Validation of a Second-Order Slip Flow Model in Rectangular Microchannels

Figures & data

FIG. 1 Experimental setup for the measurement of gaseous microflows.

FIG. 2 Typical example of volume flow rate measurement.

FIG. 3 (a) Top view of the microchannels etched in a silicon wafer (b) and front view of the wafer with its outer connections.

TABLE 1 Characteristics of the tested microchannels

Wafer n°	1	2	3	4	Uncertainty
Number of channels	1	45	380	575	—
Depth 2h (μ m)
Measured	4.48	1.84	1.15	0.541	0.1
Kept	4.48	1.88	1.16	0.545	—
Width 2b (μm)	51.6	21.2	21	50	0.3
Length L (μm)	5000	5000	5000	5000	10
Aspect ratio a	0.087	0.087	0.055	0.011	—

FIG. 4 Range of outlet Knudsen numbers for the experimental data.

FIG. 5 Theoretical and experimental mass flow rates. Wafer n°1, 2h = 4.48 μm, T = 294.2 K. a) gas: N₂, 0.002 ≤ Kn _o ≤ 0.008, P _o = 1.9 · 10⁵ Pa; b) same conditions, comparison between plane and rectangular models; c) gas: N₂, 0.005 ≤ Kn _o ≤ 0.018, P _o = 0.82 · 10⁵ Pa.

FIG. 6 Theoretical and experimental mass flow rates. Wafer n°2, 2h = 1.88 μm, T = 294.2 K. a) gas: N₂, 0.01 ≤ Kn _o ≤ 0.017, P _o = 2 · 10⁵ Pa; b) gas: N₂, 0.027 ≤ Kn _o ≤ 0.053, P _o = 0.65 · 10⁵ Pa; c) gas: He, 0.029 ≤ Kn _o ≤ 0.053, P _o = 1.9 · 10⁵ Pa; d) gas: He, 0.05 ≤ Kn _o ≤ 0.1, P _o = 1.026 · 10⁵ Pa.

FIG. 7 Theoretical and experimental mass flow rates. Wafer n°3, 2h = 1.16 μm, T = 294.2 K. a) gas: N₂, 0.016 ≤ Kn _o ≤ 0.03, P _o = 1.9 · 10⁵ Pa; b) gas: N₂, 0.04 ≤ Kn _o ≤ 0.09, P _o = 0.65 · 10⁵ Pa; c) gas: He, 0.05 ≤ Kn _o ≤ 0.09, P _o = 1.9 · 10⁵ Pa; d) gas: He, 0.1 ≤ Kn _o ≤ 0.22, P _o = 0.75 · 10⁵ Pa.

FIG. 8 Inverse reduced flow rate (1/q*) in rectangular microchannels. Comparison of experimental data with 1st and 2nd order slip flow models. Π = 1,8; T = 294,2 K. Wafer n°2 (white), n°3 (grey), n°4 (black). Gas: N₂ (circle) and He (square).