# Rapid Fabrication of Low-Cost Thermal Bubble-Driven Micro-Pumps

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Resistor Fabrication

#### 2.1.1. Single Material Resistor Design Optimization

#### 2.1.2. Laser Cutting of Resistors

#### 2.2. Microfluidic Fabrication

#### 2.3. Femtosecond UV Laser Beam Profile and Material Etch Rates

#### 2.4. Electrical Setup

#### 2.5. Imaging Setup

#### 2.6. Particle Tracking and Flow Rate Characterization

^{th}bin, a maximum velocity v${}_{m,k}$ is computed which is taken as an estimate of the flow profile at the bin’s midpoint x${}_{k}$. The set of points {x${}_{k}$,v${}_{m,k}\}$ is fitted to the theoretical profile of Equation (10) using the channel width (a), a horizontal shift ($\lambda $), and the overall height of the pseudo-parabola (${v}_{max}$) as adjustable parameters [40].

## 3. Results

#### 3.1. Electrical Signal Integrity

- A solid back copper ground plane is used to ensure that the ground is at a common voltage even with large currents flowing.
- Digital return currents from the Analog Discovery and gate drivers are separated from interfering with the analog return currents from the power MOSFETs. This is done by separate placement of components and traces on the PCB.
- A 27 $\Omega $ series gate resistor is used to “slow down” the power MOSFET turn on/off time to reduce gate ringing.
- Gate drivers with internal Miller Clamps are used to reduce capacitive ringing on turn off.
- Flyback Schottky diodes are used to minimize inductive ringing caused by connecting wires from the main power supply to the thin film resistors.
- Large bypass capacitors (100 $\mathsf{\mu}$F and 10 $\mathsf{\mu}$F) are used to maintain a steady supply voltage and provide large, transient current draws thus reducing transient spikes from the power supply.
- Smaller bypass capacitors (0.1 $\mathsf{\mu}$F and 10 $\mathsf{\mu}$F) are used to stabilize the supply voltage to the gate driver and mitigate high frequency voltage spikes in the power supplies.

#### 3.2. Temperature Sensing

#### 3.3. Open Reservoir vs. Confined Bubble Dynamics

#### 3.4. Thermal Bubble-Driven Micro-Pumps

## 4. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**TMP Thin Film Stack—(

**a**) illustrates the standard micro-fabrication thin film stack used in TMP resistors to heat ink which is based on thermal inkjet (TIJ) technology [21]. The stack is built on a silicon substrate followed by a thermal insulation layer, a resistive layer, a conductive layer, electrical passivation layers, and a cavitation plate. (

**b**) shows the simplified commercial thin film stack used in this study for rapid fabrication of TMP resistors.

**Figure 2.**Spline-Based Resistor Topology Optimization—illustrates the resistor design optimization process to minimize thermal stresses using the placement of spline knot points. (

**a**) design domain showing exploitation of symmetry in simulation region, (

**b**) computational mesh and finite element solution for the current density magnitude $\left|\right|\mathbf{J}\left|\right|$, and (

**c**) logscale contour plot of $\left|\right|\nabla \mathbf{J}\left|\right|$ used to define resistor fitness on optimized designs (sample spline knot points shown).

**Figure 3.**Resistor Fabrication Method and Cut Quality—depicts the laser cutting process and cut quality from both the Trotec fiber laser and femtosecond UV laser systems in a single line vector cut. CAD software, Autodesk Fusion 360, was used to generate a dxf file defining the resistor. (

**a**,

**b**) the FTO film was cut using the Trotec fiber laser with the following cut settings: power = 20%, speed = 0.71 mm/s (0.02% of max speed), PPI/Hz = 30,000, dpi = 500, and passes = 2. (

**a**) illustrates the cut quality from the Trotec fiber laser system. The positioning system lacks sufficient resolution to fully resolve the 250 $\mathsf{\mu}$m fillet on the resistor edges, but the dimensions of the resistor closely matched that of the dxf design. (

**b**) shows the 3D cut profile in which the cut width was 56.1 $\mathsf{\mu}$m with a depth of 0.59 $\mathsf{\mu}$m. (

**c**,

**d**) the FTO film was cut using the femtosecond UV laser with the following cut settings: power = 0.643 W (100%), repetition frequency = 250 kHz, fluence = 7.00 J/cm${}^{2}$, speed = 500 mm/s, and passes = 5. (

**c**) shows the cut quality from the femtosecond UV laser system. (

**d**) illustrates the 3D cut profile in which the cut width was 12.2 $\mathsf{\mu}$m with a depth of 0.75 $\mathsf{\mu}$m. FTO coated glass with a sheet resistance of 8 $\Omega $/sq and a film thickness of 340 nm was used.

**Figure 4.**Microfluidic Fabrication Processes—illustrates both laminate and controllable milling microfluidic fabrication processes. (

**a**,

**b**) show laminate processing in which a 58.42 $\mathsf{\mu}$m glue layer is laminated to both sides of a 200 $\mathsf{\mu}$m thick acrylic sheet, and the channel and reservoir layers are defined through laser cutting. (

**c**) shows controllable milling on the femtosecond laser cutter system to produce 2.5D microfluidic geometries. Unlike laminate processing, a single acrylic substrate is used upon which the channel and reservoir is defined. (

**d**) shows a close up of the milled channel region.

**Figure 5.**Femtosecond UV Laser Characterization—illustrates laser and etch rate characterization. (

**a**) shows the measured beam profile at the lens (which is equivalent to at laser focal plane without the 125 mm galvo focusing lens). The beam diameter at the focal plane was calculated to be 8.83 $\mathsf{\mu}$m from Gaussian beam theory. (

**b**) shows the pulse energy as a function of laser repetition frequency. (

**c**) shows the etch rate characterization test samples in which 300 × 300 $\mathsf{\mu}$m${}^{2}$ squares were etched using a cross-hatch line spacing of 3 $\mathsf{\mu}$m. (

**d**) describes the etch rate as a function of laser repetition frequency enabling controllable milling of micro-channels. (

**e**,

**f**) highlights the ability to fabricate 2.5D micro-structures through controllable milling. (

**e**) shows a repeating tapered micro-pillar array of diameter D = 28.6 $\mathsf{\mu}$m inside a 510 × 126 $\mathsf{\mu}$m${}^{2}$ channel. (

**f**) shows an integrated step height 171 $\mathsf{\mu}$m from the top channel surface inside a 306 × 274 $\mathsf{\mu}$m${}^{2}$ channel demonstrating 2.5D milling capability.

**Figure 6.**Particle Tracking Process—describes the particle tracking process. (

**a**) shows a dry milli-channel of cross-section A = 515 × 315 $\mathsf{\mu}$m${}^{2}$ and length L = 13.268 mm with a 300 × 700 $\mathsf{\mu}$m${}^{2}$ TMP resistor placed 1027 $\mathsf{\mu}$m from the reservoir edge. (

**b**) shows neutrally buoyant micro-spheres with a diameter of D = 27–32 $\mathsf{\mu}$m in a channel filled with water. A MATLAB implementation of the interactive data language, IDL, particle tracking software is used to mark particles (

**c**) and link particle movement into trajectories (

**d**). Particle trajectories are colored in accordance to average velocity in which the fastest moving particles (shown in yellow with a velocity of 19.2 $\mathsf{\mu}$m/pulse) are near the center of the channel while the slowest (shown in blue with a velocity of less than 1 $\mathsf{\mu}$m/pulse) are towards the walls.

**Figure 7.**Flow Rate Determination—illustrates the flow rate determination process. (

**a**) First, a large data set (2000–3000 tracked particles) of particle location and velocity is generated through the particle tracking process. (

**b**) Half of the particle tracks are randomly selected to form a subsample. (

**c**) The subsampled particle tracks are grouped into 25 bins of equal width. The number of bins, k, is chosen to ensure accurate sampling of the flow profile. (

**d**) For each k

^{th}bin, a maximum velocity v${}_{m,k}$ is computed which is taken as an estimate of the flow profile at the bin’s midpoint x${}_{k}$. The set of points {x${}_{k}$,v${}_{m,k}$} is fitted to the theoretical profile of Equation (10) using the channel width (

**a**), a horizontal shift ($\lambda $), and the overall height (${v}_{max}$) as adjustable parameters. The height of the pseudo-parabola fit is the ${v}_{max}$ of the given subsample. During optimization, we used an asymmetric price function: points below the theoretical curve were priced ten times less than points above the curve since points below the curve could result from insufficient data and artificially depress the sample profile. (

**e**) Steps (

**b**–

**d**) are repeated 200 times producing a distribution of ${v}_{max}$. The mean value of the distribution is taken as the final estimate of the maximum velocity and the half-width is taken as one standard deviation. (

**f**) The original scatter plot data are overlaid with the best-fit theoretical profile with error bounds.

**Figure 8.**TMP Resistor Surface Temperature—shows the temperature coefficient of resistance (TCR) and surface temperature measurements. (

**a**) illustrates TCR measurements for 3 resistors on separate FTO 8 $\Omega $/sq substrates to determine inter-sample uniformity. The TCR value for FTO 8 $\Omega $/sq substrates was 6.72 × 10${}^{-4}$± 5.37 × 10${}^{-6}$ [1/${}^{\circ}$C]. (

**b**) depicts the surface temperature of an R = 48.32 $\Omega $, 300 × 700 $\mathsf{\mu}$m${}^{2}$ FTO TMP resistor during a 8 $\mathsf{\mu}$s, 100 V heating pulse. A low pass Butterworth filter of order 12 with a half power frequency of 3.33 MHz was used to remove signal noise. Oscilloscope data was recorded at 2 GHz, with N = 64 sample averaging. Insets show stroboscopic images at t = 4 $\mathsf{\mu}$s, the onset of bubble nucleation, t = 5 $\mathsf{\mu}$s, and t = 5.5 $\mathsf{\mu}$s, full vapor layer formation. Once the vapor layer forms, the heat transfer coefficient is significantly reduced resulting in a change of slope at approximately t = 5.0 $\mathsf{\mu}$s denoted by the highlighted tangent lines. (

**c**) shows agreement between electrical and thermography measurements for the resistor surface temperature when fired in air with a 20 s, 6.5 V heating pulse. Electrical measurement data was filtered with a moving average.

**Figure 9.**Open Reservoir Femtosecond Resistor Characterization Inter-Device Reproducibility—illustrates the effect of voltage on the maximum bubble area for a 300 × 700 $\mathsf{\mu}$m${}^{2}$ FTO (8 $\Omega $/sq) resistor in water with a 250 $\mathsf{\mu}$m fillet and firing parameters as follows: pulse duration ($\tau )$ = 5 $\mathsf{\mu}$s, firing frequency (f) = 10 Hz, and resistance (R) = 44.8 $\Omega $. (

**a**–

**d**) Show the bubble evolution over time in which (

**e**–

**h**) show the calculation of bubble area using background subtraction image processing. (

**i**) Depicts the maximum bubble area as a function of applied voltage with inset (

**j**) showing the maximum bubble area at t = 12 $\mathsf{\mu}$s for V = 95 V. (

**k**) Illustrates the full time history of the bubble area during expansion, collapse, and rebound phases as a function of voltage. Stroboscopic imaging was performed using a 1 $\mathsf{\mu}$s exposure (“shutter”) time with a 500 ns light pulse for an effective 2 Mfps frame rate. N = 3 sample replicates were performed for each voltage level in which each sample is a different resistor.

**Figure 10.**Closed Channel Femtosecond Resistor Characterization Intra-Device Reproducibility—illustrates the effect of voltage on the maximum bubble area for a 300 × 700 $\mathsf{\mu}$m${}^{2}$ FTO (8 $\Omega $/sq) resistor confined in a 515 × 315 $\mathsf{\mu}$m${}^{2}$ U-shaped channel, as shown in Figure 6a, filled with water. The resistor has a 250 $\mathsf{\mu}$m fillet and firing parameters were as follows: pulse duration ($\tau )$ = 5 $\mathsf{\mu}$s, firing frequency (f) = 10 Hz, and resistance (R) = 45.9 $\Omega $. (

**a**–

**d**) Show the bubble evolution over time in which (

**e**–

**h**) show the calculation of bubble area using background subtraction image processing. (

**i**) Depicts the maximum bubble area as a function of applied voltage with inset (

**j**) showing the maximum bubble area at t = 8 $\mathsf{\mu}$s for V = 100 V. (

**k**) Illustrates the full time history of the bubble area during expansion and collapse phases as a function of voltage. Stroboscopic imaging was performed using a 1 $\mathsf{\mu}$s exposure time with a 500 ns light pulse for an effective 2 Mfps frame rate. N = 3 sample replicates were performed for each voltage level in which each sample is a different cycle of the same resistor.

**Figure 11.**Micro-Pump Flow Rate vs. Energy Analysis—shows the flow rate saturation behavior of thermal bubble-driven micro-pumps. A 300 × 700 $\mathsf{\mu}$m${}^{2}$ FTO 8 $\Omega $/sq TMP resistor of R = 45.9 $\Omega $ is placed 1027 $\mathsf{\mu}$m from the end of a length L = 13.268 mm channel of cross-sectional area A = 515 × 315 $\mathsf{\mu}$m${}^{2}$ as shown in Figure 6a. Firing voltage was varied from 98.50 to 112 V with a 5 $\mathsf{\mu}$s pulse duration corresponding to energies of 1055 to 1364 $\mathsf{\mu}$J/pulse. The firing frequency was 20 Hz. At the lower bound, the flow rate becomes 0 when applied energy no longer forms a vapor bubble; at the upper bound, the flow rate slightly increases with applied energy until the resistor burns out and fails.

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## Share and Cite

**MDPI and ACS Style**

Hayes, B.; Smith, L.; Kabutz, H.; Hayes, A.C.; Whiting, G.L.; Jayaram, K.; MacCurdy, R.
Rapid Fabrication of Low-Cost Thermal Bubble-Driven Micro-Pumps. *Micromachines* **2022**, *13*, 1634.
https://doi.org/10.3390/mi13101634

**AMA Style**

Hayes B, Smith L, Kabutz H, Hayes AC, Whiting GL, Jayaram K, MacCurdy R.
Rapid Fabrication of Low-Cost Thermal Bubble-Driven Micro-Pumps. *Micromachines*. 2022; 13(10):1634.
https://doi.org/10.3390/mi13101634

**Chicago/Turabian Style**

Hayes, Brandon, Lawrence Smith, Heiko Kabutz, Austin C. Hayes, Gregory L. Whiting, Kaushik Jayaram, and Robert MacCurdy.
2022. "Rapid Fabrication of Low-Cost Thermal Bubble-Driven Micro-Pumps" *Micromachines* 13, no. 10: 1634.
https://doi.org/10.3390/mi13101634