Micro-channels liquid flow

Specific Features of Flow in Micro-Channels liquid temperature ... 

Because most applications for micro-channel heat sinks deal with liquids, most of the former studies were focused on micro-channel laminar flows. Several investigators obtained friction factors that were greater than those predicted by the standard theory for conventional size channels, and, as the diameter of the channels decreased, the deviation of the friction factor measurements from theory increased. The early transition to turbulence was also reported. These observations may have been due to the fact that the entrance effects were not appropriately accounted for. Losses from change in tube diameter, bends and tees must be determined and must be considered for any piping between the channel plenums and the pressure transducers. It is necessary to account for the loss coefficients associated with singlephase flow in micro-channels, which are comparable to those for large channels with the same area ratio. 

Figure 5.6 Flow pattern map for a gas/liquid flow regime in micro channels. Annular flow wavy annular flow (WA) wavy annular-dry flow (WAD) slug flow bubbly flow annular-dry flow (AD). Transition lines for nitrogen/acetonitrile flows in a triangular channel (224 pm) (solid line). Transition lines for air/water flows in triangular channels (1.097 mm) (dashed lines). Region 2 presents flow conditions in the dual-channel reactor ( ), with the acetonitrile/nitrogen system between the limits of channeling (I) and partially dried walls (III). Flow conditions in rectangular channels for a 32-channel reactor (150 pm) (T) and singlechannel reactor (500 pm) (A) [13].

Steam-liquid flow. Two-phase flow maps and heat transfer prediction methods which exist for vaporization in macro-channels and are inapplicable in micro-channels. Due to the predominance of surface tension over the gravity forces, the orientation of micro-channel has a negligible influence on the flow pattern. The models of convection boiling should correlate the frequencies, length and velocities of the bubbles and the coalescence processes, which control the flow pattern transitions, with the heat flux and the mass flux. The vapor bubble size distribution must be taken into account. 

Part 1. Presentation of the model. Int J Heat Mass Transfer 47 3375-3385 Tiselj I, Hetsroni G, Mavko B, Mosyak A, Pogrebnyak E, Segal Z (2004) Effect of axial conduction on the heat transfer in micro-channels Int J Heat Mass Transfer 47 2551-2565 Triplett KA, Ghiaasiaan SM, Abdel-Khalik SI, Sadowski DL (1999) Gas-liquid two-phase flow in microchannels. Part I. Two-phase flow patterns. Int J Multiphase Flow 25 377-394 Tsai J-H, Lin L (2002) Transient thermal bubble formation on polysihcon micro-resisters. J Heat Transfer 124 375-382... 

The problems of micro-hydrodynamics were considered in different contexts (1) drag in micro-channels with a hydraulic diameter from 10 m to 10 m at laminar, transient and turbulent single-phase flows, (2) heat transfer in liquid and gas flows in small channels, and (3) two-phase flow in adiabatic and heated microchannels. The smdies performed in these directions encompass a vast class of problems related to flow of incompressible and compressible fluids in regular and irregular micro-channels under adiabatic conditions, heat transfer, as well as phase change. 

We consider the problem of liquid and gas flow in micro-channels under the conditions of small Knudsen and Mach numbers that correspond to the continuum model. Data from the literature on pressure drop in micro-channels of circular, rectangular, triangular and trapezoidal cross-sections are analyzed, whereas the hydraulic diameter ranges from 1.01 to 4,010 pm. The Reynolds number at the transition from laminar to turbulent flow is considered. Attention is paid to a comparison between predictions of the conventional theory and experimental data, obtained during the last decade, as well as to a discussion of possible sources of unexpected effects which were revealed by a number of previous investigations. 

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 transition from laminar to turbulent flow in micro-channels with diameters ranging from 50 to 247 pm was studied by Sharp and Adrian (2004). The transition to turbulent flow was studied for liquids of different polarities in glass micro-tubes having diameters between 50 and 247 pm. The onset of transition occurred at the Reynolds number of about 1,800-2,000, as indicated by greater-than-laminar pressure drop and micro-PIV measurements of mean velocity and rms velocity fluctuations at the centerline. 

Thus, the measurements of integral flow characteristics, as well as mean velocity and rms of velocity fluctuations testify to the fact that the critical Reynolds number is the same as Rccr in the macroscopic Poiseuille flow. Some decrease in the critical Reynolds number down to Re 1,500— 1,700, reported by the second group above, may be due to energy dissipation. The energy dissipation leads to an increase in fluid temperature. As a result, the viscosity would increase in gas and decrease in liquid. Accordingly, in both cases the Reynolds number based on the inlet flow viscosity differs from that based on local viscosity at a given point in the micro-channel. 

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). 

The behavior of liquid flow in micro-tubes and channels depends not only on the absolute value of the viscosity but also on its dependence on temperature. The nonlinear character of this dependence is a source of an important phenomenon - hydrodynamic thermal explosion, which is a sharp change of flow parameters at small temperature disturbances due to viscous dissipation. This is accompanied by radical changes of flow characteristics. Bastanjian et al. (1965) showed that under certain conditions the steady-state flow cannot exist, and an oscillatory regime begins. 

Estimation of adiabatic increase in the liquid temperature in circular micro-tubes with diameter ranging from 15 to 150 pm, under the experimental conditions reported by Judy et al. (2002), are presented in Table 3.7. The calculations were carried out for water, isopropanol and methanol flows, respectively, at initial temperature Tin = 298 K and v = 8.7 x 10" m /s, 2.5 x 10 m /s, 1.63 x 10 m /s, and Cp = 4,178 J/kgK, 2,606J/kgK, 2,531 J/kgK, respectively. The lower and higher values of AT/Tm correspond to limiting values of micro-channel length and Reynolds numbers. Table 3.7 shows adiabatic heating of liquid in micro-tubes can reach ten degrees the increase in mean fluid temperature (Tin -F Tout)/2 is about 9 °C, 121 °C, 38 °C for the water d = 20 pm), isopropanol d = 20 pm) and methanol d = 30 pm) flows, respectively. 

The uncertainty of calculating the Poiseuille number from the measurements must be taken into account. The viscosity-pressure relationship of certain liquids (e.g., isopropanol, carbon tetrachloride) must be kept in mind to obtain the revised theoretical flow rate. The effect of evaporation from the collection dish during the mass flow rate measurement must be taken into consideration. The effect of evaporation of collected water into the room air may not be negligible, and due to the extremely low mass flow rates through the micro-channel this effect can become significant. 

Judy J, Maynes D, Webb BW (2002) Characterization of frictional pressure drop for liquid flows through micro-channels. Int J Heat Mass Transfer 45 3477-3489 Kandlikar SG, Joshi S, Tian S (2003) Effect of surface roughness on heat transfer and fluid flow characteristics at low Reynolds numbers in small diameter tubes. Heat Transfer Eng 24 4-16 Koo J, Kleinstreuer C (2004) Viscous dissipation effects in microtubes and microchannels. Int J Heat Mass Transfer 47 3159-3169... 

Rands C, Webb BW, Maynes D (2006) Characterization of transition to turbulence in microchannels. Int J Heat Mass Transfer 49 2924-2930 Ren L, Qu W, Li D (2001) Interfacial electrokinetic effects on liquid flow in micro-channels. Int J Heat Mass Transfer 44 3125-3134... 

Gamart G, Favre-Marinet M, Asendrych D (2005) Conduction and entrance effects on laminar liquid flow and heat transfer in rectangular micro-channels. Int J Heat Mass Transfer 48 2943-2954... 

Knowledge of dominant two-phase flow patterns in micro-channels is a key factor in developing accurate and physically sound predictive tools for heat sink design. Unfortunately, interfacial interactions between the vapor and liquid phases during flow boiling in a micro-channel are often far too complex to permit accurate measurement or quantitative assessment of flow patterns. 

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