**5. Macroscale microwave applicators for microfluidic heating**

184 The Development and Application of Microwave Heating

known *priori* as would be a common case.

field is given by (Woolley et al., 1996)

and the reflected wave, as described below:

temperature profile of the fluid in the microchannel according to

**microwaves** 

as heat. The ε'' value, and consequently the dielectric conductivity, increase with increasing ionic strength at low frequencies, but interestingly, as shown in Figure 1, it becomes relatively independent of ion concentration of solution over a small region of microwave frequencies. Therefore, such solutions can be heated with microwaves of this frequency regime independently of their ionic strength. This characteristic of microwave dielectric heating is particularly advantageous when the salt concentration of the solution is not a

The water temperature also affects the microwave dielectric heating mechanism. With an increase in the water temperature, the strength and the extent of the hydrogen bonding network in water decreases, because more hydrogen bonds are already broken at a high temperature. This lowers the ε'' value and consequently a decrease in dielectric heating. It means the water becomes a poorer absorber of microwave power with increasing temperature, shifting the ε'' (or σ or Pv) versus frequency curve to higher frequencies. This

**4.4. Model of temperature gradient generation in microfluidic channel using** 

The power density in a dielectric material upon exposure to alternating electromagnetic

<sup>0</sup> *P E* 

where *ω* is the angular excitation frequency, *€*o is the vacuum permittivity, *€''* is the loss factor and *E* is the electric field strength in volts per meter within the material. For a wave traveling in the *z*-direction on a transmission line, the phasor representation of the total electric field is the sum of contributions from two separate components, the forward wave

> , | | | | *jkz j t jkz j p j t Ez t E e e E e e e*

where *jk* = *α* + *jβ, E*+ is the amplitude of the forward wave, *k* is the complex propagation constant, *E*− is the amplitude of the reflected wave, *θ*p is the phase angle between the reflected and forward waves, *α* is the attenuation constant that describes the rate of decay of microwave power per unit length, *z* is the distance along the direction of propagation and *β* is the phase constant (change in phase per unit length) (Ramo et al., 1993). The time averaged power density (*P*) is proportional to *E(z, t)*·*E(z, t)*∗. Thus, we can compute the

> 2 2 22 (| | ) 22 , *z z <sup>p</sup> T a e b e abcos z*

where *T* is the fluid temperature due to microwave heating. This simplified model describes several key features of microwave-induced temperature gradients. The dielectric properties

(6)

  '' 2

€€ | | (4)

 

(5)

 

can be an advantage when a steady temperature needs to be maintained.

The use of microwave heating has been demonstrated for a variety of applications including drug discovery, isolation of DNA, and heating of biological cells. Macro-scale microwave applicators were commonly utilized for the delivery of microwave power to sample contained in the plastic reaction tubes.

For microwave heating using a macroscale X-band rectangular waveguide, a slot is machined into one of the walls of the waveguide to allow the introduction of a microfluidic device, as shown in Figure 2. The position of the slot is chosen such that the microchip is placed perpendicular to the direction of the field propagation to maximize coupling of microwave power to fluid. The fluidic channel is micromachined into PMMA substrate using a milling machine. The channel enclosure is accomplished via thermal lamination technique with PP film. A traveling wave tube amplifier, capable of amplifying the input power up to 30 W over the 8 GHz to 18 GHz frequency range, coupled to a microwave signal generator is used to provide the desired microwave power; and a thermocouple inserted into the PMMA substrate is used to measure the fluid temperature. Further details of the system are given elsewhere (Shah, 2007b).

Thermo-cycling of de-ionized water between 60 °C and 95 °C is accomplished by this system, as shown in Figure 3. As mentioned earlier, DNA amplification by PCR relies on temperature cycling of the reaction mixture through three different temperatures between 50 °C and 95 °C. It means this system is suitable for DNA amplification by PCR. When a 20 W microwave power was applied the average heating rate of this system can be as high as 6 °C/s and the cooling rate 2.2 °C/s for a fluid volume of about 70 μL.

These values are better than what was accomplished (Figure 4) using a conventional metal block-based thermocycler whose heating and cooling rates are less than 1.7 °C/s. The results of Figure 3 confirm that microwave heating is a viable alternative for on-chip microfluidic systems, and that it can be used to obtain superior thermocycling rates compared to those obtained with conventional macroscale thermocyclers.

**Figure 2.** A schematic of an x-band rectangular waveguide heating system.

**Figure 3.** On-chip thermocycling of de-ionized water obtained using rectangular waveguide heating system.

Waveguide –

to - coax

obtained with conventional macroscale thermocyclers.

PMMA chip

Thermocouple

**Figure 2.** A schematic of an x-band rectangular waveguide heating system.

system.

**Figure 3.** On-chip thermocycling of de-ionized water obtained using rectangular waveguide heating

systems, and that it can be used to obtain superior thermocycling rates compared to those

Xband waveguide

Thickness: 1.7mm Microfluidic well

**Propagation of the microwaves**

22.7mm ID

10.0mm ID

BOPP film Thickness: ~ 30 µm

Depth: 1mm

Waveguide –

to - coax

**Figure 4.** Thermocycling of de-ionized water using macroscale conventional thermocycler. The PCR tubes were used to hold 25 μL of fluid. The average heating rate for this system was 1.69 °C/s and the cooling rate was 1.36 °C/s.
