Current methods for characterising mixing and flow in microchannels

This article reviews existing methods for the characterisation of mixing and flow in microchannels, micromixers and microreactors. In particular, it analyses the current experimental techniques and methods available for characterising mixing and the associated phenomena in single and multiphase flow. The review shows that the majority of the experimental techniques used for characterising mixing and two-phase flow in microchannels employ optical methods, which require optical access to the flow, or off-line measurements. Indeed visual measurements are very important for the fundamental understanding of the physics of these flows and the rapid advances in optical measurement techniques, like confocal scanning laser microscopy and high resolution stereo micro particle image velocimetry, are now making full field data retrieval possible. However, integration of microchannel devices in industrial processes will require on-line measurements for process control that do not necessarily rely on optical techniques. Developments are being made in the areas of non-intrusive sensors, magnetic resonance techniques, ultrasonic spectroscopy and on-line flow through measurement cells. The advances made in these areas will certainly be of increasing interest in the future as microchannels are more frequently employed in continuous flow equipment for industrial applications

Boundary-crossing identities for diffusions having the time-inversion property

We review and study a one-parameter family of functional transformations, denoted by (S (β)) β∈ℝ, which, in the case β<0, provides a path realization of bridges associated to the family of diffusion processes enjoying the time-inversion property. This family includes Brownian motions, Bessel processes with a positive dimension and their conservative h-transforms. By means of these transformations, we derive an explicit and simple expression which relates the law of the boundary-crossing times for these diffusions over a given function f to those over the image of f by the mapping S (β), for some fixed β∈ℝ. We give some new examples of boundary-crossing problems for the Brownian motion and the family of Bessel processes. We also provide, in the Brownian case, an interpretation of the results obtained by the standard method of images and establish connections between the exact asymptotics for large time of the densities corresponding to various curves of each family