**3. Rheological properties of liquid honey**

for computer-aided image analysis. The literature suggests the existence of images of such crystals made in polarized light [33]. They enable a relatively effective presentation of morphology of the crystalline phase in the honey samples. A detailed analysis of the crystalline structure of honey samples under birefractive interferometry allowed to prove that it is an extremely effective research technique, as glucose monohydrate crystals are characterized by optical birefringence [12]. Measurements of the morphology of the crystalline structure conducted based on images obtained under birefractive interferometry in transition lighting in the so-called black background using a bipolar PI interfero-polarizing microscope are very effective [12, 34]. Takes is to place a drop of honey between two microscope slides. Due to the need for sharp images of the crystalline structure, the thickness of the medium layer cannot exceed 0.1–0.2 mm. It is difficult under these conditions to photograph the crystalline agglomerates occurring in honey samples, as they have a higher thickness. In order to minimize the phenomenon of interfusing of the crystals in own research, a method was devised of displaying the crystals through introducing a thin layer of crystallized honey onto the liquid honey. In this way, it was possible to minimize the occurrence of interfusion of crystals in images. Observations can be conducted with a magnification of approximately 150× using a charge-coupled device (CCD) camera. **Figure 2** shows two sample images of crystallized rape

Quantity characteristics of the morphology of the crystalline structure of crystallized honeys can be obtained through determining the distribution of the number of crystals in reference to a characteristic dimension, for example, the maximum diameter (maximum linear dimension of crystals). In order to provide representative nature of the conducted analyses, a sufficiently large population needs to be taken into analysis, for example, one composed of 2000 crystals. The analysed images should be chosen at random. It was shown that crystals in crystallized honey samples demonstrate empirical distribution of exponential character in relations to

**Figure 2.** Images made under birefractive interferometry showing the structure of crystallized honey samples: (a) rape

and buckwheat honey [12].

124 Honey Analysis

maximum diameter:

honey and (b) buckwheat honey [12].

As mentioned earlier, liquid honey has the properties of a Newtonian fluid with a high viscosity value, which strongly depends on temperature. **Figure 3** shows two sample flow curves obtained through rotational measurements (which in this case are straight lines—Newtonian fluid) of honey at a temperature of 298 and 308 K. A 10° increase in temperature caused a decrease of viscosity from 12.95 to 5.52 Pas, which is over 57%. It is worth noting that this viscosity value is a few (a few dozen) thousand times higher than that of water, which is 0.001 Pas. By expanding the range of temperatures, it can be easily shown that its influence in the lower values is even greater. **Figure 4** shows the results of viscosity measurements of buckwheat honey with a water content of 18.1% at a temperature range of 268–295 K. The results of this experiment can be approximated to the exponential curve, whose equation is shown in **Figure 4**.

Nevertheless, water content also significantly influences the viscosity of honey. Oppen and Schuett as early as in 1939 published an equation, which describes the relations between the viscosity logarithm and water content [35]:

$$W = (62, 500 - 1567) \{ \ T(\log \eta\_{\parallel} + 1) - 2287(313 - T) . \tag{16}$$

Junzheng and Changying developed a fairly simple dependency based on empirical studies [1]:

**Figure 3.** Sample results of rheological measurements—flow curves of multifloral honey *w* = 17.6% at a temperature of 298 and 308 K.

**Figure 4.** Dependency of buckwheat honey samples viscosity on temperature in the range of 268–295 K.

$$
\eta = 14.2 \cdot 10^3 \cdot \exp(-0.31 \cdot w - 0.085 \cdot t). \tag{17}
$$

A similar equation was used to describe the viscosity of Spanish honeys [9]:

$$
\eta = 19.2 \cdot 10^3 \cdot \exp(-0.3 \cdot w - 0.087 \cdot t). \tag{18}
$$

Eqs. (**17**) and (**18**) were formed for a relatively high water content percentage, which is in the range from 17.07 to 34.06% and a narrow range of temperature in Celsius [1, 9]. They show that it is relatively easy to describe the viscosity of liquid honeys—taking into account both the temperature and the water content.

Own research conducted on a few hundred samples of Polish honeys for a wide range of temperatures from 260 to 330 K allowed to determine that there is a dependency between water content and temperature expressed in absolute terms [29]:

$$\mu = 1.72 \cdot 10^{22} \cdot \exp\{-38.363 \cdot W - 0.1398 \cdot T\} \tag{19}$$

The difference in the values of numeral coefficients of the equation above in relations to dependencies (17) and (18) is mainly the results of the usage of temperature expressed in absolute terms and expressing water content by a mass fraction. A graphic illustration of the above-mentioned dependency is shown in **Figure 5**. It is interesting that for a temperature below 0°, all types of honey show high viscosity exceeding 1000 Pas.

The dependencies presented above (17–19) can be accepted as approximated mathematical models of viscosity of liquid honey samples. It needs to be kept in mind that honey shows changeability related to various environmental factors. However, for technological purposes, these dependencies allow for sufficient approximation of the viscosity value in relations to temperature and water content. These relatively simple relations allow to determine the value of honey samples viscosity for a wide range of temperatures and water content and to perform calculations connected with hydraulic transport, mixing or heating of the honey.

**Figure 5.** Relation of the viscosity of honey samples to temperature and water content [29].

To finish the discussion on the rheological properties of liquid honeys, attention must be paid to the fact that the measurement results in a dynamic rheological test are similar to rotational measurements. The values of complex viscosity of the analysed media are similar to the values of dynamic viscosity and the relative differences between the average values of dynamic viscosity and complex viscosity do not exceed 10% [12].
