Micro-Pump Geometric Specifications

The micro-pump geometry is presented in terms of the length of the membrane ``L", in figure 5.15. This allows us to interpret the results using geometric similarity in determining the optimum pump dimensions.

The micro-pump is ideally placed in between two reservoirs. However, numerical simulation of such a system is difficult due to large reservoir size. Any finite size reservoir would require inflow and outflow numerical boundary conditions, and these must be carefully imposed, in order to avoid a preferred flow direction in the micro-pump. This difficulty is overcome by placing the micro-pump in between two symmetric micro-channel flow systems, where equal amount of liquid flow is maintained from top to bottom direction. Therefore, the flow conditions are symmetric and there is no net flow from one channel to another, when the pump is not actuated. We verified this by simulations.

  

Figure 5.16: Top: Deflection of the membrane y(x,t)=a sin(pi x/L) sin(omega t) Bottom: Loci of the valve tips y(t)= +-tanh(4 cos(omega t))

Oscillation of the membrane with a specified frequency $\omega$ and amplitude a excites the fluid within the micro-pump cavity. For our simulations we have used a=L/10, and $\omega=\frac{\pi c }{L}$,where c²= T/M, T being the uniform tension, and M being the mass per unit area of the membrane. The first-mode of vibration of the membrane is used to determine the position (See figure 5.16, top), velocity and the acceleration a function of time

The pump geometry is symmetric. Therefore, active pumping can not be achieved by only actuating the membrane. We have included inlet and exit valves, which open and close periodicly, in order to break the flow symmetry. The inlet and the exit valves are located at the mean height of y_o = 0.325 L from the membrane, and the position of the valves are specified as a function of time

The prescribed velocity of the valve tips are

The valve motion is designed to be close to a step function, oscillating between open and closed positions with finite velocity and acceleration. The gaps between the valve tips and the top wall of the micro-pump are 0.125L and 0.025L, during open and closed positions, respectively. The positions of the inlet and exit valves during a cycle of the micro-pump is presented in figure 5.16, (bottom). The phase difference between the inlet and the exit valves is $\pi$.