(302g) Experimental Studies On the Effect of Surface Roughness On Laminar, Transitional and Turbulent Flow in Microtubes

With the rapid development of microsystem technology, the investigation of liquid flow in microtubes has become one of the most important subjects. Microsystems have been widely used in industry and biological medicine, such as heat exchangers, mixing and separation processes, fuel cells, DNA analysis, artificial blood vessels and so on. To optimize microsystems, a sound understanding of the properties of liquid flow in microtubes is necessary. In the recent 15-20 years many researchers are trying to figure out whether the liquid flow behavior in microscale is the same as classical theory in macroscale. However, different researchers came up with conflicting conclusions. Some researchers found that the friction factor is below the classical theory, some said that friction factor is the same as classical theory, but many recent researchers observed higher friction factor than classical theory. The surface roughness is one of the major parameters leading to higher friction factor, but no one gave a quantitative conclusion about the differences surface roughness made between microscale and macroscale.

In this paper, an experimental study of water flow in microtubes has been performed in 5 stainless steel microtubes whose diameters (D) are 524.7, 353.2, 161.6, 127.5, and 126.3 μm to investigate the effect of surface roughness on characteristics of liquid flow in microscale. The average surface roughnesses (k) of these five microtubes are 2.32, 1.31, 2.80, 2.98, and 4.37 μm, respectively. The average surface roughness was determined by a non-contact 3D surface measurement (Wyko NT9100) using a vertical scanning interferometry mode for a wide variety of topologies, as well as phase-shift interferometry mode for more subtle profile changes.

The experiments were performed in an apparatus including pressure source, test section, pressure transducer, balance, and data acquisition system. The Reynolds number (Re) and friction factor (f) were calculated from experimental data to describe the characteristics of liquid flow.

It was found that the critical Reynolds number (Re_c, the Reynolds number when the friction factor departs from the Poiseuille equation) is a function of the relative roughness (k/D). The Re_c reduces with the increase of the k/D, and the minimum Re_c is 200 when the k/D is 3.46 % in our experiment. The f-Re relationship is the same as macroscale theory in the laminar region. However, the f-Re relationship in the transition region and turbulent region can’t be predicted by macroscale theory such as Blasius equation or Colebrook equation any more. A mathematical model was proposed to describe the relationship between Re_c and k/D, and it is also applicable to literature data. A modified Blasius equation was established to calculate f using Re for transition region and a power correlation was established to calculate f using k/D for quadratic resistance region.

The application of the correlations mentioned above is limited to the diameters and surface roughnesses in this work. To obtain more accurate parameters for these models, more experiments need to be carried out in larger and smaller tubes. We considered that Re_c can be one indicator to find the critical diameter (D_c) that distinguish microscale and macroscale (Re_c equals 2300 in macroscale and smaller than 2300 in microscale). More researches will be done to find the D_c.