**2. Properties of dielectric and conducting liquids**

#### **2.1 Dielectric liquids**

Thousands of liquid dielectrics, either organic or synthetic, are available and can be considered for microwave component reconfigurability. Their relative abundance and characteristics, such as toxicity, viscosity, electrical, and thermal properties, depending on their chemical composition. They have been widely used in different fields, including electrical, digital, and microwave circuits [1]. For microwave component reconfigurability, the key parameter of interest is the relative permittivity, which is generally complex as well as frequency and temperature-dependent. However, these liquids are typically identified by their static permittivity (ε<sup>s</sup> = εoεrs). **Table 1** summarizes the static relative permittivity of the most commonly used dielectric liquids under ambient temperature, i.e., 20°C [2, 3].

For polar liquids with single Debye relaxation behavior, the frequency-dependent complex permittivity can be calculated using the Debye relaxation formula [3]:

$$\varepsilon = \varepsilon\_{\infty} + \frac{(\varepsilon\_{\varepsilon} - \varepsilon\_{\infty})}{1 + j\alpha\tau} = \varepsilon' + j\varepsilon' \tag{1}$$

where ℇ<sup>∞</sup> is the high-frequency permittivity limit, τ is the relaxation time, and the loss tangent *δ* is given by *ε*}*ε*<sup>0</sup> . For instance, for DI (DeIonized) water at 20°C, the frequency dependency of the permittivity can be given in terms of its dielectric constant and loss tangent explicitly by [4]:

$$\begin{cases} \varepsilon\_r = 6.28 + \frac{73.91}{1 + 0.26 \times 10^{-20} f^2} \\\\ \delta = \frac{4.48 \times 10^{-9} f}{80.19 + 2.26 \times 10^{-20} f^2} \end{cases} \tag{2}$$

**Figure 1** shows the significant variation of these parameters versus frequency up to 20 GHz and illustrates how this liquid becomes increasingly lossy, which may limit its usability at very high frequencies. It should also be noted that ℇ∞, ℇs, and τ are temperature dependent [4].

#### **2.2 Liquid metals**

Metals are abundant materials on earth. Most of them are present in a solid state at room temperature. Only a few metals are liquids under ambient temperature.


**Table 1.**

*Static permittivity of most common liquid dielectrics at 20°C.*

*Fluidics for Reconfigurable Microwave Components DOI: http://dx.doi.org/10.5772/intechopen.104857*

**Figure 1.** *DI water dielectric constant and loss tangent versus frequency at 20°C.*


#### **Table 2.**

*Key physical properties of most commonly used liquid metals.*

Francium (Fr), cesium (Cs), rubidium (Rb), mercury (Hg), and gallium (Ga)-based metals are the known liquid metals [5]. The radioactivity of the Francium and the reactivity of cesium and rubidium are the main reasons these liquid metals are avoided in microwave component reconfigurability applications. On the other hand, mercury is considered a toxic fluid that cannot be manipulated safely and should be avoided or used under extremely well-controlled conditions. Gallium is a risk-free metal that melts at 29.7°C, which is slightly higher than room temperature. However, the melting points of Gallium-based alloys such as Eutectic Gallium Indium (EGaIn), Eutectic Gallium Tin (EGaSn), and Eutectic Gallium Indium Tin (known as Galinstan) are lower, and they are around 15, 21, and 19°C, respectively [5]. **Table 2** summarizes the key physical properties of the most suitable liquid metals for use in microwaves.
