# Microwave dielectric heating of drops in microfluidic devices

Original entry: Donald Aubrecht, APPHY 226, Spring 2009

"Microwave dielectric heating of drops in microfluidic devices"

David Issadore, Katherine J. Humphry, Keith A. Brown, Lori Sandberg, David A. Weitz, and Robert M. Westervelt

Lab on a Chip *Online advance article* (2009)

## Contents

## Soft Matter Keywords

microfluidic, emulsion, dielectric heating

## Summary

The authors present experimental work and simple theory for a microfluidic device that heats water droplets using microwaves. The device relies on dielectic heating to raise the temperature of the droplets. A time-varying electric field causes the induced and intrinsic dipole moments within the water drop to align. The energy driving this alignment is viscously dissipated as heat in the droplet, leading to an increase in temperature above ambient. Since water has a strong dielectric loss at GHz frequencies, the microwave signal is absorbed much more strongly by the water drop than by the oil, PDMS, and glass.

The schematic in Figure 1 shows that on the same PDMS-glass microfluidic chip, continuous phases of water and fluorocarbon oil are combined to form drops which are then twice split in half to form a population of smaller drops. These smaller drops pass through the microwave heater region, where a 3.0GHz signal heats the droplets.

## Practical Application of Research

The research begins to open up the possibility of localized temperature control in microfluidic systems. Most systems to date have spatial control down to a few centimeters, but this work pushes temperature control to the 100s of microns scale. The heating and cooling of the water droplets occurs on timescales much shorter than previously accessible. With temperature changes of nearly 30 degrees above ambient achievable, the microwave heating paradigm can be applied to biologically relevant systems, including PCR reactions for DNA analysis, as well as protein denaturing studies and enzyme optimization. Combining this rapid heating with the high-throughput capabilities of microfluidic emulsions has the potential to allow researchers to analyze large sample populations of temperature sensitive reactions.

## Dielectric Heating of Water Drops On-Chip

As mentioned above, the energy associated with dipoles in water aligning with a time-varying electric field is viscously dissipated as heat into the water. The power density,<math>P</math>, absorbed by a dielectric material is given by the following relationship:

<math>P = \omega \epsilon_0 \epsilon* |E|^2</math>*

where <math>\omega</math> is the frequency of the applied field, <math>\epsilon*</math> is the loss factor of the material, <math>\epsilon_0</math> is the permittivity of free space, and <math>|E|</math> is the electric field strength. The loss factor bears a dependence on the applied frequency and characteristic dielectric relaxation time of the material, as given by the following expression:*

<math>\epsilon* = \frac{(\epsilon_S - \epsilon_{\infty}) \omega \tau}{1 = (\omega \tau)^2}</math>*

Using this information and the following values (<math>\epsilon_S = 78.4 \epsilon_0</math>, <math>\epsilon_{\infty} = 1.78 \epsilon_0</math>, <math>\tau = 9.55</math>ps), the authors decide to use a 3.0GHz signal. This frequency is slightly greater than that used in commercial microwave ovens but is below the frequency associated with the relaxation time of water. Though the water absorbs roughly 1/3 of the power it would at the frequency associated with the relaxation time, the electronic components necessary to produce the 3.0GHz signal are relatively inexpensive, providing motivation to operate at this frequency.

A simple model of the droplet/oil/electrode system considers the drop as having a heat capacity connected to the thermal reservoir of the device through the thermal resistance of the oil. The steady-state temperature is reached when the microwave power entering the drop is equal to the power leaving the drop. Equating these two terms, the expected steady-state temperature increase is:

<math>\Delta T_{SS} = \frac{V}{A} \frac{L}{k_{oil}} P</math>

where <math>V</math> is the drop volume, <math>A</math> is the drop surface area, <math>L</math> is the characteristic length between the drop and the channel wall, <math>k_{oil}</math> is the thermal conductivity of the oil, and <math>P</math> is the microwave power. The heat capacity of the drop is <math>C = V C_W</math> (<math>C_W</math> is the heat capacity per volume of water), while the thermal resistance of the oil layer is <math>R = L/Ak_{oil}</math>. The thermal response of the system is described by a characteristic time scale, <math>\tau_S = RC</math>. The time scale is found to be:

<math>\tau_S = \frac{V}{A} \frac{L}{k_{oil}} C_W</math>

This time scale describe the characteristic time over which the droplet comes to equilibrium with its surrounds, either while being heated or allowed to cool.

The results in Figure 2 indicate that drop temperature is indeed increasing when the microwave signal is on. Cadmium selenide nanocrystals are suspended in the aqueous solution before droplets are formed. The nanocrystals exhibit a temperature-dependent fluorescence, with signal intensity decreasing as temperature increases. After obtaining a calibration curve of fluorescence intensity versus temperature for the nanocrystal/water solution, the authors run drops of the solution through the microwave heating device and capture 2 second fluorescence exposures. From these exposures, the line averaged intensity versus horizontal position can be computed and then converted to a temperature difference using the calibration curve. Finding the droplet velocity allows conversion of the x-axis from length to velocity. The results in Figure 2c indicate that a temperature increase of approximately 25 degrees C is achievable in about 15 milliseconds.

Repeating these steps for various input powers of the microwave signal yields the inset plot in Figure 3a. It is clear that the characteristic time for the system is independent of input power, as predicted by the simple theory developed above. The temperature change also agrees with the simple theory, showing a linear dependence on input power. Taking the slope of the line in Figure 3a and plugging into the simple expression for steady state temperature change above, the authors calculate the characteristic length scale between the droplet and wall to be 28 microns. Using the slope in Figure 3b (which is a plot of the steady-state temperature change minus the temperature change versus time that the drop has been in the microwave field), the characteristic length scale can again be computed, this time using the expression above for the time constant. Doing so yields a value of 35 microns for the characteristic length scale. The authors note that the difference in the two predictions of the characteristic length scale can be partially explained by the fact that the heat capacity in the time constant expression should be larger than calculated, since the channel walls are not perfect heat sinks. However, two independent measures of the characteristic length yielding results within 20% of one another supports the simple model developed for the microwave heating.

written by Donald Aubrecht