Some Isoperimetric Inequalities in Electrochemistry and Hele Shaw Flows

Isoperimetric inequalities are applied to a moving-boundaryproblem for doubly-connected domains. This problem occurs forexample in electrochemistry, in which case the domains in questionare the electrolyte of an electrolytic cell. The two electrodessurrounding the electrolyte are assumed to grow or dissolve,at different rates in general, by electrochemical reaction.We obtain optimal estimates showing, for example, that the leastchange in volume of each electrode always occurs in sphericalsymmetry.     

Scale-up of the vortex wave microfilter using the power ratio

The vortex wave technique enhances microfiltration performance by combining the mixing characteristics of oscillatory flow and flow deflectors. The ability to reproduce these highly convective mixing patterns on a scale applicable to pilot plant studies has been investigated in this paper. The scale-up of a single channel membrane unit (18200 mm²) to a double channel element (106080 mm²) has been investigated in terms of geometric, kinematic and dynamic similarity. A non-dimensional approach has been adopted, wherever possible, to characterise the performance of both microfilters. The kinetics of each system are dominated by the Reynolds number, and the dynamics have been classified in terms of a new non-dimensional number — the power ratio. The power ratio has been employed to predict accurately the performance of the scaled-up filter, and also to provide an indication of transitional flow patterns. The inhibition of a gel-layer within the vortex wave modules has been demonstrated by the non-linear relationship between flux and transmembrane pressure. Experimental results and a theory which includes the effects of osmotic-pressure show that the flux is directly proportional to the cube root of the transmembrane pressure. Non-dimensional analysis of the experimental results indicates a similar trend, whereby the flux is directly proportional to the cube root of power dissipation under two-dimensional, laminar flow conditions.     

Investigations of gas and particle dynamics in first generation needle-free drug delivery devices

Abstract. Transdermal powdered drug delivery involves the propulsion of solid drug particles into the skin by means of high-speed gas-particle flow. The fluid dynamics of this technology have been investigated in devices consisting of a convergent-divergent nozzle located downstream of a bursting membrane, which serves both to initiate gas flow (functioning as the diaphragm of a shock tube) and to retain the drug particles before actuation. Pressure surveys of flow in devices with contoured nozzles of relatively low exit-to-throat area ratio and a conical nozzle of higher area ratio have indicated a starting process of approximately 200 s typical duration, followed by a quasi-steady supersonic flow. The velocity of drug particles exiting the contoured nozzles was measured at up to 1050 m/s, indicating that particle acceleration took place primarily in the quasi-steady flow. In the conical nozzle, which had larger exit area ratio, the quasi-steady nozzle flow was found to be overexpanded, resulting in a shock system within the nozzle. Particles were typically delivered by these nozzles at 400 m/s, suggesting that the starting process and the quasi-steady shock processed flow are both responsible for acceleration of the particle payload. The larger exit area of the conical nozzle tested enables drug delivery over a larger target disc, which may be advantageous. Received 12 March 2000 / Accepted 8 June 2000