Experiments in Micro-Channels

Micro-channels on the order of a few microns to a few hundred microns 

In Fig. 5.25 the void fraction a is plotted versus a homogeneous void fraction jS with different symbols used for different ranges of liquid superficial velocity [/ls-The void fraction can be correlated with the homogeneous void fraction  

On the other hand, in the study by Serizawa et al. (2002) the cross-sectional averaged void fraction was correlated with the Armand (1946) correlation as shown in Fig. 5.26. This trend does not contradict the data reported for conventional size channels, but it is different from results obtained by Kawahara et al. (2002). Disagreement between results of void fraction in micro-channels obtained by different investigators was shown by Ide et al. (2006) and will be discussed in the next section. 

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Using the properties of water Li and Cheng (2004) computed from the classical kinetics of nucleation the homogeneous nucleation temperature and the critical nu-cleation radius ra. The values are 7s,b = 303.7 °C and r nt = 3.5 nm. However, the nucleation temperatures of water in heat transfer experiments in micro-channels carried out by Qu and Mudawar (2002), and Hetsroni et al. (2002b, 2003, 2005) were considerably less that the homogeneous nucleation temperature of 7s,b = 303.7 °C. The nucleation temperature of a liquid may be considerably decreased because of the following effects dissolved gas in liquid, existence of corners in a micro-channel, surface roughness. 

Table II. Data on mixing experiments in micro-channels...

Hetsroni G, Mosyak A, Pogrebnyak E, Yarin LP (2005c) Heat transfer in micro-channels comparison of experiments with theory and numerical results. Int J Heat Mass Transfer 48 5580-5601 Hetsroni G, Mosyak A, Segal Z, Pogrebnyak E (2003b) Two-phase flow patterns in parallel microchannels. Int J Multiphase Flow 29 341-360... 

In Spite of the existence of numerous experimental and theoretical investigations, a number of principal problems related to micro-fluid hydrodynamics are not well-studied. There are contradictory data on the drag in micro-channels, transition from laminar to turbulent flow, etc. That leads to difficulties in understanding the essence of this phenomenon and is a basis for questionable discoveries of special microeffects (Duncan and Peterson 1994 Ho and Tai 1998 Plam 2000 Herwig 2000 Herwig and Hausner 2003 Gad-el-Hak 2003). The latter were revealed by comparison of experimental data with predictions of a conventional theory based on the Navier-Stokes equations. The discrepancy between these data was interpreted as a display of new effects of flow in micro-channels. It should be noted that actual conditions of several experiments were often not identical to conditions that were used in the theoretical models. For this reason, the analysis of sources of disparity between the theory and experiment is of significance. 

In experiments related to flow and heat transfer in micro-channels, some parameters, such as the flow rate and channel dimensions are difficult to measure accurately because they are very small. For a single-phase flow in micro-channels the uncertainty of ARe is (Guo and Li 2002,2003)... 

There is a significant scatter between the values of the Poiseuille number in micro-channel flows of fluids with different physical properties. The results presented in Table 3.1 for de-ionized water flow, in smooth micro-channels, are very close to the values predicted by the conventional theory. Significant discrepancy between the theory and experiment was observed in the cases when fluid with unknown physical properties was used (tap water, etc.). If the liquid contains even a very small amount of ions, the electrostatic charges on the solid surface will attract the counter-ions in the liquid to establish an electric field. Fluid-surface interaction can be put forward as an explanation of the Poiseuille number increase by the fluid ionic coupling with the surface (Brutin and Tadrist 2003 Ren et al. 2001 Papautsky et al. 1999). 

Qu et al. (2000) carried out experiments on heat transfer for water flow at 100 < Re < 1,450 in trapezoidal silicon micro-channels, with the hydraulic diameter ranging from 62.3 to 168.9pm. The dimensions are presented in Table 4.5. A numerical analysis was also carried out by solving a conjugate heat transfer problem involving simultaneous determination of the temperature field in both the solid and fluid regions. It was found that the experimentally determined Nusselt number in micro-channels is lower than that predicted by numerical analysis. A roughness-viscosity model was applied to interpret the experimental results. 

The effect of viscous dissipation on temperature change along the micro-channel axis is illustrated in Fig. 4.11, where the dependences dT),/ dx on d that correspond to water and isopropanol flows are presented. One can see that under the conditions corresponding to the Judy et al. (2002) experiments = 74.1 pm, L = 114 mm, Ljd = 1,543), the rise of bulk temperature due to viscous dissipation is small enough. So, at d > 100 pm the temperature gradient is dT),/ dx < 1 K/m. In this case, the difference between outlet and inlet temperature is about 0.1 K. Under conditions that are typical for micro-channels of electronic devices L/d r j 102) this difference is about 0.01 K. The rise of temperature due to viscous dissipation is small enough even at water flow in micro-channels with d 20 pm. Thus, for micro-channels with d = 20 pm and L/d = 10, we have Tout — Tin 0.8 K. 

A variety of studies can be found in the literature for the solution of the convection heat transfer problem in micro-channels. Some of the analytical methods are very powerful, computationally very fast, and provide highly accurate results. Usually, their application is shown only for those channels and thermal boundary conditions for which solutions already exist, such as circular tube and parallel plates for constant heat flux or constant temperature thermal boundary conditions. The majority of experimental investigations are carried out under other thermal boundary conditions (e.g., experiments in rectangular and trapezoidal channels were conducted with heating only the bottom and/or the top of the channel). These experiments should be compared to solutions obtained for a given channel geometry at the same thermal boundary conditions. Results obtained in devices that are built up from a number of parallel micro-channels should account for heat flux and temperature distribution not only due to heat conduction in the streamwise direction but also conduction across the experimental set-up, and new computational models should be elaborated to compare the measurements with theory. 

The experimental data obtained in conventional size channels and micro-channels with diameters between 100 pm and 6.0 mm are examined to further elucidate and understand the differences in two-phase flow characteristics between the microchannels and conventional size channels. Since two separate sets of experiments have been conducted using air and water in acrylic channels with diameters between 500 pm and 6.0 mm, and nitrogen gas-water in fused silica channels with diameters between 50 and 500 pm, the authors refer to the former channels as conventional size channels, and the latter channels as micro-channels for convenience. Two different inlet sections were covered in micro-channel experiments, a gradually reducing section and a T-junction. 

The convective and nucleate boiling heat transfer coefficient was the subject of experiments by Grohmann (2005). The measurements were performed in microtubes of 250 and 500 pm in diameter. The nucleate boiling metastable flow regimes were observed. Heat transfer characteristics at the nucleate and convective boiling in micro-channels with different cross-sections were studied by Yen et al. (2006). Two types of micro-channels were tested a circular micro-tube with a 210 pm diameter, and a square micro-channel with a 214 pm hydraulic diameter. The heat transfer coefficient was higher for the square micro-channel because the corners acted as effective nucleation sites. 

G. Hetsroni, A. Mosyak, E. Pogrebnyak, and L.P. Yarin, Heat transfer in micro-channels Comparison of experiments with theory and numerical results, International Journal of Heat and Mass Transfer 25-26, 5580-5601 (2005). 

TABLE 2. Comparison of simulation and experiments for local Nusselt numbers in micro-channel (x = L/2 and x = L). 

The experiments with the micro-TAS elements were carried out to evaluate liquid flow and mixing in micro-channels, and the characteristics of the switching valves. The evaluation relies on the possibility of studjnng the liquid flow in the micro-TAS elements through the transparent glass wafer, and the experimental set-up used for investigating liquid mixii in mini-channels was also used for the characterisation of the micro-TAS elements. 

Experiments were conducted with air through micro-channel A = 319 (friction factor. The relative surface roughness was low k /H = 0.001) and Kn < 0.001, thus the experiments were effectively isolated from the influence of surface roughness and rarefaction. The local friction factor is plotted versus Ma in Fig. 2.25 for air. The experimental A increases about 8% above the theoretical A as Ma increases to 0.35. 

Pressure drop measurements. For the majority of experiments the instrumentation was relatively similar. Due to limitations associated with the small size of the channels, pressures were not measured directly inside the micro-channels. To obtain the channel entrance and exit pressures, measurements were taken in a plenum or supply line prior to entering the channel. It is insufficient to assume that the friction factor for laminar compressible flow can be determined by means of analytical predictions for incompressible flow. 

This chapter has the following structure in Sect. 3.2 the common characteristics of experiments are discussed. Conditions that are needed for proper comparison of experimental and theoretical results are formulated in Sect. 3.3. In Sect. 3.4 the data of flow of incompressible fluids in smooth and rough micro-channels are discussed. Section 3.5 deals with gas flows. The data on transition from laminar to turbulent flow are presented in Sect. 3.6. Effect of measurement accuracy is estimated in Sect. 3.7. A discussion on the flow in capillary tubes is given in Sect. 3.8. 

We begin the comparison of experimental data with predictions of the conventional theory for results related to flow of incompressible fluids in smooth micro-channels. For liquid flow in the channels with the hydraulic diameter ranging from 10 m to 10 m the Knudsen number is much smaller than unity. Under these conditions, one might expect a fairly good agreement between the theoretical and experimental results. On the other hand, the existence of discrepancy between those results can be treated as a display of specific features of flow, which were not accounted for by the conventional theory. Bearing in mind these circumstances, we consider such experiments, which were performed under conditions close to those used for the theoretical description of flows in circular, rectangular, and trapezoidal micro-channels. 

The frictional pressure drop for liquid flows through micro-channels with diameter ranging from 15 to 150 pm was explored by Judy et al. (2002). Micro-channels fabricated from fused silica and stainless steel were used in these experiments. The measurements were performed with a wide variety of micro-channel diameters, lengths, and types of working fluid (distilled water, methanol, isopropanol), and showed that there were no deviations between the predictions of conventional theory and the experiment. Sharp and Adrian (2004) studied the fluid flow through micro-channels with the diameter ranging from 50 to 247 pm and Reynolds number from 20 to 2,300. Their measurements agree fairly well with theoretical data. 

The deviation of the data related to flow in smooth (Table 3.3) and rough (Table 3.4) micro-channels may be a result of heterogeneity of the actual roughness, where height of some roughness peaks signiflcantly exceeds its mean value. For example, under conditions of experiment by Pfund et al. (2000) the mean heigh of... 

One of the possible ways to account for the effect of roughness on the pressure drop in a micro-tube is to apply a modified-viscosity model to calculate the velocity distribution. Qu et al. (2000) performed an experimental study of the pressure drop in trapezoidal silicon micro-channels with the relative roughness and hydraulic diameter ranging from 3.5 to 5.7% and 51 to 169 pm, respectively. These experiments showed significant difference between experimental and theoretical pressure gradient. 

For the most part of the experiments one can conclude that transition from laminar to turbulent flow in smooth and rough circular micro-tubes occurs at Reynolds numbers about RCcr = 2,000, corresponding to those in macro-channels. Note that other results were also reported. According to Yang et al. (2003) RCcr derived from the dependence of pressure drop on Reynolds number varied from RCcr = 1,200 to RCcr = 3,800. The lower value was obtained for the flow in a tube 4.01 mm in diameter, whereas the higher one was obtained for flow in a tube of 0.502mm diameter. These results look highly questionable since they contradict the data related to the flow in tubes of diameter d> mm. Actually, the 4.01 mm tube may be considered... 

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