Simple Mixing Channels

In addition to the CFD results, estimates of the mixing length based on the Fourier number 

When the Reynolds number is increased, a regime with a flow pattern of broken symmetry is reached, as found by Bothe et al. [54]. At a Reynolds number of about 140 the symmetric flow pattern becomes unstable and an engulfment flow with an increased area of material interface between the two fluids is found. This is illustrated in Fig. 3.13 that shows maps of the computed concentration field over cross sections of the mixing channel for Reynolds numbers ranging from 119 (a) to 239 (f). The increase in material interface is related to an increase in mixing efficiency, thus making a mixing tee more efficient than predicted by simple 

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Version (b) has a four-channel flow guidance that encompasses two mixing tees in two simple mixing tees (Figure 4.5) [8]. An example of this function is the flow guidance for the Michael addition. In a first step, the base and 1,3-dicarbonyl compound streams merge. The enolate stream thus formed is then mixed with the Michael acceptor. Microporous silica frits are set into the channels to minimize... 

This micro mixer, named electrohydrodynamic (EHD) microfluidic mixer, comprises a simple T-channel structure (see Figure 1.5) [91]. After passing the T-junction, a bi-laminated stream is realized. Following a downstream zone for such flow establishment, a channel zone with several electrode wires on both sides of the channel is located. In this way, an electric field perpendicular to the fluid interface is generated. Thereafter, an electrode-free zone of the channel is situated for completion of the mixing initiated. 

The channel structure of the mixer is a simple cross, i.e. four channels which all merge at one junction [71]. A cross was preferred over a T-channel mixer since two interfaces instead of only one are initially created when the fluids are contacted. The top channel feeds one fluid, while the other fluid is injected via the left and right channels. The last, bottom channel functions as mixing and outlet zone. Squares, much smaller than the channel width, are positioned at the walls of this mixing channel and function as static mixing elements. The squares are positioned on alternate sides of the channels and at a distance corresponding to multiple square widths. 

For better visualization, the end of the units is marked by a black line [27]. From there, a simple unstructured channel follows until the outlet connector. The combined length of structured and unstructured sections is always kept the same. Dotted lines show the respective increase in mixing length for the mixer devices from left to right. 

Chaotic mixing based on viscoelastic flow instability in rather simple microfluidic channel geometries was successfully demonstrated. These viscoelastic micromixers bypass the limitation of low Reynolds number in microfluidic flows and could potentially be implemented in a Lab-on-a-Chip platform with minimum requirements for design and fabrication. However, this type of micromixer is yet to be optimized. 

Numerous fabrication techniques have been used for making micromixers. In the past few years, there have been two obvious developments in micromixer fabrication the substrate was changed from silicon to polymers and the structures were changed from simple planar structure to complex 3D structure. Most of the early micromixers were fabricated in silicon. The mixing channels were either wet etched with KOH [16, 35, 42, 52, 53, 66] or dry etched using DRIB (deep reactive ion etching) [23, 26, 31, 37, 45, 54, 59, 96]. Anodically bonded glass on top of the channel... 

The equations above are based on the assumption that the flow is laminar, which will generally be the case for polymer melts due to their high viscosity. If, however, turbulent flow takes place, then even in a simple circular channel efficient mixing can occur. When two fluids of equal density are introduced side by side into an empty pipe with diameter D, then the degree of mixing after length L can be expressed as [260] ... 

Alloxenic solutions are wide-spread in clathrate chemistry. These are the natural gas hydrates, mixed hydroquinone clathrates and mixed channel inclusion compounds. The conditions of their formation seem to be sufficiently simple and are in fact the same as those of the formation of the individual clathrate compound. 

Qian and Bau [144] have analyzed such electroosmotic flow cells with embedded electrodes on the basis of the Stokes equation with Helmholtz-Smoluchowski boimdary conditions on the channel walls. They considered electrode arrays with a certain periodicity, i.e. after k electrodes the imposed pattern of electric potentials repeats itself An analytic solution of the Stokes equation was obtained in the form of a Eourier series. Specifically, they analyzed the electroosmotic flow patterns with regard to mixing applications. A simple recirculating flow pattern such as the one... 

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