**Table 2.**


#### **Table 3.**

*Fatty acid content of palm kernel oil.*

$$
\boldsymbol{\pi} = \boldsymbol{\pi}\_0 + \mathbf{K} \left( \mathbf{d} \mathbf{y} / \mathbf{d} \mathbf{t} \right)^{\mathbf{n}} \tag{1}
$$

In this model, τ<sup>0</sup> represents the voltage or the effort of flow, signifying the minimum voltage that must be applied to initiate the flow. Obviously, being a voltage it is measured in Pascali (1 Pa = 1 N. m�<sup>2</sup> ). K is the consistency coefficient, the value of which depends on the nature and temperature of the fluid. It is measured in Pa. s<sup>n</sup> , formally being a viscosity. The flow behavior index is the exponent of the shear rate, n. It is a dimensionless quantity, which depends on the nature of the fluid, its value being very little influenced by temperature.

The Herschel-Bulkley model is simplified and will take the form of the Ostwald model or the law of power:

$$\boldsymbol{\pi} = \mathbf{K} \left( \mathbf{d} \mathbf{y} / \mathbf{d} \mathbf{t} \right)^{\mathbf{n}} \tag{2}$$

Fluids for which the flow behavior index is unitary, as in Newtonian fluids, but there is flow effort (or tension) (τ<sup>o</sup> > 0), are called plastic fluids or Bingham plastic. For such a material, its behavior is like an elastic solid when the stress is below the value of the flow stress (or stress) τ*o*. For voltages greater than the flow voltage, the mathematical expression for the model is [6–8]:

$$
\boldsymbol{\pi} = \boldsymbol{\pi}\_0 + \eta\_{\rm p} \,\mathrm{(d}\boldsymbol{\chi}/\mathrm{dt)} \tag{3}
$$

This mathematical expression of the Bingham model derives from the Herschel-Bulkley equation when n = 1, and K = ηp. Given that the flow behavior index is unitary, the unit of measurement for the consistency index (K) is Pa, that is, the unit of measurement for viscosity. This is why K is replaced by ηp.

This article includes the study of the rheological behavior of palm oil at temperatures between 40 and 100°C and shear rates between 3 and 120 s�<sup>1</sup> [9–12].

### **2. Material and methods**

The rheological behavior of palm oil was determined using a Haake VT 550 Viscotester developing shear rates ranging between 3 and 120 s�<sup>1</sup> and measuring


#### **Table 4.**

*Physical and chemical properties of palm oil [8].*

viscosities from 10<sup>4</sup> to 10<sup>6</sup> mPa.s when the HV1 viscosity sensor is used. The accuracy of the temperature was 0.1°C. The physicochemical properties of palm oil are given in **Table 4**.

### **3. Results and discussion**

**Figures 1**–**7** show the rheograms of the palm oil. As can be seen in the rheograms, the shear stress increases with increasing shear rate and has a linear dependence.

In addition to the rheological models found in the literature, this article proposes two rheological models found on the basis of experimental data (**Tables 5** and **6**):

$$
\boldsymbol{\pi} = \mathbf{A} + \mathbf{B} \left( \mathbf{d} \boldsymbol{\eta}/\mathbf{d} \mathbf{t} \right) \tag{4}
$$

$$\boldsymbol{\pi} = \mathbf{A} + \mathbf{B} \mathbf{exp}[(-\mathbf{d}\boldsymbol{\eta}/\mathbf{dt})/\mathbf{C}] \tag{5}$$

**Figure 1.** *Dependence shear stress versus shear rate for palm oil at temperature 40°C.*

*Dependence shear stress versus shear rate for palm oil at temperature 50°C.*

**Figure 3.** *Dependence shear stress versus shear rate for palm oil at temperature 60°C.*

**Figure 4.** *Dependence shear stress versus shear rate for palm oil at temperature 70°C.*

*Evolution of the Rheological Behavior of Palm Oil DOI: http://dx.doi.org/10.5772/intechopen.106505*

**Figure 5.** *Dependence shear stress versus shear rate for palm oil at temperature 80°C.*

**Figure 6.** *Dependence shear stress versus shear rate for palm oil at temperature 90°C.*

**Figure 7.** *Dependence shear stress versus shear rate for palm oil at temperature 100°C.*


#### **Table 5.**

*The temperature, value of parameters of the model described by Eq. (4), coefficient correlation for olive oil.*


#### **Table 6.**

*The temperature, value of parameters of the theoretical model described by Eq. (5), coefficient correlation for olive oil.*

Applying model (4), the correlation coefficients have values between 0.9989 and 0.9999, which demonstrates that this model correctly describes the rheological behavior of unadditive palm oil used as a biodegradable agent.

Model (5) has the values of the correlation coefficients between 0.9995 and 0.9999, dedi, and it correctly describes the rheological behavior of palm oil. The two models were obtained by linear and exponential fitting of the experimental data.

### **4. Conclusions**

The article proposes two rheological models obtained by linear and exponential fitting of unadditive palm oil. The range of shear rates at which the oil was studied is between 3.3 and 120 s�<sup>1</sup> and temperatures between 40 and 100°C over the entire range of shear stresses. The rheological models found accurately describe the rheological behavior of palm oil.

*Evolution of the Rheological Behavior of Palm Oil DOI: http://dx.doi.org/10.5772/intechopen.106505*
