Fluid Resistance: Micro-channels of the Valve Design

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

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.

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

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.

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

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

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= 0.0125 cm3/sec=12.5uL/sec • 1 Torr= 133.3 Pa

Calculations • Fluid Down the Reservoir (D=0.4 cm, A=0.126 cm2) • Length= 1.04 cm • v~0.1 cm/sec • R= 16.56 g/sec*cm4 • Re= 4 • ΔP= 0.207 g/cm*sec2=0.0207 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= 76800 g/cm*sec2=7680 Pa

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= 39000 g/cm*sec2=3900 Pa

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= 37500 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= 16.23 g/sec*cm4 • Re= 4 • ΔP= 0.202 g/cm*sec2=0.0202 Pa

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

Fluid Resistance: Micro-channels of the Valve Design

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