**2. Need for heating microfluidic devices**

Heat energy has been in use for stimulating (increasing) chemical and biochemical reactions (reaction rates), which otherwise proceed slowly under ambient conditions. Rapid, selective, and uniform heating of fluid volumes ranging from a few microliters to as low as a few nanoliters is vital for a wide range of microfluidic applications. For example, DNA amplification by polymerase chain reaction (PCR) is critically dependent on rapid and precise thermo-cycling of reagents at three different temperatures between 50 °C and 95 °C. Another important and related application, temperature induced cell lysing, necessitates fluid temperature in the vicinity of 94 °C. Other potential applications of heating in a microchip format include organic/inorganic chemical synthesis (Tu., 2011), the investigation of reaction kinetics, and biological studies, to name a few.

© 2012 Rao et al., licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2012 Rao et al., licensee InTech. This is a paper distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

A number of conduction-based heating approaches have been reported for microfluidic systems that include embedded resistive heaters, peltier elements, or joule heating under electro-osmotic and pressure driven flow conditions. Generally speaking, these methods require physical contact or close proximity between a fluid and a heated surface to transfer heat from that surface to the fluid. In microfluidic devices, when the fluid volumes approach nanoliters, heating rates will be potentially limited by the added thermal mass of the substrates used for heat transfer, and not by the fluid volume. The transfer of heat in such manner can also result in heating of large, undesired substrate areas creating spatial limitations for integration of multiple analysis functions on a single substrate. Additionally, the implementation of these heating methods will be limited to high thermal diffusivity substrates, such as silicon and glass, to maximize heat transfer rates. However, such substrates due to their high cost and complexity of the fabrication process are unsuitable for use in disposable devices. Due to a number of inherent problems associated with contact-mediated temperature cycling, a number of research groups have focused on the development of non-contact heating approaches. These noncontact heating approaches include heating based on hot air cycling, heating based on IR light, laser-mediated heating, halogen lamp-based heating, induction heating, and heating based on microwave irradiation. Hot air based heating method utilizes rapidly switching air streams of the desired temperature and transfer of air onto either polypropylene tubes or glass capillaries. However, the control and application of hot air streams on microfabricated integrated systems may not be easily accomplished without an impact on other structures or reactions to be executed on the chip. An inexpensive tungsten lamp as an IR source for rapidly heating small volumes of solution in a microchip format can potentially limit the heating efficiency when applied to microchips with smaller cross-section because the tungsten lamp is a non-coherent and non-focused light source leading to a relatively large focus projection. Other light based heating methods have been demonstrated for microfluidic heating, but such systems, generally speaking, require lenses and filters to eliminate wavelengths that could interfere with the reaction, and accurate positioning of the reaction mixture at the appropriate focal distance from the lamp, which further complicates their implementation.

Microwave dielectric heating is a candidate to address these issues. Most chemical and biochemical species are mainly comprised of water or solvated in water. Water is a very good absorber of microwave energy in the frequency range 0.3 GHz – 300 GHz. Due to this reason, microwave dielectric heating has been exploited for over five decades for heating and cooking fluids and food items containing water molecules (Brodie., 2011). It is also a very good candidate for implementing the heating function in chemical and biochemical reactions as well.

#### **3. Advantages of microwave dielectric heating of microfluidic devices**

Advantages of microwave dielectric heating include its preferential heating capability and non-contact delivery of energy. The first advantage stems from the fact that the microwave energy can be directly delivered to the microfluid sample with little or no absorption from the substrate material (glass, PDMS). The latter advantage facilitates not only the faster heating rates but also the faster cooling rates. These characteristics of microwave dielectric heating allow the application of heat-pulse approaching a delta function, because the heating stops at the moment the microwave power is turned off. This aspect of microwave heating has been used by (Fermer et al., 2003) and (Orrling et al., 2004) for high-speed polymerase chain reactions. The mechanisms of chemical reactions assisted by microwave heating have been found to conform close to theory yielding much more reliable endproducts (Zhang et al., 2003; Whittaker et al., 2002; Gedye et al., 1998; Langa et al., 1997). The chemical reactions assisted by the microwave heating have also been performed at much lower temperatures compared to the conventional heating methods (Bengtson et al., 2002; Fermer et al., 2003). Localized microwave heating of fluids has also been demonstrated in the systems having silicon field-effect-transistors in the vicinity of microfluids (Elibol et al., 2008; Elibol et al., 2009).

180 The Development and Application of Microwave Heating

complicates their implementation.

reactions as well.

A number of conduction-based heating approaches have been reported for microfluidic systems that include embedded resistive heaters, peltier elements, or joule heating under electro-osmotic and pressure driven flow conditions. Generally speaking, these methods require physical contact or close proximity between a fluid and a heated surface to transfer heat from that surface to the fluid. In microfluidic devices, when the fluid volumes approach nanoliters, heating rates will be potentially limited by the added thermal mass of the substrates used for heat transfer, and not by the fluid volume. The transfer of heat in such manner can also result in heating of large, undesired substrate areas creating spatial limitations for integration of multiple analysis functions on a single substrate. Additionally, the implementation of these heating methods will be limited to high thermal diffusivity substrates, such as silicon and glass, to maximize heat transfer rates. However, such substrates due to their high cost and complexity of the fabrication process are unsuitable for use in disposable devices. Due to a number of inherent problems associated with contact-mediated temperature cycling, a number of research groups have focused on the development of non-contact heating approaches. These noncontact heating approaches include heating based on hot air cycling, heating based on IR light, laser-mediated heating, halogen lamp-based heating, induction heating, and heating based on microwave irradiation. Hot air based heating method utilizes rapidly switching air streams of the desired temperature and transfer of air onto either polypropylene tubes or glass capillaries. However, the control and application of hot air streams on microfabricated integrated systems may not be easily accomplished without an impact on other structures or reactions to be executed on the chip. An inexpensive tungsten lamp as an IR source for rapidly heating small volumes of solution in a microchip format can potentially limit the heating efficiency when applied to microchips with smaller cross-section because the tungsten lamp is a non-coherent and non-focused light source leading to a relatively large focus projection. Other light based heating methods have been demonstrated for microfluidic heating, but such systems, generally speaking, require lenses and filters to eliminate wavelengths that could interfere with the reaction, and accurate positioning of the reaction mixture at the appropriate focal distance from the lamp, which further

Microwave dielectric heating is a candidate to address these issues. Most chemical and biochemical species are mainly comprised of water or solvated in water. Water is a very good absorber of microwave energy in the frequency range 0.3 GHz – 300 GHz. Due to this reason, microwave dielectric heating has been exploited for over five decades for heating and cooking fluids and food items containing water molecules (Brodie., 2011). It is also a very good candidate for implementing the heating function in chemical and biochemical

**3. Advantages of microwave dielectric heating of microfluidic devices** 

Advantages of microwave dielectric heating include its preferential heating capability and non-contact delivery of energy. The first advantage stems from the fact that the microwave energy can be directly delivered to the microfluid sample with little or no absorption from Enhanced thermo-cycling rates and reduced reaction times compared to conventional techniques can be achieved because of the inertialess nature of microwave heating. Microwave-mediated thermocycling has been demonstrated for DNA amplification application (Kempitiya et al., 2009; Marchiarullo et al., 2007; Sklavounos et al., 2006). Heating can also be made spatially selective by confining the electromagnetic fields to specific regions of the microfluidic network. Further, the dielectric properties of the fluid can also be exploited to deliver heat using signal frequency as a control parameter in addition to the power.

Microwave heating is also very attractive than other alternatives for obtaining spatial temporal temperature gradients for a variety of on-chip applications, including investigation of thermophoresis (Duhr et al., 2006), control and measurement of enzymatic activity (Arata et al., 2005; Mao et al., 2002; Tanaka et al., 2000), investigation of the thermodynamics (Baaske et al., 2007; Mao et al., 2002), chemical separation (Buch et al., 2004; Huang et al., 2002; Ross et al., 2002; Zhang et al., 2007), and of the kinetics characterizing molecular associations (Braun et al., 2003; Dodge et al., 2004). Most techniques for generating on-chip temperature gradients integrate Joule heating elements to conduct heat into microchannels/microchambers (Arata et al., 2005; Buch et al., 2004, Selva et al., 2009). However, temporal control is limited by the heat capacity of the microfluidic device and thermal coupling of the device to the heating elements. It is easy to locally and rapidly generate temperature gradients within microchannels using the pattern of the microwave electric field intensity of a standing wave. The temperature distribution in the channel fluid is proportional to the time average of the square of the microwave electric field, which contains a sinusoidal component in the presence of a standing wave in the transmission line used to couple microwaves to the fluid in the microchannel. Using microwaves, a nonlinear sinusoidally shaped gradient along a channel of several millimeter length with a quasilinear temperature gradient can be achieved within a second (Shah et al., 2010) . The electric field distribution can also be controlled via the operating frequency and input power, which provides flexibility in changing the temperature profile for different specimens, reactions or applications.

### **4. Mechanism of dielectric heating of water-based fluids**

#### **4.1. Physical viewpoint**

The water molecule has a permanent dipole (the central oxygen atom is electronegative compared to the hydrogen atoms, which are covalently bonded to the oxygen atom) and tends to align itself with an applied electric field. The resistance experienced by the water dipole molecule in aligning itself with the applied electric field is directly related to the intermolecular forces (hydrogen bonds formed by the oxygen atom of one water molecule with the hydrogen atoms of other water molecules) it encounters. Under an influence of sinusoidal applied electric field at a microwave frequency, the ensemble of water dipole molecules experience a rotational torque, in orienting themselves with the electric filed. The rotation caused by the applied field is constantly interrupted by collisions with neighbors. This process results in hydrogen bond breakage and the energy associated with the hydrogen bonds gets translated into the kinetic energy of the rotating dipoles. The higher the angular velocity of a rotating molecule, the higher the angular momentum, and consequently the higher is the kinetic energy. Thus, intermolecular collisions lead to friction, which causes dielectric heating. Dielectric heating is quantified by the imaginary part (ε'') of the dielectric constant. The value of ε'' (also called as the dielectric loss factor) depends on the frequency. As the frequency increases from the MHz range into the GHz range, the rotational torque exerted by the electric field increases; consequently, the angular velocity of the rotating dipoles increases, resulting in an increase in the value of ε''.

#### **4.2. Mathematical viewpoint**

The orientation of the molecular dipoles in response to the applied electric field results in the displacement of the charges, which generates displacement current according to the Maxwell-Ampere law. Dielectric heating is the result of interaction between the displacement current and the applied electric field. At low frequencies (MHz range) the molecular dipoles are able to follow the changes in polarity of the applied electric field (E). Thus, even though a displacement current (I) is generated, it is 90 out of phase with the applied electric field, resulting in a E × I = E・I・cos(90) = 0. Thus, no dielectric heating occurs at such frequencies. At frequencies ≥ 0.5 GHz, the molecular dipoles cannot keep pace with the rapidly changing polarity of the applied electric field, and hence the displacement current acquires a component, I・sinδ, in phase with the applied electric field, where δ is the phase lag between the applied electric field and molecular dipole orientation. This results in a E × I = E・I・cos(90- δ) ≠ 0, and consequently dielectric heating. At very high frequencies (≥ 50 GHz), the field changes too quickly for the molecular dipoles to orient significantly, hence, the displacement current component in phase with the applied electric field vanishes. Consequently, the extent of dielectric heating decreases at high frequencies.

#### **4.3. Dependence on ionicity of the fluid and temperature**

The absorption depth of microwave power for liquid water in the 2 – 25 GHz region is few to several tens of centimeters (Jackson et al., 1975). Since the microchannels are typically 5 – 10 μm in depth, the electric field intensity is more or less constant throughout the microchannel.

The microwave power absorbed per unit volume in a dielectric material is given by:

$$P\_v = \sigma E^2 \tag{1}$$

where

182 The Development and Application of Microwave Heating

**4.1. Physical viewpoint** 

**4.2. Mathematical viewpoint** 

**4. Mechanism of dielectric heating of water-based fluids** 

the rotating dipoles increases, resulting in an increase in the value of ε''.

**4.3. Dependence on ionicity of the fluid and temperature** 

The water molecule has a permanent dipole (the central oxygen atom is electronegative compared to the hydrogen atoms, which are covalently bonded to the oxygen atom) and tends to align itself with an applied electric field. The resistance experienced by the water dipole molecule in aligning itself with the applied electric field is directly related to the intermolecular forces (hydrogen bonds formed by the oxygen atom of one water molecule with the hydrogen atoms of other water molecules) it encounters. Under an influence of sinusoidal applied electric field at a microwave frequency, the ensemble of water dipole molecules experience a rotational torque, in orienting themselves with the electric filed. The rotation caused by the applied field is constantly interrupted by collisions with neighbors. This process results in hydrogen bond breakage and the energy associated with the hydrogen bonds gets translated into the kinetic energy of the rotating dipoles. The higher the angular velocity of a rotating molecule, the higher the angular momentum, and consequently the higher is the kinetic energy. Thus, intermolecular collisions lead to friction, which causes dielectric heating. Dielectric heating is quantified by the imaginary part (ε'') of the dielectric constant. The value of ε'' (also called as the dielectric loss factor) depends on the frequency. As the frequency increases from the MHz range into the GHz range, the rotational torque exerted by the electric field increases; consequently, the angular velocity of

The orientation of the molecular dipoles in response to the applied electric field results in the displacement of the charges, which generates displacement current according to the Maxwell-Ampere law. Dielectric heating is the result of interaction between the displacement current and the applied electric field. At low frequencies (MHz range) the molecular dipoles are able to follow the changes in polarity of the applied electric field (E). Thus, even though a displacement current (I) is generated, it is 90 out of phase with the applied electric field, resulting in a E × I = E・I・cos(90) = 0. Thus, no dielectric heating occurs at such frequencies. At frequencies ≥ 0.5 GHz, the molecular dipoles cannot keep pace with the rapidly changing polarity of the applied electric field, and hence the displacement current acquires a component, I・sinδ, in phase with the applied electric field, where δ is the phase lag between the applied electric field and molecular dipole orientation. This results in a E × I = E・I・cos(90- δ) ≠ 0, and consequently dielectric heating. At very high frequencies (≥ 50 GHz), the field changes too quickly for the molecular dipoles to orient significantly, hence, the displacement current component in phase with the applied electric field vanishes. Consequently, the extent of dielectric heating decreases at high frequencies.

The absorption depth of microwave power for liquid water in the 2 – 25 GHz region is few to several tens of centimeters (Jackson et al., 1975). Since the microchannels are typically 5 –

$$
\sigma = 2\pi f \varepsilon\_o \varepsilon \,\tag{2}
$$

is the dielectric conductivity of the material, f is the frequency in Hz,ε<sup>o</sup> is the permittivity of free space, ε'' is the imaginary part of the complex permittivity of the material (which depends on the frequency and temperature), and E is the electric field strength in V/m within the material. The ε'' is given by:

$$
\varepsilon'' = \left[ (\varepsilon\_s - \varepsilon\_\wp) \alpha \tau \right] / \left( 1 + \alpha^2 \tau^2 \right) \tag{3}
$$

where, τ is the relaxation time, ω = 2πf is the angular frequency, εs is the static field permittivity, and ε∞ is the optical domain permittivity at frequencies much greater than the relaxation frequency (1/τ). The ε'' value first increases with increasing frequency reaching a peak value, before it starts decreasing with a further increase in frequency.

**Figure 1.** Experimental values for the permittivity and total loss factor as a function of frequency for aqueous KCl solutions of differing ionic concentrations (adapted from Gabriel et al., 1998).

The ions dissolved in water influence the rotational ability of the water molecules that are in close proximity to them. Under an external field, the mobile ions collide with the nearby water molecules transferring their kinetic energy to the water molecules, which is given out 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 known *priori* as would be a common case.

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

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

The power density in a dielectric material upon exposure to alternating electromagnetic field is given by (Woolley et al., 1996)

$$P = o\mathfrak{C}\_0 \mathfrak{E}^{''} \left( o\mathfrak{o} \right) \|E\|^2 \tag{4}$$

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 and the reflected wave, as described below:

$$E\left(z,\ t\right) = \mid E\_{+} \mid e^{-j k z} e^{j \alpha t} + \mid E\_{-} \mid e^{j k z} e^{j \theta p} e^{j \alpha t} \tag{5}$$

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 temperature profile of the fluid in the microchannel according to

$$T = a^2 e^{-2\alpha z} + b^2 e^{2\alpha z} + 2ab \cos(2 \mid \beta \mid z + \theta\_p), \tag{6}$$

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 of the transmission medium are non-homogeneous due to the presence of the microchannel resulting in impedance mismatch at the boundaries of the microchannel. The constructive and destructive interference caused by impedance mismatch between the forward and reflected waves at these boundaries generate a standing wave in the electric field and a corresponding stationary temperature field within the microchannel. The shape and magnitude of the temperature field depends on the microchannel geometry, the position of the microchannel relative to the transmission line, the frequency of operation and the input power. The rate of decay of the temperature field is governed by the transmission-line attenuation factor *α*, which is a function of the transmission-line geometry and the frequency-dependent loss factors of the transmission line materials. Hence, the higher the operating frequency of the microwave electric field, the lower the wavelength of the temperature field producing more peaks and valleys in the spatial temperature profile; and the higher the attenuation constant, the higher the average slope in the temperature field from the front to the back of the channel. Rest of the chapter focuses on macroscale and microscale types of microwave applicators for microfluidic heating applications.
