1. Mathematical Simulations of Heat Transfer and Fluid Dynamics in a Microfluidic Calorimeter with Integrated Thin-film Thermopiles G. G. Nestorova 1, Niel D. Crews 2, and E. J. Guilbeau 1 1 Center for Biomedical Engineering and Rehabilitation Science, 2 Institute for Fabrication and Manufacturing Louisiana Tech University, Ruston, Louisiana
Since the reference junctions are maintained at a constant temperature, the temperature difference depends only on the temperature increase of the measuring junction. When the reference junctions are not positioned over a heat sink, some of the reaction heat dissipates towards the reference junctions reducing the temperature difference between both junctions and as a result the magnitude of the thermoelectric output.
Abstract
Experimental results were obtained using a microfluidic device that has two inlets, one outlet, and 100µM channel height. The upper channel wall of the microfluidic device was fabricated using 1mm thick glass while the lower channel wall was 0.17mm thick glass cover slip. The thermopile was fabricated on a 125µM thick Kapton tape. Glucose oxidase was immobilized over the lower channel wall of the device within the measuring junctions of the thermopile. The enzyme was conjugated to biotin and immobilized to a streptavidin coated glass cover slip. The flow rates through the two inlets were adjusted such that the fluid through Inlet 1 hydrodynamically focuses the fluid entering the device via Inlet 2 down the centerline of the device. Glucose was introduced via an injection valve into the fluid flowing through Inlet 2 (Figure 2). A thin-film antimony/bismuth thermopile detected the heat of the enzymatic reaction and converted it to electric signal that was recorded by a digital nanovoltmeter. The output of the nanovoltmeter was processed and analyzed using LabVIEW SignalExpress software and baseline transformed using Mathlab.
We developed mathematical model that simulates the reaction kinetics between glucose and glucose oxidase in a microfluidic calorimeter with integrated antimony/bismuth thin-film thermopile. The predicted thermopile response was validated with experimental results. A thin-film thermopile attached to the external surface of the lower channel wall measures the dynamic change in temperature between the measuring and the reference junctions of the sensor caused by the enzymatic reaction.
Overview
Materials and Methods
The mathematical model predicts the output voltage change of a thin-film thermopile attached to the lower channel wall of a microfluidic device. The model assumes that the solution is well mixed, the mass flow rate and the physical properties of the materials and the solution are constant and the reaction occurs at the surface of the coverslip. Other assumptions that are included in the model are homogeneous heat generation and negligible radial and axial mass diffusion. Energy balance was performed for the fluid flowing within the channel, the channel walls adjacent to the reaction zone, the thermopile support, and the protective acrylic tape attached to the thermopile (Figure1).
Figure 3. Temperature Change for each Component of the System
Figure 4. Predicted Thermopile Response
Figure 2. Schematic diagram of the experimental set-up
Results
Figure 5. Thermopile Response when the Reference Junctions were in Contact with an Aluminum Heat Sink
Figure 6. Thermopile Response when the Reference Junctions were not Controlled
The results for the predicted thermopile response are presented in Figure 3. The temperature change within each layer of the device is presented in Figure 4. he model predicts that the temperature change between the junctions of the thermopile is 0.4mK and the peak height of the thermopile response is 2.8µV. The experimental results measured 2.4μV signal response (Figure 5). The duration of the predicted response was 230 seconds while the duration of the actual response was 180 seconds. Figure 6 show the response of the sensor when the thermopile was not in contact with a heat sink. The experiments were performed using the same device and sensor.
Conclusions
Figure 1. Side View schematic of microfluidic device
Five ordinary differential equations that predict the change of the temperature within each layer of the device were developed and solved using Radau numerical integration method for stiff systems using Mathcad.
We have developed a mathematical model that predicts the enzymatic reaction kinetics between glucose and glucose oxidase as well as heat transfer in a microfluidic calorimeter with integrated thin-film thermopiles.
The values of the predicted and the experimental values for the peak height of the thermoelectric signal confirm the accuracy of the mathematical model to simulate heat transfer and temperature change in a microfluidic device.
Discussion
The predicted thermopile response correlates with the experimental results. The mathematical model predicted that the peak height of the thermopile response is 2.8μV while the experimental results confirm that the signal response was 2.4μV. The model assumes that there is no lateral heat dissipation towards the reference junctions of the thermopile. In the experimental set up, the aluminum heat sink absorbed the heat that dissipated towards the reference junctions of the thermopile and provided constant temperature control.
Acknowledgements
We acknowledge Mr. Varun Kopparthy for his help with the fabrication of the thermoelectric sensor.
For further information contact or