Static intersecting elements

M 72] [M 73] [P 65] The analysis of cross-sectional velocity profiles (water as fluid Re =12) shows that the intersecting structures have intricate gradient fields near the bars of the internals, while the helical device displays entrance and exit effects over more than one-quarter of the flow field (see [155] e.g. for fluid flow through macroscopic helical static elements) [2],... 

Fig. 5 Sequential lamination micromixer (II) (a) Static micromixer, with intersecting channel (top) and helical elements (bottom) (Reproduced from [91] by permission of The Royal Society of Chemistry), (b) Internal structure of crossing manifold micromixer (CMM) (Reproduced from [92] by permission of The Royal Society of Chemistry)...

The real three-phase region (tube) is replaced by a triple line (TL) as the new model element for thermodynamic considerations. In theory, its position results from the extrapolation of the three undisturbed D-faces to their common intersection. Accordingly, the tangent lines on these extrapolated D-faces Dsl and Dlv to the point of intersection lead by definition to the thermodynamic contact angle For reasons of exactness, 0 is introduced for the thermodynamic equilibrium of the three-phase system. The static contact angle 0o in Sect. 4.1 refers to the triple line at rest, i.e., to mechanical equilibrium which is a necessary but insufficient condition for thermodynamic equilibrium. 6 is the first excess quantity for the TL. As the position of any of the three D-faces can be chosen arbitrarily, the position of the TL and the value for 8 are arbitrary too. Fortunately, this vagueness is of no serious consequence as long as the two-phase and three-phase boundaries possess microscopic thicknesses. Note that 0 is... 

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