# Microwave dielectric heating of drops in microfluidic devices

"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)

## Soft Matter Keywords

microfluidic, emulsion, dielectric heating

Figure 1. (a) Schematic of the microfluidic microwave heating system. (b) Microfluidic drop maker. Water drops in fluorocarbon oil are being produced. (c) Parallel drop splitters reduce drops to 63% of their original diameter. (d) Section of microfluidic channel between heating electrodes. The white circles are drops flowing in oil between the two dark metallic electrodes. (e) Image of the actual device as set up on the fluorescence microscope.
Figure 2. (a) Long time fluorescence exposure overlaid onto bright field image of the heating region. A decrease in fluorescence signal from the cadmium selenide nanocrystals indicates an increase in temperature. (b) Line average of the normalized fluorescence intensity versus horizontal position. (c) Change in drop temperature versus time, calculated from (b) and a calibration curve.
Figure 3. (a) Steady state increase in temperature as a function of microwave power, determined from inset plot of temperature change versus time for multiple microwave powers. (b) Log-linear plot of scaled inset data, showing that the drop temperature change has a single time constant.

## 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 heat 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 split in half twice 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,$P$, absorbed by a dielectric material is given by the following relationship:

$P = \omega \epsilon_0 \epsilon |E|^2$

where $\omega$ is the frequency of the applied field, $\epsilon$ is the loss factor of the material, $\epsilon_0$ is the permittivity of free space, and $|E|$ 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:

$\epsilon = \frac{(\epsilon_S - \epsilon_{\infty}) \omega \tau}{1 = (\omega \tau)^2}$

Using this information and the following values ($\epsilon_S = 78.4 \epsilon_0$, $\epsilon_{\infty} = 1.78 \epsilon_0$, $\tau = 9.55$ps), the authors decide to use an 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 and motivated operating in this range.

written by Donald Aubrecht