Question

Assume that you are using a piezoelectric material to build a micro/MEMS actuator beam in order to pick up a red-blood cell (with mass of ~1picogram or 10-12grams). If the dimensions of this actuator beam are length=100µm, width=10μm, and thickness=1μm, what is the minimal voltage you need to apply to this piezoelectric actuator in order to pick up the red-blood cell? Please write down all your assumptions used to estimate the voltage required.

Answer 1

Answer:

Assume that you are using a piezoelectric material to build a micro/MEMS actuator beam in order to pick up a red-blood cell (with mass of ~1picogram or 10-12grams).

Mass = 1 picogram or upto 10^-12 grams

Length = 100 um

Width = 10 um

Thickness = 1um

we have to see the specification of sensor MEMS (Micro Electro Mechanical Sensos)

Formula Relating pressure , voltage and few other parameters

p = C 33 * CO * V/C kt *d 33*t)...........(1)

Where,

P= Pressure output

C33 = relative dielectric

CO = Premitivity in vacuum

V = voltage from piczoelectric sensor

kt = coupling factor,

d33 piezoelectric constant

t = thickness of piezoelectric layer

first let's calculate force by using the info so

F = m.g

F = 0.012 *10

F = 0.012 N .........(2)

Now we know

P = F/A ..............(3)

So to calculate area we will use above given information

Area = length * width

Area = 100 * 10^ - 6 * 10 * 10 ^-6

Area = 10 ^ - am^2.............(4)

Now putting values from equation .......(2)

P = 0.12 *10^ a

P = 12 * 10^ 7 pascal ..............(5)

Now we have to assume different values as per the need

So ,

C³³ * CO = Electric Permitivity

But electrical primitivity of Blood can be different at different frequencies a am taking frequency as 100 MHZ

Now

C33 *CO = 76.8

kt = 0.19

d33 = 2*10^ -12 C/N

t = 10^-6

so putting the all the values in equation one we get

V = 0.0059 * 10^ - 11 volts

The above value is calculated for m = 12 grams now you replace value of m = 1   picogram in equation.........(2)