1. Deflection of PDMS ENMA 490 October 16, 2003 Shawna Dean

2. Outline Used equations for deflection in rectangular area ‘Breaking pressure’, the minimum pressure that can cause a failure. Calculated with a range of parameters. Especially thickness, because it is our main variable for controlling what pressures we can use.

3. Deflection Equations and Variables Deflection: w =.00265P(ab)^ 2 /D D=Et^3/(12*(1-v)) Deflection for circular membrane: w = 3Pr 4 (1-v 2 )/(16Et 3 ) P: pressure E: elastic modulus v: poisson’s ration a and b: width and length of membrane r: radius FOR PDMS E (shear): 2.03 x 10 5 MPa v: 0.5

4. Tensile Strength and Breaking Pressure From the Polymer Data Handbook found a tensile range from 1.55-9 Mpa for PDMS, depending on how the polymer was cured during processing. This gives us an idea of the magnitude of stress we can not surpass. Otherwise the membrane will fail. What does this mean to us in terms of pressure? Strain equation for membranes: Strain=0.3081P(ab/t 2 ) oUsing this equation the ‘breaking pressure’ was found to have a magnitude of 1000MPa.

5. Calculations Thickness (microns) Target Deflection (microns) Resulting Pressure (Mpa) Resulting Pressure (atm) 50750.19151.89 50 0.12771.26 50400.10081.00 75 0.28722.835 75500.19151.89 75400.15321.512 100750.38303.780 100500.25532.52 100400.20432.016  The chart has several thickness coupled with targeted deflections to get several different pressures needed.  All calculations were assuming a square area, 500 x 500 microns.

6. Looking Forward All resulting pressures were less than the ‘breaking pressure’ making these dimensions plausible for use. Next steps: Relate pressure to flow rates. All the pressure where calculated so they are positive. We have assumed negative will have the same effect on deflection as positive. Is this true?