Wetted Perimeter

For laser micromachining, the cross-section area is rectangular, so the hydraulic diameter is equal to Dh=2WH/(W+H), where W and H are the channel width and channel height, respectively. On the other hand, the EMM process produces a trapezoidal cross-section. We can calculate the hydraulic diameter in Eq.14.2 by substituting the cross-sectional area and the wetted perimeter of this trapezoidal structure. The cross-sectional area of this structure is equal to the average of the top width a and bottom width b of the channel multiplied by the channel height H, or A = (a + b)H /2 , where the wetted perimeter will equal to a+b+2{H2+(1/4(a-b)2}-12. The Reynolds number, Re, can be calculated from

Where, v is the dynamic viscosity of the liquid. As stated in the Moody chart for the laminar flow regime, the relationship of the friction factor in laminar flow, and the Reynolds number is linear, f = Cf /Re, where Cf is the friction coefficient for the system. In this study, a simple analysis of the effect of the surface roughness generated by different fabrication techniques on friction coefficients within single channel devices was investigated.

14.4.3 Microchannel Fabrication

Simple single channel devices (Fig. 14.4) were laminated in 304 stainless steel for performing the analysis. The bottom end plate and top interconnect layer were machined from 3 mm thick sheet stock. One batch of the middle stainless steel laminae was machined by one-sided through-mask EMM. The important parts of the patterns were 3 mm diameter sumps and the microchannel. Channel widths and depths explored are shown in Table 14.2. These dimensions were verified by metallography after fabrication and testing of the microchannels. The EMM laminae were set to be machined in the transpassive regime of the electrochemical system to provide a smooth finish. The laser micromached laminae were patterned using a Nd:YAG laser (266 nm) with an average power of 300 mW, an effective spot size of 35 ^m and a frequency of 4.5 kHz. Each machined lamina was then diffusion bonded between the two thick end caps with mirror-like finishes (Ra = 0.2 |im). Both end caps were polished to provide extremely smooth surfaces for the bonded microchannel to minimise the effect of sidewall friction. Details of the fabrication procedures are given elsewhere (Wattanutchariya et al. 2003).

The bonded microchannels were pressure drop tested at various flow rates in the laminar flow regime. According to Wu and Little (1983) and Peng et al. (1994) the transition zone from laminar flow to turbulent flow in microchannels occurs much earlier than conventional values. They reported that for different test devices with hydraulic diameters ranging from 0.1 to 0.3 mm, the transition zone varies from Reynolds numbers of 200 to 900. In this study, the maximum Reynolds number was kept to no more than 200, which was still in the laminar flow regime.

Table 14.2. Dimensions and theoretical friction coefficients of experimental channels. Theoretical friction coefficients are from Shah and London (Shah and London 1978)

Channel No.

Machining Method

Width (^m)

Depth (|lm)

Cf

1

Laser

225.4

225.4

78.2

12000

116.1

67.7

2

Laser

319.3

319.3

77.2

12000

124.3

73.5

3

Laser

474.1

474.1

72.3

12000

125.5

80.0

4

Laser

563.8

563.8

74.3

12000

131.2

81.7

5

Laser

678.4

678.4

74.3

12000

133.9

83.8

6

Laser

1037

1037

77.2

12000

143.4

87.3

7

EMM

277.2

162.8

76.2

12000

106.3

62.8

8

EMM

372.2

306.8

74.3

12000

119.9

72.0

9

EMM

507.7

454.2

74.3

12000

127.6

80.0

10

EMM

591.3

510.5

75.3

12000

130.3

76.0

11

EMM

656.2

656.2

78.2

12000

139.7

82.9

12

EMM

1296.3

1111.1

73.4

12000

133.7

Microchannel layer

Microchannel layer

©

©

Fig. 14.4. Schematic of a microchannel layer and end caps

14.4.4 Results

To obtain the microchannel dimensions, metallography was performed on the test devices. Fig. 14.5 and Fig. 14.6 represents the cross-section views of the diffusion bonded test devices of channel number 3 and 9, which were fabricated by laser micromachining and by electrochemical micromachining respectively. Fig. 14.7 shows a comparison of the theoretical and experimental friction coefficients for the set of microchannels from which the channels in Fig. 14.6 came. A summary comparison of the theoretical and experimental friction coefficients are shown in Fig. 14.8 as a function of aspect ratio.

Fig. 14.5. Laser Micromachining;

100

95

90

<u

85

<>

¡r

80

e

o

75

o

o

70

Ll_

65

60

Laser(Theory)

50 100 150

Reynolds Number

Fig. 14.7. Friction coefficient as a function of Reynold's number for channels 3 (aspect ratio 7:1) and 9 (aspect ratio 6:1). The theoretical friction coefficients happen to coincide for these two channels

From the results, the friction coefficients of both laser-machined channels and electrochemically-machined channels were found greater than the corresponding theoretical values and the differences from theory are significantly greater for laser-machined channels. In Fig. 14.8, at 2:1 aspect ratio, the friction coefficient of the laser-machined microchannel differs by about 40% from that of the electrochemically-machined microchannel. As the aspect ratio of the microchannels increases, the difference in friction coefficient decreases generally and when the aspect ratio reaches 9:1, the value of friction coefficient becomes almost the same. This provides some evidence that the machining method does play a significant role in MECS device performance at lower aspect ratios. Lower aspect ratio features produced by methods yielding higher surface roughnesses will result in increased flow friction causing the need for greater pumping powers. Based on this analysis, it would seem that this impact on fluid flow behavior in microchannels is directly related to the end wall surface roughness of the microlaminated microchannels. Further, this particular study indicates that the effect of the machining method in microlamination is no longer significant if the aspect ratio of the microchannel is greater than about 9:1.

120

100

"c o

80

it=

O

60

c

o

o

40

LL

20

8 12 Aspect Ratio

Fig. 14.8. Average friction coefficient and aspect ratios of the microchannels

It is also interesting to note that the difference between the theoretical and experimental values for the friction coefficient in the electrochemically-machined channels is minimal below an aspect ratio of about 8:1 but then increases significantly beyond this point. This phenomenon can be explained by noting that at low aspect ratios, where the end walls have strong influence, the surface roughness of end walls dominates pressure drop across the channel. Since EMM is known to produce perhaps the best surface finish of all non-traditional machining processes, the good agreement between the experiment and theory in those channels at low aspect ratio is not surprising. The deviation from theoretical friction coefficient at higher aspect ratio is explained in Fig. 14.9. Investigation of the higher aspect ratio channels showed a slight deflection in the sidewalls of these channels resulting in a decrease in the cross-section of the channels. This suggests that at aspect ratios above 10:1, sidewall deflection appears a more dominant constraint to aspect ratio than machining method. It is interesting that this type of shape variation appeared even though the thickness of the sidewall end plates was increased significantly to circumvent this problem. It is anticipated that this type of fin warpage behavior will become more pronounced at higher aspect ratios especially inside of spatially-intensified MECS devices where fin thicknesses will be more on the order of microchannel heights. Therefore, the effect of patterning methods on end wall surface roughness should be considered in the design and fabrication of microlaminated MECS devices with low aspect ratio features.

Fig. 14.9. Cross section of channel number 12

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