Particle-pressure induced transient changes in oscillated particle-fluid systems

From the general flow equations for a particle-fluid mixture both the oscillatory behaviour and the secular (that is, quasi-static) process can be derived. The two are coupled via a mean net stress component, called the particle pressure, in a rapidly agitated medium. In a septum-vibrated dead-end filter the particle pressure is generated near the septum. The secular changes that take place as the vibration is increased can be gathered in a set of coupled equations. The effects that are observed in permeation experiments are then reproduced from the theory. These include a critical point at which the flow rate rapidly increases. The rheology of a packed bed that is agitated by a cyclic strain is then investigated and its non-linear character is elucidated. The non-linear clogged septum rheology is also investigated, so as to obtain an impression of the stress dependence of the clogged septum permeability. Combining rheology and incremental secular equations of motion enable an understanding of the features of the flow rate vs. oscillation amplitude. Rough estimates of the various parameters show that the effects the theory describes are corroborated by experiments. Of special interest is the critical point, at which the flow rate through the filter increases rapidly with incremental oscillation amplitude.