing assumptions are investigated for Brownian agglomeration. The volume of mixing is estimated by scaling arguments. Monte Carlo simulation techniques have been used to show that particle populations in the local mixing volume may be sufficiently small to cause correlation effects implying that the population balance predictions can be in error.
Brownian coagulation in a submicron aerosol: Comparison of experiment with theory☆
Abstract This is an experimental study of the coagulation of a dibutyl phthalate aerosol consisting of a narrow distribution of submicron spheres. The aerosol is in Poiseuille flow. Light-scattering data are obtained early in the life history of the aerosol and again after it has undergone coagulation. The size distribution of the initial aerosol is obtained by inversion of the light-scattering data, and the size distribution is calculated at later times by numerical solution of Smoluchowski's integrodifferential equation adapted to the Poiseuille flow. The new distribution is then used to calculate light-scattering results which are compared with the experimental data. The results are in agreement with Smoluchowski's theory of Brownian coagulation.
Mathematical Time and Physical Time in the Theory Of Relativity
In the Theory of Relativity time is an imaginary quantity that can not be observed; it is a multiplication of a number that indicates duration of material change and number i that is an imaginary number. i on the square is -1. Time i⁄t is a mathematical time that describes the speed and the duration of material change. In the Universe one can observe physical time only as a stream of material change. It is not that change run in physical time, change itself is physical time.. Distinction between imaginary mathematical time and visible physical time opens some new perspectives into interpretation of Theory of Relativity. c