1. Fluid Resistance: Micro-channels of the Valve Design
Bryan Sadowski
Kunal Thaker

2. Outline
Description of our current Micro-channel Layout in the Valve Design.
Basics of fluid flow in Micro-channels.
Calculations of pressure, velocity, flow rate, and resistance for our current design.
Effects of the valve on the fluid flow and pressure gradients.

3. Current Micro-channel Design
Dimensions (Rectangular Cross Section)
Width: 500 μm
Height: ~100 μm
Height: ~100 μm
Width: 500 μm

4. Fluid Path
Down: ~10.4 mm
Across: 25.6 mm
Up: ~0.2 mm
Across: 13.1 mm
Up: 10.2 mm
Assumed:
Pyrex is 10mm wide.
PDMS Thin Flex
Layer is 50 microns.
All other Layers:
100 microns.

5. Basics of Fluid Flow Q= Flow Rate= A*(vbar) A= Cross sectional Area
vbar= Average velocity of the fluid
Bernoulli’s Equation (zero viscosity fluids)
P1+ (1/2)pv12 + pgy1= P2+ (1/2)pv22 + pgy2
P= Pressure
p= Density of Fluid
v= Average velocity of the fluid
g= gravity
Fluid Flow 1 2

6. Basics of Fluid Flow Fluidic Resistance = R= ΔP/Q [(N*s)/m5]
R(circular cross section)= 8μL/(πr4)
μ= Fluid Viscosity= 0.01 g/sec*cm
L= Length of channel
r= Radius of channel
R(Rectangular cross section)~ 12μL/(wh3)
w= Width of the channel
h= Height of the Channel

7. Basics of Fluid Flow Reynolds number= Re= (pvDh)/μ
Dh(Circle)=Diameter
Dh(Rectangle)=2wh/(w+h)
p(Water)= density=1 g/cm3
Assumed Fluid Flow Rate based on Fluid velocity
Based on literature search
1500 cm/minute= 2.5 E5 μm/sec
1.25 E 10 μm3/sec= cm3/sec=12.5uL/sec
1 Torr= Pa

8. Calculations Fluid Down the Reservoir (D=0.4 cm, A=0.126 cm2)
Length= 1.04 cm
v~0.1 cm/sec
R= g/sec*cm4
Re= 4
ΔP= g/cm*sec2= Pa
Fluid Across the Bottom Fluid Layer
w= 500 μm, h ~100 μm, A= 5.0 e-4 cm2
Length~2.56 cm
v= 25 cm/sec
R=6.144 E 6 g/sec*cm4
Re= 41.7
ΔP= g/cm*sec2=7680 Pa

9. Calculations Fluid up the Interconnect
w= 1000 μm, h= 1000 μm, A= 0.01 cm2
Length= 200 μm
v= 1.25 cm/sec
R= 24 g/sec*cm4
Re= 12.5
ΔP= 3 g/cm*sec2=0.3 Pa
Fluid Across the Top Fluid Layer
w= 500 μm, h ~100 μm, A= 5.0 e-4 cm2
Length~ 13.0 mm
v= 25 cm/sec
R= 3.12 E7 g/sec*cm4
Re= 41.7
ΔP= g/cm*sec2=3900 Pa

10. Calculations Fluid Through the Valve Opening
w= 500 μm, h ~20 μm, A= 1.0 e-4 cm2
Length~ 100 μm
v= 125 cm/sec
R= 3 E6 g/sec*cm4
Re= 48.1
ΔP= g/cm*sec2=3750 Pa
Fluid Up the Reservoir (D=0.4 cm, A=0.126 cm2)
Length= 1.02 cm
v~0.1 cm/sec
R= g/sec*cm4
Re= 4
ΔP= g/cm*sec2= Pa

11. Final Results 1.25 E 10 μm3/sec= 0.0125 cm3/sec
Total Pressure Gradient:
~50430Pa~378 Torr
Pressure Gradient at the Valve:
3750 Pa~28 Torr
Fluid Flow Rate
1.25 E 10 μm3/sec= cm3/sec
Total Cycle Time:
~21.2 seconds