Flow characteristics of water in microtubes

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Abstract

Water flow through microtubes with diameters ranging from 50 to 254 μm was investigated experimentally. Microtubes of fused silica (FS) and stainless steel (SS) were used. Pressure drop and flow rates were measured to analyze the flow characteristics. The experimental results indicate significant departure of flow characteristics from the predictions of the conventional theory for microtubes with smaller diameters. For microtubes with large diameters, the experimental results are in rough agreement with the conventional theory. For lower Re, the required pressure drop is approximately the same as predicted by the Poiseuille flow theory. But, as Re increases, there is a significant increase in pressure gradient compared to that predicted by the Poiseuille flow theory. The friction factor therefore is higher than that given in the conventional theory. The results also indicate material dependence of the flow behavior. For the same flow rate and the same diameter, an FS microtube requires a higher pressure gradient than a stainless steel microtube. The measured high pressure gradient may be due to either an early transition from laminar flow to turbulent flow or the effects of surface roughness of the microtubes. These phenomena are discussed in this paper. A roughness-viscosity model is proposed to interpret the experimental data.

Introduction

Over the years, significant attention has been given to liquid flow in microchannels due to the development in microfluidic devices and systems. Components such as liquid cooled microchannel heat sinks, micro-pumps, micro-valves and actuators have been miniaturized, integrated and assembled forming various microfluidic devices and systems. The fundamental understanding of flow characteristics such as velocity distribution and pressure loss is essential in design and process control of microfluidic devices.

Peiyi and Little (1983) measured the friction factors for the flow of gases in fine channels, 130–200 μm wide. Their results showed different characteristics from that predicted by conventional theories of fluid flow. They attributed these differences largely to surface roughness of the microchannels. Wu and Little, 1983, Wu and Little, 1984 measured friction and heat transfer of gases in microchannels. They observed different experimental results of convective heat transfer from that obtained in conventional macroscale channels. They found that friction factors were larger than those obtained from the traditional Moody charts and indicated that the transition from laminar to turbulent flow occurred much earlier at Reynolds number of about 400–900 for various tested configurations.

Tuckerman (1984) conducted one of the initial investigations of liquid flow and heat transfer characteristics in microchannels. He observed that the flow rates approximately followed Poiseuille flow predictions. Pfahler et al. (1990) conducted an experimental investigation of fluid flow in microchannels. They found that for large flow channels the experimental observations were in rough agreement with the conventional theory whereas for small channels the deviations increased. Later, Pfahler et al. (1991) presented measurements of friction factor or apparent viscosity of isopropyl alcohol and silicon oil flowing in microchannels. They observed that for larger channels the experimental results indicated a very good agreement with the predictions of classical theory. However, as the channel size decreased, the apparent viscosity began to decrease from the theoretical value for a given pressure drop, though distinctly different behaviors were observed between the polar isopropyl alcohol and non-polar silicon oil. Choi et al. (1991) investigated the friction factor, convective heat transfer coefficient and the effects of inner wall surface roughness for laminar and turbulent flow in microtubes. Their experimental results were significantly different from the correlations in the conventional theories.

Wang and Peng (1994) experimentally studied the forced convention of liquid in microchannels, 0.2–0.8 mm wide and 0.7 mm deep. They found that the transition from laminar to turbulent flow occurred when Re < 800, and that the fully developed turbulent convection was initiated in the Reynolds number range of 1000–1500. Peng et al., 1994a, Peng et al., 1994b reported experimental investigation of forced flow convection of water in rectangular microchannels with hydraulic diameters ranging from 0.1333 to 0.367 mm and aspect ratios from 0.333 to 1. Their results indicated that the upper limits of the laminar flow and the beginning of the fully developed turbulent heat transfer regimes occurred at Reynolds number ranges of 200–700 and 400–1500, respectively. The transitional Reynolds number diminishes and the transition range becomes smaller as the microchannel dimensions decrease. They found that the geometrical parameter such as height to width ratio also affects the flow characteristics in microchannels.

As the fluid flow characteristics in microchannels are quite different from those predicted by using the relationships established for macro-channels, it is therefore necessary to undertake fundamental investigations to understand the difference in these characteristics. The objective of this work is to investigate experimentally the characteristics of water flow in microtubes and attempt to explain the obtained results.

Section snippets

Experimental apparatus, procedure and results

The experimental apparatus is shown in Fig. 1. The apparatus consists of a precision pump, a microfilter, a flow meter, a pressure transducer, tube inlet and outlet assemblies and a PC data acquisition system. The pump used is a high precision pump (Ruska Instruments) having a flow rate range of 2.5–560 ± 0.02 cc/h. A 0.1-micron microfilter is placed between the pump and the microtube inlet to eliminate any particles and bubbles. Deionized water at room temperature is used as the working fluid.

Early transition to turbulence

From conventional theory, we know that when the Reynolds number increases to certain values, the internal flow undergoes a remarkable transition from laminar to turbulent regime. The origin of turbulence and the accompanying transition from laminar to turbulent flow is of fundamental importance to the science of fluid mechanics. In a flow at low Reynolds number through a straight pipe of uniform cross-section and smooth walls, every fluid particle moves with a uniform velocity along a straight

Friction characteristics

For a constant volume flow rate Q, the pressure gradient ΔP/Δl required to force the liquid through the microtube was measured. As discussed earlier the measured value of the ΔP/Δl is greater than that predicted by Eq. (1). The coefficient of flow resistance f, also known as friction factor, for a pipe of a length l and a diameter D is related to the pressure gradient by the Darcy–Weisbach Equation asf=ΔPl2Dρuav2.For fully developed laminar flow in a macroscale pipe, Eq. (7)can be shown to bef=

Effects of surface roughness

The presence of surface roughness affects the laminar velocity profile and decreases the transitional Reynolds number. This has been shown by a number of experiments and a comprehensive review can be found elsewhere (Merkle et al., 1974; Tani, 1969). In the present work, based on Merkle's modified viscosity model the effects of the surface roughness on laminar flow in microtubes are considered in terms of a roughness-viscosity function. Generally, the roughness increases the momentum transfer

Summary

Flow characteristics of water flowing through cylindrical microtubes of stainless steel and fused silica were studied. The diameter of the microtubes ranges from 50 to 254 μm. It was observed that for a fixed volume flow rate, the pressure gradient required to force the liquid through the microtube is higher than that predicted by the conventional theory. For small flow rates, i.e. small Reynolds numbers, the conventional theory and the experimental data are in a rough agreement. However, as

Acknowledgements

The authors wish to acknowledge the support of a University of Alberta Dissertation Fellowship (Gh. Mohiuddin Mala) and Research Grant of the Natural Science and Engineering Research Council of Canada (D. Li).

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