Chaotic mixing efficiency in different geometries of Hele-Shaw cells

Numerical modeling of DNA-chip hybridization with chaotic advection

“…This explains why d h plays no role in the result, in accordance with the idea that the detailed structure of the interaction potential plays little role in the particle dynamics. This also explains why the gain in hybridization velocity when comparing static and dynamical hybridizations is lower than the gain found in mixing time with our 2D model (mixing about 1000 times more rapid in the dynamical case, 14 while we have a factor 100 "only" here): although the horizontal dispersion is 1000 times more rapid at mid-height, the fresh fluid is brought to the bottom by molecular diffusion only.…”

“…In this study, a % 0:7, but we stress the fact that this mixing protocol is quite robust regarding variations of a (the quality of mixing is basically unchanged if a is divided or multiplied by a factor two 14 ). Therefore, in an experiment where the size of the chip S, the height of the chamber h, and maybe the flow-rate q imposed by the pump are given, it is always possible to adapt the period of the flow-field T so as to obtain an acceptable a; note, however, that all time-scales (including the total time involved for the experiment) will be changed in the same proportions as T. Finally, we remind that a chemical reaction is involved in the end: it is, therefore, very important not to dilute too much the biological material and to keep the total volume (including that of external elements such as pipes and pumps) as small as experimentally possible.…”

“…In order to guide experimentalists on how to rely our own parameters with different experimental conditions (e.g., flow speed and chip dimensions), we remind that, as explained in a previous paper, 14 the mixing problem is unchanged if the non-dimensional pulse volume…”

“…22 We previously used such a 2D-model in order to decide between different protocols and chamber geometries. 14 However, such a 2D model where the depth-dependence of the velocity field is ignored cannot be used for our purpose: in the Hele-Shaw flow, the vertical profile is parabolic, so that the velocity vanishes on the top of the cell, but also (and more annoyingly) on the bottom where the chip is placed. This means that a target located near the bottom of the hybridization chamber will move much slower than one moving at half-depth.…”

An experimental study on thermal mixing in a square body inserted inclined narrow channels

“…In their another study, they tested the effects of type of fluid as using air and water on flow and mixing effectiveness for various temperature differences between the confined opposing jets of different geometries. Beuf et al [5] studied the influence of the geometry of the cell on mixing efficiency using three different geometries as circle, square and rectangle. They indicated that the flows in Hele-Shaw cells are generally laminar and it can be in a first approximation considered as quasi-two dimensional.…”