# Design, Modeling, and Analysis of Piezoelectric-Actuated Device for Blood Sampling

^{1}

^{2}

^{*}

## Abstract

**:**

^{®}simulations were performed on four quarter piezoelectric bimorph actuator (FQPB) at 2.5 volts. The modal and harmonic analysis were carried out with various load conditions for FQPB. The extended microneedle lengths inside the pump chamber showed improved flow characteristics. Enhanced volume flow rate of 1.256 µL/s was obtained at 22,000 Hz applied frequency at the biosensor location.

## 1. Introduction and Purpose of the Study

## 2. Physical Modeling of the Device

^{3}and a viscosity of 0.0035 Pa·s [25].

#### 2.1. Microneedle

#### 2.2. Biosensor

^{2}[27,28].

#### 2.3. FQPB Actuator

#### 2.4. Working Principle

^{E}is the elasticity matrix at the constant electric field, S is the elastic strain vector, e is the piezoelectric stress matrix, E is the electric field intensity vector, and ε

^{S}is the dielectric matrix at constant mechanical strain. Thus, in the piezoelectric actuator analysis, these coupled piezoelectric equations are solved numerically through the following finite element formulation [31]:

_{u}, M

_{u,}and K

_{u}are the damping, the mass matrices, and stiffness matrices, respectively; Q and F are the electrical and mechanical loads, respectively; and Φ and U are the electrical potentials and the displacement vectors, respectively. The dielectric conductivity and the piezoelectric coupling, are given by K

_{ØØ}, K

_{uØ}, respectively. The fluid-flow study is based on the momentum and continuity equations. It is assumed that blood flow is governed by Navier–Stokes equations [32,33]:

_{e}is the viscosity, t is the time, and P is the pressure. The software ANSYS

^{®}was used for solving the governing equations numerically using the finite volume method, as implemented in the software.

## 3. Finite Element Modeling of the Micropump

#### 3.1. Fluid–Structure Interaction (FSI)

#### 3.2. Boundary Conditions

#### 3.2.1. Opening Condition

#### 3.2.2. Wall Condition

#### 3.2.3. Symmetry Condition

#### 3.2.4. Interface Condition

#### 3.3. Mesh Independence Test for FQPB and Micropump

## 4. Results of the Micropump Simulation

#### 4.1. Static and Modal Analysis of the Actuator (FQPB)

#### 4.2. Flow Analysis with Flushed Microneedle

_{p}= V sin (2πft)

_{p}is the applied voltage, V = 2.5 V, f is the applied frequency (35,338 Hz), and t is the time.

#### 4.3. Flow Analysis with Modified Microneedle

- Extension of the microneedle into the pump chamber,
- Provision of the orifice (hole) towards biosensor location, and
- Filleting of microneedle tip.

_{m}) and orifice (f

_{o}) were calculated as follows:

_{m}= (π/4) (2d

_{o})

^{2}(2/3) U

_{m}

_{o}= (π/4) (d

_{o})

^{2}U

_{o}

_{o}is the orifice diameter, U

_{o}is the velocity at orifice, and U

_{m}is the maximum velocity

^{2}), U is the velocity, and f = 0.314 mm

^{2}× 5.6 mm/s = 1.758 µL/s (with the 0.5-mm extended microneedle).

#### 4.4. Flow Analysis at Reduced Actuation Frequency

## 5. Conclusions

- The design may be implemented as a wearable device. Considering advancements in the manufacturing of microfluidic systems, manufacturability should not be a problem.
- The design may be modified to accommodate more sensors for testing other diseases.
- The FQPB-based micropump with extended microneedle length inside the pump chamber brings the benefit of flow channelization towards the biosensor location, resulting in a reduction in applied voltage (2.5 V) and reduced operating frequency (22 kHz).
- The simulation results showed that 1.256 µL of the sample was collected at the biosensor in 1 s, which is more than the required volume.
- The designed device will be easy to use and may allow multiple samplings with a single replacement.
- The blood was collected in a closed chamber, thereby giving higher accuracy in comparison to the finger-stick, as well as preventing environmental contamination.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Schematic diagram of blood sampling device, (

**a**) design of wristwatch with micropumps, and (

**b**) detail representation of a piezoelectric micropump with FQPB actuator.

**Figure 2.**(

**a**) Meshing of the FQPB actuator with silicon diaphragm, (

**b**) meshing of the complete micropump, (

**c**) boundary conditions at various interfaces, (

**d**) mesh independency test of the actuator, and (

**e**) mesh independency test of the complete micropump.

**Figure 3.**Schematic diagram of (

**a**) flushed pentagonal microneedle and (

**b**) 0.5-mm microneedle extension with a hole.

**Figure 4.**Streamline plot (

**a**) with flushed microneedle, (

**b**) 0.25-mm extended microneedle, and (

**c**) 0.50-mm extended microneedle.

**Figure 5.**Velocity at biosensor location in the case of the 0.50-mm extended microneedle: (

**a**) applied frequency of 35,338 Hz, (

**b**) volume flow rate vs. applied frequency, and (

**c**) applied frequency of 22,000 Hz.

Materials | Properties | Value | |
---|---|---|---|

Piezoelectric | Piezoelectric charge constant (C/N) | d_{31} = d_{32} | ‒320 × 10^{−12} |

d_{33} | 650 × 10^{−12} | ||

Relative dielectric constant | ε | 3600 | |

Density (kg/m^{3}) | ρ | 7800 | |

Epoxy Glue | Module of elasticity (GPa) | 2.478 | |

Density (kg/m^{3}) | 1400 | ||

Stainless steel | Module of elasticity (GPa) | 200 | |

Density (kg/m^{3}) | 7700 | ||

Silicon | Module of elasticity (GPa) | 168.3 | |

Density (kg/m^{3}) | 2329 |

Microneedle Type | Velocity at Biosensor Location (mm/s) | Volume Flow Rate at Biosensor Location (µL/sec) | Max Pressure (MPa) |
---|---|---|---|

Flush type | 3 | 0.471 | 8 |

0.25 mm extended | 4.5 | 1.413 | 4 |

0.50 mm extended | 5.6 | 1.758 | 3 |

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**MDPI and ACS Style**

Haldkar, R.K.; Gupta, V.K.; Sheorey, T.; Parinov, I.A. Design, Modeling, and Analysis of Piezoelectric-Actuated Device for Blood Sampling. *Appl. Sci.* **2021**, *11*, 8449.
https://doi.org/10.3390/app11188449

**AMA Style**

Haldkar RK, Gupta VK, Sheorey T, Parinov IA. Design, Modeling, and Analysis of Piezoelectric-Actuated Device for Blood Sampling. *Applied Sciences*. 2021; 11(18):8449.
https://doi.org/10.3390/app11188449

**Chicago/Turabian Style**

Haldkar, Rakesh Kumar, Vijay Kumar Gupta, Tanuja Sheorey, and Ivan A. Parinov. 2021. "Design, Modeling, and Analysis of Piezoelectric-Actuated Device for Blood Sampling" *Applied Sciences* 11, no. 18: 8449.
https://doi.org/10.3390/app11188449