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.
Particle size correlations in brownian agglomeration. Closure hypotheses for product density equations
Abstract In a previous paper the authors have demonstrated inaccuracies in the population balance equation, as applied to agglomerating particulate systems, which arise due to an inherent assumption regarding the statistical independence of particle pairs. When this assumption is removed, an intractable hierarchy of product density equations results. In this paper a closure hypothesis for the product density equations is proposed, evaluated against alternatives, and used in an approximate solution to the product density equations. The closure hypothesis is shown to improve significantly upon the population balance equation which is itself the result of the simplest closure.
The potential vorticity flux through the Yucatan Channel and the Loop Current in the Gulf of Mexico
Two‐year‐long time series of current and density structure measurements across the Yucatan Channel's main section allow the calculation of the time‐dependent potential vorticity flux between the Gulf of Mexico and the Caribbean Sea, which is characterized by alternating periods of positive (cyclonic) and negative (anti‐cyclonic) vorticity influx. Periods of negative cumulative vorticity influx are related to the Loop Current extending into the Gulf of Mexico, whereas periods of positive cumulative vorticity influx relate to a Loop Current retraction, sometimes coincident with the shedding of an anti‐cyclonic eddy.