Estimating Roughness Parameters Resulting From Various ... · pipes with relatively low values of...

Proceedings of the 5th

International Conference on Nanochannels, Microchannels and Minichannels ICNMM2007

June 18-20, 2007, Puebla, Mexico

ICNMM2007-30033

ESTIMATING ROUGHNESS PARAMETERS RESULTING FROM VARIOUS MACHINING TECHNIQUES FOR FLUID FLOW APPLICATIONS

Perry L. Young Rochester Institute of Technology

[email protected]

Timothy P. Brackbill Rochester Institute of Technology

[email protected]

Satish G. Kandlikar Rochester Institute of Technology

[email protected]

Proceedings of the Fifth International Conference on Nanochannels, Microchannels and Minichannels ICNMM2007

June 18-20, 2007, Puebla, Mexico

ICNMM2007-30033

ABSTRACT Recently, a set of new roughness parameters was proposed

by Kandlikar et al. [1] and Taylor et al. [2] for reporting surface roughness as related to fluid flow. The average roughness Ra parameter is often used in microfluidic applications, but this parameter alone is insufficient for describing surface roughness; a specimen with deep grooves and sharp obstructions can share the same average roughness value as a relatively smooth surface with low uniform surface roughness. Since the average roughness parameter is broad, it is difficult to access the surface topography features that result from different machining processes or etches. A profilometer and a digital microscope are used to examine the surface roughness profiles of various materials submitted to different machining techniques. The materials studied will be similar to those used for microchannels including aluminum, stainless steel, copper, and silicon. Depending on the material, these samples are submitted to several machining processes including milling, grinding, fly cutting, and microfabrication techniques. These machining processes and microfabrication techniques are of practical interest in microfluidics applications. After studying the surface roughness patterns exhibited in these samples, the roughness parameters employed in some of the recent roughness models are evaluated. This study is expected to provide more understanding of assorted surface roughness.

INTRODUCTION The correlation between surface roughness and fluid flow

was initially drawn by Darcy, among others, in the early nineteenth century [3]. He conducted careful pressure drop experiments and concluded that the surface roughness was an important factor in fluid flow. Fanning later performed more experiments and proposed correlations between surface roughness and pressure drop [4]. More experiments were done

by Nikuradse [5], who sifted sand into groups of known diameters. He then lined pipes of 250, 500, and 1000 mm diameters with a combination of the sand grains and Japanese lacquer. These pipes were then studied to determine the effect of the surface roughness on the pressure drop of the fluid flow through the pipe [5]. The Reynolds numbers studied in his experiments ranged from 600 to 10

6. Colebrook later

conducted studies on sixteen spun concrete pipes, including the Ontario Tunnel [6]. These concrete pipes ranged in diameters of 101.6 mm to 5486 mm. He developed the well known Colebrook equation through these experiments. Moody then used the Colebrook equations, as well as the experimental data from Nikuradse’s work, to develop the Moody diagram for pipes with relatively low values of surface roughness in the range of 0-5% relative roughness [7].

There are various ways to measure the surface roughness of a material. Many studies have used a profilometer to obtain a surface profile. However, this process can cause localized damage to the surface being examined. Sundararajan et al. [8] used profilometry and Atomic Force Microscopy (AFM) to investigate the effects of various etching processes on silicon surfaces. The two etches the authors focused on were potassium hydroxide (KOH) and tetramethyl ammonium hydroxide (TMAH). They also studied the effects of adding isopropyl alcohol (IPA) additive to these etches. They found that the TMAH etch produced rougher surfaces than the KOH etch at larger scan sizes than 5 µm. Other researchers employ optical or scanning electron microscopy to evaluate surface roughness. Chen et al. [9] have proposed using atomic force microscopy with a bent tapered fiber probe to measure surface roughness and profiles. Using Digital Holographic Microscopy (DHM) has also been investigated by Montfort et al. [10] as another approach to measuring the topography of a surface.

Kandlikar et al. [1] and Taylor et al. [2] proposed six new roughness parameters in recent work in order to better depict

1 Copyright © 2007 by ASME

mailto:[email protected]



surface roughness characterization for single-phase fluid flow applications. Of the six parameters, three correspond to surface roughness and three correspond to localized hydraulic diameter variations. The three roughness characterization parameters that were proposed are Rp (maximum profile peak height), Rsm (mean spacing of profile irregularities), and FdRa (floor distance to mean line). A new roughness parameter, εFp, was proposed in place of average roughness (Ra). These parameters will be discussed in more depth later.

NOMENCLATURE AFM atomic force microscope DHM digital holographic microscope DRIE deep reactive ion etching εFp roughness FdRa floor distance to mean line IPA isopropyl alcohol KOH potassium hydroxide Ra average roughness RP maximum profile peak height Rv maximum profile valley Rsm mean spacing between profile irregularities TMAH tetramethyl ammonium hydroxide XeF2 xenon diflouride

SURFACE ROUGHNESS PARAMETERS There are many surface roughness parameters that can be used to analyze a surface. The most common surface roughness parameter used in industry is the average roughness. The average roughness can be calculated using equation 1:

∑=

=

n

i

ia Yn

R1

1 (1)

In this equation, n is the number of sample points evaluated, and Yi represents the absolute value of the profile deviation from the mean line. This roughness parameter is well known in industry, and is very easy to calculate and use. Manufacturers often specify an average roughness value and are confident they will receive a surface that fits their needs. However, the average roughness parameter fails to accurately represent the surface topography. To make up for this shortcoming other surface roughness parameters are often used in addition to the average roughness. Kandlikar et al. [1] proposed the use of three surface roughness parameters, as well as a new roughness parameter, εFp, to be used to represent the roughness in replacement of average roughness for fluid flow. A diagram of these surface roughness parameters is shown in Fig. 1. These surface roughness parameters include Rsm, Rp and Rv. Rsm represents the mean spacing of profile irregularities. It is calculated using equation 2:

∑=

=

n

i

sm Smin

R1

1 (2)

To calculate this, two lines are drawn near the mean line. These two lines could be a percentage value away from the mean line or represent a standard height of the profile. The area between these two lines represents the dead zone of the profile. Smi represents the peak and valley pairs of the profile; the distance between when the data drops below the dead zone to where it rises above the dead zone. This parameter represents the pitch of the surface profile. The maximum profile peak height, Rp, represents the distance between the mean line and the highest point of the profile. The maximum profile valley, Rv, is a similar parameter and represents the distance between the mean line and the lowest point of the profile. These two parameters can be calculated using equations 3 and 4:

RP = max(Zi) - mean(Zi) (3)

RV = min(Zi) – mean(Zi) (4)

where Zi represents all the points of the surface profile. Another useful surface parameter is FdRa, which represents the floor distance to mean line. FdRa can be calculated by finding the average of all profile data points that fall below the mean line, as shown in equation 4.

Let z⊆Z such that all zi = Zi iff Zi < Mean Line

∑=

=

zn

i

i

z

zn

FdRa1

1 (5)

The roughness parameter, εFp, that was proposed to be used rather than the average roughness has also been reviewed in this paper. This roughness parameter is equal to the sum of the roughness parameters Rp and FdRa: εFp = Rp + FdRa (6) This distance, shown in Fig. 1, is represented as the distance from the average of the peak values to the averages of the floor values of the surface roughness profile. Kandlikar et al. [1] can be referred to for more information. OBJECTIVES OF THE PRESENT WORK

• Collect and examine a variety of surface roughness samples of practical interest in microfluidics applications

• Examine the surfaces using a Mitutoyo SJ-401 Stylus Profilometer with a 5 micron diamond tip, and a

Figure 1: Diagram of Surface Roughness Parameters, from

Taylor et al. [8]


Keyence VHX-500K Digital Microscope with a VHX-515 profile measurement unit

• Calculate Ra and εFp for all surfaces, and discuss the suitability of the roughness parameters in representing different roughness features

ANALYSIS The following surface roughness samples were collected for analysis:

• Copper, aluminum, and stainless steel pieces were milled with a 12.7 mm (½”) diameter 2 flute high speed end mill

• Samples of copper, aluminum, and stainless steel were flycut with a single point, carbide tipped tool bit with a 1 mm (0.040”) radius

• Samples of copper, aluminum, and stainless steel were surface ground using a 60 grit wheel

• Copper, brass, and stainless steel capillary tubes were milled open to examine the surface roughness inside

• Copper microchannels, machined with a 200 µm thick roller

• A pure nickel microfinish surface comparator, having 22 surfaces from a range of machining techniques including

o grinding o blanchard grinding o shape turning o lapping o profiling o milling

• Three silicon wafers with etched microchannels were also analyzed. The etching processes included

o potassium hydroxide (KOH)

o xenon diflouride (XeF2)

o deep reactive ion etching (DRIE)

For this review, two methods were used to measure the surface roughness of all the specimens gathered; a Mitutoyo SJ-401 Stylus Profilometer with a 5 micron diamond tip, and a Keyence VHX-500K Digital Microscope with a VHX-515 profile measurement unit. Various roughness parameters were accessed for all the surface roughness specimens, including Ra, Rp, and Rv. The parameters proposed by Kandlikar et al. [1] were also examined; FdRa and the

Tab

roughness, εFp. Mitutoyo Surfpak software was used with the profilometer to collect surface profile data and the average roughness values. Microsoft Excel was used to calculate the Rp, Rv, and FdRa parameter values using the profilometer profile data. The profilometer was run to collect data eight times for each surface examined. The measurement length of each test was 4 mm, and out of the eight surface profiles generated using the profilometer, the top six profiles were chosen for calculating the surface roughness parameters in order to reduce faulty data. The surface roughness parameters Ra, Rv, Rp, FdRa, and εFp were calculated for every surface examined using equations 1-6, and the results are tabulated and shown in Table 1. In the following sections, detailed results for the surfaces examined are presented. The roughness parameter, εFp, is being considered for replacing the currently accepted average roughness value, Ra, and the validity of this roughness parameter will be assessed.

FLYCUT SAMPLES The samples of copper, aluminum, and stainless steel that had been flycut were examined first. Fly cutting is a process where a single point cutting bit similar to that of a lathe is mounted in an end mill using a special holder. This process can be used for many machining techniques, including cutting, drilling, grinding, and sanding. Figure 2 shows a three dimensional photograph of the copper flycut surface as well as a surface roughness profile obtained from the stylus profilometer. Color was added to the

le 1: Surface Roughness Parameters


Figure 2: Copper Flycut Surface, magnified 450x, and Surface Profile [Ra=0.31 µm, εFp =1.04 µm]

three-dimensional surface picture to make the height differences more visible. The stainless steel and the aluminum flycut surfaces looked very similar to the copper flycut surface. However, the stainless steel flycut surface appeared slightly rougher, and the aluminum surface appeared smoother than the copper flycut surface. As seen from Table 1, the average roughness of the aluminum, copper, and stainless steel flycut surfaces were 0.22 µm, 0.31 µm and 0.29 µm, respectively. These average roughness values portray that the aluminum has the smoothest of all three flycut surfaces and that the copper surface is the roughest. The roughness parameter, εFp, shows a slightly different picture, with aluminum having the smallest εFp of 0.10 µm, copper having a εFp of 1.04 µm, and stainless steel having the highest value of 1.06 µm. These values are shown in table 1, as well as the calculated Rp, Rv, and FdRa values. The photographs of each flycut surface obtained from the

microscope correspond better to the roughness value, εFp than to the average roughness values. The aluminum surface looked the smoothest, and had the lowest εFp value. The stainless steel flycut sample appeared to be the roughest, and had the highest εFp value of all three materials. The aluminum flycut surface looked to be overall more smooth but with areas where the surface roughness was more prominent than others. The copper and the stainless steel flycut surfaces appeared to be more uniformly rough.

SURFACE GROUND SAMPLES

Surface grinding was performed on samples of copper, aluminum, and stainless steel in a 60 grit wheel. Grit is a unit of measurement used with sandpaper and grinding wheels; it refers to the number of abrasive particles within a square inch of the grinding wheel. The higher the grit, the smoother the

Figure 3: Stainless Steel 60 grit Surface Ground, 3-D photograph magnified 450x, and Surface Profile [Ra=0.37 µm, εFp =1.33 µm]


Figure 4: Aluminum Milled Surface, 3-D photo magnified 450x, and Surface Profile [Ra=0.64 µm, εFp=2.12 µm]

ground surface will be. Used mainly for heavy sanding and stripping purposes, 60 grit is considered coarse. The three samples that had been surface ground with a 60 grit grinding wheel were examined with the profilometer. The Ra values that were calculated for these three materials reported that the aluminum was the smoothest surface of the three, with Ra equal to 0.25 µm. The highest Ra value was calculated to be 0.37 µm for the stainless steel sample. The copper sample fell in between these two, with an average roughness of 0.29 µm. Figure 3 shows a three-dimensional picture of the stainless steel surface ground sample. In the three-dimensional photographs, the aluminum surface ground sample looks the smoothest of the three, but also looks to be somewhat wavy. The roughness value εFp for the aluminum sample is the lowest of the three at 1.12 µm. The highest value of εFp is for the copper sample, at 1.34 µm. The stainless steel falls in between these two values at 1.33 µm. The copper surface ground sample seemed to have more peaks and valleys than the aluminum and stainless steel samples, which appeared of more uniform roughness. The tabulated values for the surface roughness parameters can be found in Table 1.

END MILLED SAMPLES The next set of samples analyzed were the aluminum, copper, and stainless steel samples that had been milled in a 12.7 mm (½”) diameter 2 flute high speed end mill. A three-dimensional photograph of the aluminum milled surface, and a surface profile obtained from the profilometer is shown in Fig. 4. In this photograph, the path taken by the end mill across the surface is evident. While this path is visible on all three surfaces, it is most prominently viewed on the aluminum milled surface. Though the aluminum surface shows the machining processes the most vividly, it had the lowest calculated Ra value of 0.64 µm, and appears to be the smoothest of the three surfaces. The stainless steel milled surface appears to be much rougher than the aluminum or copper milled samples, and had the highest Ra value of 1.2 µm. The εFp values followed a

different pattern than the average roughness, with the copper taking the smallest value of 0.90 µm. The stainless steel had a much higher roughness value of 4.27 µm. These surface roughness parameters, and others, are shown in Table 1. The milled surfaces were more noticeably rough than the flycut or surface ground samples. The εFp values that were calculated seemed to be a better correlation for discussing surface roughness in terms of fluid flow than the average roughness values; the average roughness values have been consistently lower than the εFp values for all surface roughness samples examined. Since the εFp roughness value better represents the height of the profile peaks than the average roughness value, it more accurately represents the obstructions the fluid flow observes. NICKEL SURFACE COMPARATOR - LAPPED The lapped surfaces on the nickel surface comparator were the smoothest samples that were investigated. The 2L surface represents that the surface has been lapped with a roughness height of 2 microinches (0.05 µm). Only two lapped surfaces were available for analysis. The 2L surface had an average roughness value of 0.04 µm and a roughness value, εFp, of 0.15 µm. The second lapped surface had a roughness height of 4 microinches, and was represented with the characterization 4L. This lapped surface brought in a higher average roughness value of 0.08 µm and a roughness value εFp of 0.24 µm. It is interesting to note that as the roughness height value doubles from two to four, the roughness value, εFp, increases by a factor of approximately 1.65.

NICKEL SURFACE COMPARATOR - GROUND The nickel microscale surface comparator had six different ground surfaces. Four were surface ground with the periphery of a grinding wheel, and the last two were blanchard ground, which is where the flat of the grinding wheel is used to grind the sample smooth. The four samples that were ground with the periphery of the wheel had roughness heights of 0.2, 0.41,


0.81, and 1.6 µm (8, 16, 32, and 63 microinches). The blanchard ground surfaces had roughness heights of 0.41 and 0.81 µm (16 and 32 microinches). The tabulated values for the surface roughness parameters can be found in Table 1. Figure 5 displays the three-dimensional photographs of the 16G and 16BL surfaces and their corresponding surface profiles. It was assumed that the average roughness and εFp value would increase as the roughness heights of the samples increased, which proved to be a valid assumption. For the ground surfaces, the average roughness was the lowest for the 8G surface, at 0.13 µm. This surface also had the lowest roughness value, with εFp of 0.58 µm. The 16G surface had the next lowest Ra value of the six ground surfaces, with Ra equal to 0.389 µm. The εFp value of the 16G surface was also the second lowest, at 1.63 µm. The blanchard ground 16BL surface was just slightly rougher than the 16G surface, with Ra equal to 0.45 µm and εFp equal to 1.76 µm. Table 1 provides are more in-depth summary of the surface roughness parameters calculated.

As would be expected, the 32G and 32BG surfaces were rougher than the ground surfaces with roughness heights of 0.41 µm (16 microinches). The average roughness value for the 32G surface was 1.008 µm and εFp was equal to 3.6 µm. Interestingly enough, the blanchard ground surface was now smoother than the ground surface. The 32BG surface had an average roughness of 0.65 µm and εFp was equal to 2.48 µm. There is no identifiable relationship between the blanchard ground surface and the ground surface roughness values; one type of grinding is not consistently rougher than the other. The next ground roughness height on the surface comparator was 1.6 µm (63 microinches). The average roughness of the 63G surface was 1.44 µm while the value for εFp was equal to 6.85 µm. As expected, both the average roughness value and the value εFp of the samples increased as the roughness height increased.

Figure 5: Nickel Surface Comparator, 16BL 3-D Drawing and Surface Profile [Ra=0.45 µm, εFp=1.77 µm] (Top) and 16G 3-D Drawing and Surface Profile [Ra=0.39 µm, εFp=1.64 µm] (Bottom)


Figure 6: Silicon Wafer with DRIE etch (left) and Silicon Wafer with XeF2 etch (right)

NICKEL SURFACE COMPARATOR - MILLED The next type of surface machining that was available on the nickel surface comparator was milling. The smallest height of a milled surface available was 1.6 µm. As shown in Table 1, the average roughness value for this sample was equal to 1.22 µm. This value was lower than the average roughness of the ground surface with a 1.6 µm roughness height. For this milled surface, the εFp value equaled 5.05 µm, which was also smaller than that of the ground surface with a roughness height of 1.6 µm.

SILICON MICROCHANNELS While it was possible to use the profilometer to obtain a surface profile and roughness parameters for the silicon wafer that had been etched with KOH, it was not possible to use the profilometer on the silicon wafers etched with XeF2 or deep reactive ion etching. The silicon wafer etched with XeF2 had tiny serpentine microchannels that were not straight or long enough to examine with the profilometer. The wafer that had been etched with DRIE couldn’t be examined with the profilometer due to the localized damage that would result. The KOH wafer was examined, and it was found that the Ra value was 0.13 µm and the εFp value was 0.34 µm. Table 1 depicts the surface roughness parameters calculated for the

Figure 7: Copper Capillary Tube, magnified 450x

surface etched with KOH. Three dimensional photographs were obtained for the silicon wafers etched with XeF2 and DRIE, and are shown in Fig. 6. CAPILLARY TUBES The three capillary tubes that were milled open were examined using the VHX-500 digital microscope. The brass and copper capillary tubes had a larger diameter of 1.067 mm

Figure 8: Copper Capillary Tube, magnified 450x

with added color and height

Figure 9: Brass Capillary Tube, magnified 450x

with added color and height


and the stainless steel capillary tube had a diameter of 0.62 mm. These samples had not been milled deeply enough to allow for examination with the profilometer, yet despite the lack of a surface profile to perform roughness parameter calculations, the capillary tubes were examined under the microscope. The stainless steel and copper capillary tubes looked to have similar surface roughness, but the brass capillary tube had more evident roughness peaks. Figure 7 displays the interior of the copper capillary tube as photographed with the digital microscope and Fig. 8 displays the same photograph but with added color and height to enhance visualization of the surface roughness. Figure 9 shows a photograph acquired from the microscope of the brass capillary tube, with enhanced color and height to show the difference in the surface roughness. From these photographs, it is evident that the brass capillary has more prominent peaks than the other two capillary tubes.

SURFACE ROUGHNESS IN FLUID FLOW A companion paper by Brackbill and Kandlikar [11]

examines and further confirms the effect of surface roughness parameters on the friction factor for fluid flow. In this experiment, three surfaces were used for analysis. The first surface was a smooth lapped surface. The two other samples

were surface ground, one with a 60 grit grinding wheel and the second with a 100 grit grinding wheel. This paper also discusses the new roughness value proposed by Kandlikar et al. [1]. Brackbill and Kandlikar [11] noticed that the parameter εFp

was more representative of the sand grain roughness in Nikuradse’s experiments than the average roughness parameter.

DISCUSSION The roughness parameter values calculated are shown in Table 1 for all the surface roughness samples investigated. It is interesting to note that surfaces resulting from different machining processes or etches could have a similar average roughness value but have values that do not match for εFp. For example, the average roughness value for the silicon wafer etched with KOH and the 8G sample of the nickel surface comparator are the same, at 0.13 µm. Though the two surfaces share an average roughness value, the values of εFp for the two surfaces differ. For the silicon wafer etched with KOH, the εFp value is 0.34 µm, and for the 8G nickel surface comparator surface εFp is equal to 0.58 µm. The two surfaces have the same average roughness values, yet the difference in the values of εFp is 0.24 µm. For fluid flow applications, the εFp value is more representative of the effect of the surface features on the fluid flow, and provides a more accurate model of the surface

Figure 10: Relationships between Ra and εFp values for surface roughness samples


topography than the currently accepted average roughness parameter. Brackbill and Kandlikar [11] confirm this in their paper. Using a new constricted diameter calculated using the proposed roughness parameter εFp, they calculated the friction factor of microscale flows. It was found that these theoretical results more accurately predicted the friction factors experimentally determined than if a non-constricted diameter had been used. A chart of the values of Ra and εFp calculated for all the surfaces examined is shown in Fig. 10. From looking at this chart, another example of two surfaces that share a common average roughness value but have unique values for εFp is evident between the 63M surface of the nickel surface comparator and the stainless steel milled surface. The average roughness of the 63M nickel comparator surface is 1.21 µm and for the stainless steel milled surface, it is 1.20 µm. The εFp values for these two surfaces shows that the two surfaces aren’t as alike as the average roughness value implies; the εFp for the 63M nickel comparator surface is 5.05 µm and for the stainless steel milled sample it is only 4.27 µm. Another example where the average roughness parameter portrays an inaccurate representation of surface roughness is evident from a comparison between the copper ground surface and the stainless steel flycut surface. The copper ground surface has an average roughness equal to 0.31 µm, and the stainless steel flycut surface has a similar Ra value of 0.3 µm. However, the εFp value for the copper ground surface is higher than that of the stainless steel. The εFp value for the stainless steel flycut surface is 1.07 µm while that of the copper surface ground sample is 1.34 µm. This trend repeats itself with other surfaces that have been examined, further proving that the εFp value would provide better correlations between surface roughness and fluid flow than the currently accepted surface roughness value. CONCLUSIONS The average roughness value, while commonly used in fluid flow applications, is not adequate for characterizing surface roughness. A surface that has many deep pits but is otherwise smooth could have a similar average roughness value as a surface that has a low uniform roughness, such as sandpaper. Kandlikar et al. [1] propose the use of a new surface roughness parameter, εFp. This value is equal to the distance between the floor mean line and the peak value of the surface profile. The samples examined were of practical interest for microfluidics applications; the materials, microfabrication techniques, and machining processes employed to create the surface roughness samples examined are often used to fabricate minichannels, microchannels, and capillary tubes. When both the average roughness and εFp parameters were calculated for various surfaces examined in this paper, it was evident that the value of εFp is often greater than that of the average roughness. It was also noticed that many scenarios arise where the average roughness of two surfaces can be similar while the εFp values may differ greatly. Since the εFp parameter is more indicative of the height of the surface roughness, it better models the obstructions the fluid flow encounters. Thus, the εFp parameter would provide a more accurate parameter for modeling the effects of surface roughness on fluid flow.

REFERENCES [1] Kandlikar, S.G., Schmidt, D., Carrano, A.L., and Taylor,

J.B., “Characterization of Surface Roughness Effects on Pressure Drop in Single-Phase Flow in Minichannels and Microchannels.” Phys. Fluids 17, 100606 (2005).

[2] Taylor, J.B., Carrano, A. L., and Kandlikar, S. G., 2005, “Characterization of the effect of surface roughness and texture on fluid flow – Past, present, and future,” 3

rd

International Conference on Microchannels and Minichannels, ICMM2005, Jun 13-15 2005, Anonymous American Society of Mechanical Engineers, New York, NY 10016-5990, United States, Toronto, ON, Canada, PART A, pp. 11-18.

[3] Darcy, H., Recherches experimentales relatives au movement de l’Eau dans les Tuyaux, Mallet-Bachelier, Paris, 1857.

[4] Fanning, J.T., A Practical Treatise on Hydraulic and Water Supply Engineering, Van Nostrand, New York, 1877. Revised ed. 1886.

[5] Nikuradse, J., “Forschung auf dem Gebiete des Ingenieurwesens”, Verein Deutsche Ingenieure, Vol. 4, pp. 361, 1933.

[6] Colebrook, F. C., “Turbulent flow in pipes, with particular reference to the transition region between the smooth and rough pipe laws,” J. Inst. Civ. Eng., Lond., 11, pp.133-156, 1939.

[7] Moody, L.F., Friction factors for pipe flow, ASME Trans. 66 (1944) 671-683.

[8] Sundararajan, S., Chandrasekaren, S., and Check, J., 2005, “The Effect of Anisotropic Wet Etching on the Surface Roughness Parameters and micro/nanoscale Friction Behavior of Si(100) Surfaces,” Sensors and Actuators A (Physical), 121(1), pp. 121-30.

[9] Chen, S., Lin, H., and Yang, C., 2000, “Surface Roughness Measurement on Microchannels by Atomic Force Microscopy using a Bent Tapered Fiber Probe,” Review of Scientific Instruments, 71(10) pp. 3953-3954.

[10] Montfort, F., Emery, Y., and Solanas, E., 2006, “Surface roughness parameters measurements by Digital Holographic Microscopy (DHM),” Third International Symposium on Precision Mechanical Measurements, Aug 2-6 2006, Anonymous International Society for Optical Engineering, Bellingham WA, WA 98227-0010, United States, Xinjiang, China, 6280 I, pp. 62800.

[11] Brackbill, T.P., and Kandlikar, S.G., "Effects of low uniform relative roughness on single-phase friction factors in microchannels and minichannels", Proceedings of the International Conference on Nanochannels,

Microchannels, and Minichannels ICNMM2007-30031, 2007.

[12] Brackbill, T.P., and Kandlikar, S.G., “Effect of Triangular Roughness Elements on Pressure Drop and Laminar-Turbulent Transition in microchannels and minichannels,” Proceedings of the International Conference on Nanochannels, Microchannels, and Minichannels ICNMM2006-96062, 2006.

[13] Chivers, T.C., 2002, “The Influence of Surface Roughness on Fluid Flow through Cracks,” Fatigue and Fracture of Engineering Material and Structures, 25(11) pp. 1095-102.


[14] Kandlikar, S.G., Joshi, S., and Tian, S., 2003, “Effect of Surface Roughness on Heat Transfer and Fluid Flow Characteristics at Low Reynolds Numbers in Small Diameter Tubes,” Heat Transfer Engineering, 24(3) pp. 4-16.

[15] Schmitt, D., Kandlikar, S.G., Effects of repeating microstructures on pressure drop in rectangular minichannels, ASME Paper No. ICMM2005-75111, Third International Conference on Microchannels and Minichannels, Toronto, Canada, 2005.

[16] Sundararajan, S., Bhushan, B., Namazu, T., Isono,, Y., Mechanical property measurements of nanoscale structures using an atomic force microscope, Ultramicroscopy 91 (2002) 111.

[17] Tristan Colomb, Etienne Cuche, Florian Charriere, Jonas Kuhn, Nicolas Aspert, Frederic Montfort, Pierre Marquet, and Christian Depeursinge, “Automatic procedure for aberration compensation in digital holographic microscopy and applications to speciment shape compensation,” Appl. Opt. 45, 851-863 (2006).


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