**7. Measuring saline cell permittivity with mis**

122 Advanced Aspects of Spectroscopy

perform these measurements with electrodes.

small values, reaching values used to 1 kΩ .

with various degrees of salinity.

**Figure 20.** Measurement of Z12 of four saline cells

The values obtained for both measurement and calculation as shown in Table 2 allows us to make the cell preparation of constant section for measuring conductivity. For this preparation had to consider the mechanical error sources such as physical dimensions of the saline cell, the effects of temperature on the cell, and error handling and positioning of it. It also ponder the discrepancy between the measurements of a real physical element such as a capacitor in parallel with a resistor, and the resistivity and permittivity expected of an electrolytic cell, it was therefore necessary to have a truer reference of known salt solution to evaluate deviation of our measurements and bring the measuring physical model to a virtual model and simulate their behavior in this way to "induce" their performance, come to

In Figure 19 shows a sample obtained from a series of measurements made under the scheme of Figure 18, changing the values of the capacitances in parallel with resistors first

**Figure 19.** Comparisons between reference measurements with physical components and estimated values

Although performing multiple measurements and their subsequent acquisition of information due to the speed and flexibility of use of equipment to automate this process, include only the most representative of the behavior of a saline cell, as seen in Figure 20,

> The resistivity of an aqueous sodium chloride dissolution (NaCl) [21] is obtained from considering the current density (J), determined this by the ions types (Na + and Cl – are the most abundant ions) of the solution, this is directly proportional to the factor "α" of dissociation of molecules, approximately equal to 1 if the electrolyte is strong, with a concentration "c "gram-equivalent, and a mobility" μ "of the ions, also the electric field" E "as shown in the following relationship: J = F α c μ E.

> A solution consisting of 9 grams of sodium chloride dissolved in one liter of water in medicine2 is called Normal Saline, since the concentration of 9 grams per liter divided by 58 grams per mole (approximate molecular weight of sodium chloride ) provides 0.154 moles per liter, that is, contains 154 mEq / L of Na + and Cl -. The fact contain more solute per liter,

<sup>2</sup> In chemistry, the normal concentration of sodium chloride is 0.5 mol of NaCl assuming complete dissociation. Physiological dissociation is approximately 1.7 ions per mole, so that a normal NaCl is 1/1.7 = 0.588 molar. This is approximately 4 times more concentrated than the medical term "normal saline" of 0.154 mol

makes this solution with a slightly higher osmolarity3 than blood, on an average day the natremia4 can range between 130-150 mEq / L (normonatremia) . However, the osmolarity of normal saline is very close to the osmolarity of the NaCl in the blood[22].

From Figure 22 and considering the dimensions of our saline cells, presents three values of resistivity, ρ = 2.65Ωm, ρ = 0.55Ωm and ρ = 1.3Ωm, respectively.

**Figure 22.** Measured frequency behavior of three electrolytic cells

**Figure 23.** Saline solutions response at resonance frequency of the coil system

<sup>3</sup> Measuring solute concentration

<sup>4</sup> Concentration of sodium in the blood

Figure 23 presents a summary of values acquired with the network analyzer, Figure 24 represents the values obtained with the HP4192A impedance analyzer.

**Figure 24.** Frequency responses of Saline Solutions.

#### **8. Biological suspensions**

124 Advanced Aspects of Spectroscopy

makes this solution with a slightly higher osmolarity3 than blood, on an average day the natremia4 can range between 130-150 mEq / L (normonatremia) . However, the osmolarity of

From Figure 22 and considering the dimensions of our saline cells, presents three values of

normal saline is very close to the osmolarity of the NaCl in the blood[22].

resistivity, ρ = 2.65Ωm, ρ = 0.55Ωm and ρ = 1.3Ωm, respectively.

**Figure 22.** Measured frequency behavior of three electrolytic cells

**Figure 23.** Saline solutions response at resonance frequency of the coil system

3 Measuring solute concentration 4 Concentration of sodium in the blood Typically, in vitro measures, is considered a sample of uniform section (A) and length (L), in the majority of cases it is more practical to consider the volume (V) in aqueous solutions. In this case the ratio between the conductivity and the permittivity of the sample with the resistance and reactance are:

$$\mathcal{L} = \frac{\varepsilon \varepsilon\_0 \mathcal{V}}{\mathcal{L}^2} \text{ [ $F$ ]} \tag{22}$$

$$R = \frac{L^2}{\sigma V} \text{ [ $\Omega$ ]} \tag{23}$$

$$Z = \frac{L^2}{\left(\sigma + \int \omega \,\varepsilon \,\varepsilon\_0\right) V} \tag{24}$$

Following experiments with saline solutions, was considered to have the information needed to proceed to carry out experiments with biological solutions, hence the first use of coil system as a reference and according to the above expressions, and also with a 500 mL volume, and a tank length of 85 mm was obtained with a suspension of high concentration of biomass (80 g / l of yeast), a 8.305 dB attenuation, comparing this with a 13.71 dB attenuation of coil system, this means a representation of a 65% increase in impedance in the suspension.

 It should be mentioned that the embodiment of the vast majority of measurements for suspension was made with the HP4192A impedance analyzer, considering the structure and existing coil system, the utilization ratio of the impedance analyzer is because the probes used to interconnect arrangement coils are constructed on purpose, greatly decreasing the amount of error attributable to the length of the coaxial cables.

**Figure 25.** Impedance Representation of Biological Suspension, comparatively to the coil system.

After 35 minutes, the yeast was deposited at the bottom of the container; we proceeded to extract 350ml of water and recovered the same amount of water (350ml), but now with a salinity 8.78mS/cm.

The interesting thing in this experiment as shown in Figure 25, having increased conductivity, as a result of water replaced without electrolytes, with water with electrolytes (8.78mS/cm) decreased by 6% the impedance of the suspension by the lower proportion of yeast and major salinity, Zlev = 384.37Ω, Zlev + NaCl = 361.87Ω, ΔΩ = 22.5
