Flows mixing-diffusion microscale

A passive micromixer is one of the microfluidic devices. It utilizes no energy input except the mechanism (pressure head) used to drive the fluid flow at a constant rate. Due to the dominating laminar flow on the microscale, mixing in passive micromixers relies mainly on chaotic advection realized by manipulating the laminar flow in microchannels or molecular diffusion with increasing the contact surface and time between the different fluid flows. 

In microscale channels, the viscous forces dominate the inertial effect resulting in a low Reynolds numbers. Hence, laminar flow behavior is dominant and mixing occurs via diffusion. However, in a liquid-liquid system, the interfacial forces acting on the interface add complexity to the laminar flow as the relationship between interfacial forces and other forces of inertia and viscous results in a variety of interface and flow patterns. Gunther and Jensen [202] illustrated this relationship as a function of the channel dimension and velocity as shown in Figure 4.12. The most regularly shaped flow pattern is achieved when interfacial forces dominate over inertia and viscous forces at low Reynolds numbers, as represented in Figure 4.12 by the area below the yellow plane [202,203]. 

In this work, heat and fluid flow in some common micro geometries is analyzed analytically. At first, forced convection is examined for three different geometries microtube, microchannel between two parallel plates and microannulus between two concentric cylinders. Constant wall heat flux boundary condition is assumed. Then mixed convection in a vertical parallel-plate microchannel with symmetric wall heat fluxes is investigated. Steady and laminar internal flow of a Newtonian is analyzed. Steady, laminar flow having constant properties (i.e. the thermal conductivity and the thermal diffusivity of the fluid are considered to be independent of temperature) is considered. The axial heat conduction in the fluid and in the wall is assumed to be negligible. In this study, the usual continuum approach is coupled with the two main characteristics of the microscale phenomena, the velocity slip and the temperature jump. 

The use of microscale reactors is not confined to single-phase systems. Both striated and droplet flows of two-phase liquid mixtures have been studied, as have suspensions of solid particles. It seems that almost any chemistry can be used at the microscale. Effectiveness factors in heterogeneous catalysis will be nearly 1.0 since diffusion distances are so small. As pointed out below, rapid molecular diffusion gives nearly instantaneous cross-channel mixing and may cause significant axial mixing. 

Microscale In channel structures with dimensions <200 mm (microfiuidic devices), fluids (liquids) follow predictable laminar paths characteristic of low Reynolds numbers. This allows two or more layers of fluid to flow next to each other without any mixing other than by molecular or particulate diffusion. As a result of this property, it is possible to have multiple inputs into a single chaimel and have them flow side by side in an orderly fashion (Fig. 2b). Since the channel dimensions in many cases are comparable to the size of single cells, we can use laminar flow patterning to expose subceUular regions to specific signals. Also it is possible to allow different regions of the same cell to different conditions. 

Due to the small characteristic dimension, the flow in microchemical systems is laminar. As a result, mixing relies only on molecular diffusion instead of the more efficient turbulence that large-scale systems typically exhibit. At the same time, the diffusion time scale is much shorter due to the small size of a microscale device. However, structural elements that play the role of static micromixers may be necessary to spread fast flows, enhance fluid-solid contact, increase mixing of incoming gases, etc. One such example is the post-micromixer discussed in Ref. [5]. 

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