Straight microchannels

For laminar flow in channels of rectangular cross section, the velocity profile can be determined analytically. For this purpose, incompressible flow is assumed. 

The flow profile can be expressed in the form of a series expansion (see [23] and references therein) that, however, is not always useful for practical applications where often only a fair approximation of the velocity field over the channel cross section is needed. Purday [24] suggested an approximate solution of the form 

Depending on the aspect ratio of the channel, values between 0.01 and 0.1 are found for the nondimensional entrance length [23]. From Eq. (3.6) it can be deduced - with Liy being Re independent - that Lhy increases linearly with the hydraulic diameter and the Reynolds number. 

A number of authors have considered channel cross sections other than rectangular [25-27]. In general, an analytical solution of the Navier-Stokes and the enthalpy equations in such channel geometries would be quite involved due to the implementation of the wall boundary condition. For this reason, usually numerical methods are employed to study laminar flow and heat transfer in channels with arbitrary cross-sectional geometry. 

Figu re 3.1 Different channel shapes for which flow distributions have been computed, a zigzag (upper left), a sinusoidally curved (upper right) and a converging-diverging channel (bottom). 

If the locally produced or consumed heat by chemical reaction is different from the locally evacuated or supplied heat, isothermal operation is impossible and axial temperature profiles will develop leading to locally higher or lower temperatures compared to the cooling/heating medium. So-called hots pots or cold spots will be observed. As mentioned above, the developed temperature profile in chemical reactors is of crucial importance for the obtainable product selectivity, yield, and productivity. Therefore, high heat transfer performances are important to keep the temperature within a defined narrow range. 

In microstructured tubular reactors, the heat is generally evacuated or supphed by maintaining constant temperature of the cooling medium (T ). The heat transfer performance of the system depends on the overall heat transfer coefficient U) and exchange surface (A). 

Within the entrance zone the heat transfer coefficient diminishes, reaching an asymptotic value. The dependency for constant wall temperature can be described in terms of the Nusselt numbers [8] 

For laminar flow and completely developed radial velocity and temperature profiles the local heat transfer is constant and the mean Nusselt number reaches an asymptotic value, given by Nu. The same value is obtained for the asymptotic Sherwood number, Sh characterizing the mean mass transfer between the fluid and the channel wall (see Chapter 6). 

The asymptotic Nusselt and Sherwood numbers depend on the geometry of the channel as summarized in Table 5.1. 

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We prepared microchannel reactor employing stainless steel sheet 400tan thick patterned microchannel by a wet chemical etching. The microchannel shape and dimension were decided by computer simulation of flow distribution and pressure drop of the reactants in the microchaimel sheet. Two different types of patterned plates with mirror image were prepared [5]. The plate has 21 straight microchannels which are 550/an wide, 230/an deep and 34mi long as revealed in Fig. 1(b). 

Campo, A. Low Reynolds number flow inside straight microchannels with irregular cross sections, J. Heat Mass Transfer 36, (2000) 187-193. 

Boundary-Element Method in Microfluidics, Fig. 2 Schematic drawing of the computational domain (a) straight microchannel (b) microchannel with hurdle... 

Further Simplification for Combined Pressure-Driven and Electroosmotic Flow in Straight Microchannels... 

As a straight microchannel constitutes the basic segment in microfluidic structures, several examples of the combined pressure-driven and electroosmosis-driven flow in straight microchannels are demcmstrated in this entry. Usually a microchannel length dimension is much larger than its lateral dimensions, and the flow in such a channel can be considered as unidirectional this implies that the flow can be modeled as a fully developed flow, namely, du/dx = 0, V = 0, and w = 0, in terms of... 

Liquid Flow in a Straight MicroChannel Under Applied Pressure and Electrical Potential Difference... 

Electroosmotic Flow in a Straight MicroChannel with Two Closed Ends... 

If we consider a steady-state, laminar, constant property (i.e., dynamic viscosity p, specific heat Cp, thermal conductivity k) flow in a straight microchannel of constant cross-sectional area (see Fig. 1), in the absence of free convection, mass diffusion, and change of phase, the governing equations can be written as follows ... 

Convective Heat Transfer in Microchannels, Fig. 1 Sketch of a straight microchannel with constant crosssection and Cartesian coordinate system... 

So far we have discussed the droplet dynamics in single straight microchannels only. Droplet dynamics in other microchannel geometries, on the other hand, may be associated with certain distinctive features that are not usually apparent with flows in single straight microchannels. As an example, one may cite the case of droplet motion in a microchannel geometry that is characterized with a sudden contraction in the cross-sectional... 

To simulate the motion of the heterogeneous particle in a straight microchannel (Fig. 3), a set... 

Consider a heterogeneous particle suspended in a straight microchannel (Fig. 3) while the inlet and the outlet are defined as open boundaries. The computational domain is fully covered by unstructured three-dimensional tetra meshes to increase the accuracy of the simulation. The motion of this heterogeneous particle in the microchannel can be simulated using the equations, initial conditions, and boundary conditions listed in above section. 

Induced-Charge Electrokinetic Motion of Particle in a MicroChannel, Fig. 4 3D streamlines in a straight microchannel with a (a) nonconducting particle and (b) heterogeneous particle suspended in the middle of this microchannel. Vortices are induced around the conducting hemisphere of the heterogeneous particle. 

Figure 1 shows a two-dimensional straight microchannel which is charged homogeneously... 

Although the electroosmotic flow in smooth straight microchannels has been much studied, the results are some way from realistic applications because there are much roughness and cavitations on the wall surfaces instead of ideal smoothness. Sometimes the roughness or cavitation could be used for some special function in microchannel flows. To the author s knowledge, there is only a small amount of published literature which presents an analysis of the EOF in rough channels [1]. This section will introduce... 

Presstu e-driven flows in straight microchannels with uniform cross section are purely shearing flows (useful information about molecular conformation (through [ 7]) and shear flow behavior, they cannot yield information about a liquid s response to any flow... 

For a laminar flow through a straight microchannel, the fluid particles move in definite paths called streamlines and there are no components of fluid velocity normal to the duct axis. The projection of Eq. 6 along the axial direction (z) gives... 

Let us consider a liquid flowing through a straight microchannel having an axially unchanging and uniform cross section with an area equal to Q and the perimeter equal to F. It is possible to define... 

Shi et al. demonstrated another optofluidic microlens utilizing active pressure control of an air-liquid interface [19]. The working mechanism of this microlens is shown in Figure 7.18. DI water was introduced into a straight microchannel. The microchannel made a T-junction with an air reservoir. As the water flowed past the T-junction, air was trapped in the reservoir and a movable air-water interface formed at the T-junction, with the air bending into the water due to the air-liquid contact angle and the hydrophobic-hydrophilic interaction between the surface and the liquid. The air-water interface acted as a divergent lens. 

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