Birth-death processes with an instantaneous reflection barrier

A new structure with the special property that an instantaneous reflection barrier is imposed on the ordinary birth-death processes is considered. An easy-checking criterion for the existence of such Markov processes is first obtained. The uniqueness criterion is then established. In the nonunique case, all the honest processes are explicitly constructed. Ergodicity properties for these processes are investigated. It is proved that honest processes are always ergodic without necessarily imposing any extra conditions. Equilibrium distributions for all these ergodic processes are established. Several examples are provided to illustrate our results.

Modelling dosator filling and discharge of powder

Dosators and other dosing mechanisms operating on generally similar principles are very widely used in the pharmaceutical industry for capsule filling, and for dosing products that are delivered to the customer in powder form such as inhalers. This is a trend that is set to increase. However a significant problem for this technology is being able to predict how accurately and reliably, new drug formulations will be dosed from these machines prior to manufacture. This paper presents a review of the literature relating to powder dosators which considers mathematical models for predicting dosator performance, the effects of the dosator geometry and machine settings on the accuracy of the dose weight. An overview of a model based on classical powder mechanics theory that has been developed at The University of Greenwich is presented. The model uses inputs from a range of powder characterisation tests including, wall friction, bulk density, stress ratio and permeability. To validate the model it is anticipated that it will be trialled for a range of powders alongside a single shot dosator test rig.

Review of models for predicting the discharge rates of bulk particulates from silos and bins

Various models for predicting discharge rates have been developed over the last four decades by many research workers (notably Beverloo [1], Johanson [2], Brown [3], Carleton [4], Crewdson [5], Nedderman [6], Gu [7].). In many cases these models offer comparable approaches to the prediction of discharge rates of bulk particulates from storage equipment when solely gravity is acting to initiate flow (since they invariably consider the use of mass-flow design equipment). The models that have been developed consider a wide range of bulk particulates (coarse, incompressible, fine, cohesive) and most contemporary works have incorporated validation against test programmes. Research currently underway at The Wolfson Centre for Bulk Solids Handling Technology, University of Greenwich, has considered the relative performance of these models with respect to a range of bulk properties and with particular focus upon the flexibility of the models to cater for different geometrical factors for vessels.