# Design, Modeling, and Analysis of Piezoelectric-Actuated Device for Blood Sampling
## 4 Results of the Micropump Simulation
### Flow Analysis with Modified Microneedle  
There are many ways to enhance extracted blood volume. The micropump can be actuated for longer duration or at higher voltage. Both these operations would demand more power. Instead, attention was focused on avoiding spread of the extracted volume. This can be achieved by channelizing the extracted volume towards the biosensor location. Accordingly, microneedle attachment with the pump chamber was modified by:  
1. Extension of the microneedle into the pump chamber,
2. Provision of the orifice (hole) towards biosensor location, and
3. Filleting of microneedle tip. Microneedle was modified by extending the microneedle into the pump chamber and providing a hole of 20-\(\upmu\)m diameter on the microneedle surface above the pump chamber wall. Additionally, a fillet of a 10-\(\upmu\)m radius was provided at the top of the microneedle for a smooth flow of extracted blood from the microneedle to the pump chamber, as detailed in Figure 3b. The fluid, after entering from the microneedle to the pump chamber, was allowed to flow only towards the biosensor, instead of spreading in all directions. Simulations were carried out with two extended lengths (0.25 mm and 0.5 mm, respectively). Flow characteristics were compared with the flushed microneedle. The selection of extended length was done so as to create appropriate obstruction in the flow path to channelize sufficient volume. With an extended length of the microneedle, flow lines can be seen directing towards the biosensor location through the hole provided for the purpose, as shown in Figure 4b,\(c\). Table 2 summarizes velocity and pressure in all three cases. Flow velocity was observed to enhance by 1.5 and 1.86 times with 0.25-mm and 0.5-mm extended length of the microneedle, respectively. The benefits obtained in terms of flow channelization can be seen clearly in Figure 4b,\(c\). This also reduced built-up pressure in the pump chamber by half and less than half, respectively. In addition to channelizing the flow, it served to avoid stagnation of return flow due to the orifice effect, reducing the chaotic flow at the microneedle-pump interface. The flow in the microneedle was fully developed (parabolic profile) and uniform through the orifice. Then, the flow volume through the orifice and the filleted area together were at least half of the extracted volume through the microneedle as compared to one-seventh in the case of the flushed microneedle. The difference in velocity of the blood diverting due to the orifice and that moving up in the pump chamber with the 0.25-mm extended length of the microneedle can be seen clearly in Figure 4b. Volume flow rate at the microneedle (\(f_{m}\)) and orifice (\(f_{o}\)) were calculated as follows:  
\[f_{m}=(\pi/4)\;(2d_{o})^{2}\;(2/3)\;U_{m} \tag{8}\]  
\[f_{o}=(\pi/4)\;(d_{o})^{2}\;U_{o} \tag{9}\]  
where \(d_{o}\) is the orifice diameter, \(U_{o}\) is the velocity at orifice, and \(U_{m}\) is the maximum velocity  
The volume flow rate obtained with the 0.25-mm extension of the microneedle was slightly less than half. To further check the advantage of obstruction in the flow path, extension length was increased to 0.5 mm, resulting in more than half the volume flow rate at the biosensor. Figure 5a shows the plot of flow velocity with time. After a short initialization time, flow was seen accumulating and reached to almost a constant average velocity of 5.6 mm/s at around 1600 \(\upmu\)s. The volume flow rate available at the biosensor was 1.758 \(\upmu\)L/s. The plot clearly shows that the actuation time required was quite less. \[f=AU \tag{10}\]  
where \(f\) is the volume flow rate, \(A\) is the biosensor area (0.314 mm\({}^{2}\)), \(U\) is the velocity, and \(f=0.314\) mm\({}^{2}\)\(\times\) 5.6 mm/s = 1.758 \(\upmu\)L/s (with the 0.5-mm extended microneedle).