Liquid Mixing in Small Volumes and Microfluidics

Two consecutive processes dominate the mixing of liquids: fusion of the liquid boundaries and diffusion of the components. Although both processes are similar in bulk fluid and microfluidics, their outcome is significantly different; unexpected mixing results in microfluidics were reported. Two liquid streams can flow alongside in a tube a few micrometers wide over a period of time without mixing, almost as if they were separated by glass (Knight 2002). tte fusion step is not only the first step, but is also the rate-limiting step in the mixing process. Macroscopically stirring can speed up fusion, as turbulence increases the interfacial area between the liquids, but in small channels it is almost impossible to produce such a turbulent flow. Mechanical forces as in shaking or thermal forces inducing convective flows are less effective and more difficult to apply in very small volumes. A recent approach to accelerate mixing of small volumes is electrosmosis, where components are displaced by electric fields. For the aim of protein nanocrystallization mixing of protein droplets on a small scale can best be achieved during the dispensing phase. For example, in the Microdrop robot system droplets are shot from the nanodispenser with a linear velocity of 3-5 m/s and they dive in the bulk solution without splashing as there is not enough energy for splashes to be formed - droplets with a diameter less than 100 ^m have more surface energy than kinetic energy at the speeds generated (see

When two droplets meet on a solid surface they usually fuse if the liquids involved are miscible. Little is known about what happens next: the subsequent diffusion of dissolved components (e.g., proteins) in high concentrations within the fused nanovolumes. Techniques like dynamic light scattering and fluorescence correlation spectroscopy probe diffusion in (very) small volumes but are always conducted in a total volume of a few microliters, far away from interfaces (Nijman et al. 2001; Schmauder et al. 2002). Although usually homogeneous mixing is aimed for, the lack of homogeneous mixing can sometimes also be an advantage as demonstrated in free-interface diffusion methods used in protein crystallization without evaporation (Hansen et al. 2002; Zheng et al. 2004).

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