**2.1. Research methods used in the identification of the rheological properties of liquid honey**

Liquid honey is a homogeneous fluid, a concentrated solution of sugars and other liquid substances. The majority of liquid honeys have characteristics of Newtonian fluids, which is why there are few limitations to research methods. From a researcher's point of view, the most beneficial measurement systems are the cone-plate or plate-plate ones. Such systems are easy to use and only a few millilitres of honey samples are required for rheological identification. The exchanging of the analysed medium in these systems is easy and the thermostating is satisfactory. Nevertheless, one may use the cylinder-cylinder measurement systems using the Searle or Couette flow. It is then necessary to have a larger amount of the pressure fluid and its exchange is more difficult. The identification of the viscosity of strained honey sample requires measurements to be conducted in at least a few or at best a few dozen measurement points, at which the shear stress for the assigned shear rates would be noted. The viscosity value is obtained by approximating the results to a linear function. The results of such an experiment are presented in **Figure 1**. Due to the fact that honey samples viscosity greatly depends on the temperature and water content, the values of these parameters are worth noting for every measurement. The viscosity value is a numeric coefficient in the obtained equation after the approximation of the experiment's results. In the example shown in **Figure 1**, the dynamic viscosity value is 12.95 Pas. Whether it is a Newtonian fluid is decided by the fact the points align themselves in a straight line. A fine measure of linearity (Newtonian properties) is the determination coefficient. If its value is greater than *R*<sup>2</sup> > 0.95 it may be stated that the fitting of the results to a Newtonian model is very good.

**Figure 1.** Method of determining the dynamic viscosity of liquid honeys.

A similar test can be conducted for any fluid of unknown rheological properties. It is the first effect of a rheological identification of a fluid. If the points do not align along a straight line, it serves as proof of the fluid being non-Newtonian, and a precise research methodology can be chosen.

There are numerous mathematical models used to describe rheological properties of honey in its liquid state [2, 21, 22]. Their main focus is on the description of the viscosity in the function of temperature. Arrhenius's equation is most often used for this purpose [8, 23]:

 *η* = *η*<sup>0</sup> exp( *E*\_*a* RT ). (2)

There is an opinion that this equation describes the dependency between viscosity and temperature relatively well, and the obtained results have an error margin no greater than 4.41% [23, 24].

In the literature analysing the issue, the William-Landel-Ferry (WLF) equation is also used to model the influence of temperature on honey viscosity [21]. This dependency uses glasstransition temperature and the viscosity in glass state to describe the dynamic viscosity of honey [22]. The mathematical equation is in the following form [21, 22]:

$$\ln\left(\frac{\eta}{\eta\_{\text{g}}}\right) = \frac{-C\_{\text{i}}(T - T\_{\text{g}})}{C\_{\text{2}} + (T - T\_{\text{g}})}.\tag{3}$$

It is also noted that the WLF dependency describes honey viscosity in the function of temperature very precisely, while this description is very sensitive to changes of the composition of the medium [21, 22]. The usage of the WLF model is relatively valuable in a general rheological analysis of honey and the identification of glass-transition temperature, which is made possible based on rheological measurements.

The main drawback of the dependencies described above used to describe honey viscosity is the omitting of water content in the product. This is a parameter, which influences honey viscosity as significantly as temperature. This is why two-parametric models are used for practical purposes, which include both water content and temperature [1].

Dynamic measurements are also becoming more common in the analysis of rheological properties of honey [2, 22]. This also includes mixtures of honey and propolis as well as other food products [25]. The measurements are mainly connected with the identification of the value of the complex modulus *G*\*, storage modulus (elasticity) *G'* and viscosity modulus (loss) *G"*, phase angle *δ* and complex viscosity *η*\* in relations to the frequency [20]. The results are also presented in the form of graphs showing the changes of the elasticity modulus, the loss modulus and the complex viscosity in the function of yaw rate [2, 22]. There is no uniform opinion on the range of frequencies used in the measurements. The results are characterized by a generally linear dependency of both the storage modulus and the loss from frequency. The determined complex viscosity values in dynamic measurements do not always correspond to the dynamic viscosity. The measurements of the complex modulus *G*\* and the phase angle yield a uniform assessment of the rheological behaviour of the medium and determine the storage modulus (elasticity) *G'* and the loss modulus (viscosity) as simple dependencies [20]:

$$G' = G' \cdot \cos \delta \tag{4}$$

$$G' = G' \cdot \sin \delta \tag{5}$$

The value of the phase angle *δ* is determined by the division of energies in the deformed medium into stored energy and energy lost to induce flow [20]. The closer the value of the angle is to *δ* = 90°, the closer the properties of the substance are to a completely liquid state (Newtonian body). If *δ* = 0°, the substance is completely elastic and is a hook's body [19].

#### **2.2. Research methods used in the identification of the rheological properties of crystallized honey**

A similar test can be conducted for any fluid of unknown rheological properties. It is the first effect of a rheological identification of a fluid. If the points do not align along a straight line, it serves as proof of the fluid being non-Newtonian, and a precise research methodology can

There are numerous mathematical models used to describe rheological properties of honey in its liquid state [2, 21, 22]. Their main focus is on the description of the viscosity in the function

There is an opinion that this equation describes the dependency between viscosity and temperature relatively well, and the obtained results have an error margin no greater than 4.41%

In the literature analysing the issue, the William-Landel-Ferry (WLF) equation is also used to model the influence of temperature on honey viscosity [21]. This dependency uses glasstransition temperature and the viscosity in glass state to describe the dynamic viscosity of

*C*2

It is also noted that the WLF dependency describes honey viscosity in the function of temperature very precisely, while this description is very sensitive to changes of the composition of the medium [21, 22]. The usage of the WLF model is relatively valuable in a general rheological analysis of honey and the identification of glass-transition temperature, which is made

*E*\_*a* RT

(*<sup>T</sup>* <sup>−</sup> *Tg* ) \_\_\_\_\_\_\_\_

+ (*T* − *Tg* )

). (2)

. (3)

of temperature. Arrhenius's equation is most often used for this purpose [8, 23]:

honey [22]. The mathematical equation is in the following form [21, 22]:

*η*\_ *ηg* ) <sup>=</sup> <sup>−</sup>*C*<sup>1</sup>

*η* = *η*<sup>0</sup> exp(

**Figure 1.** Method of determining the dynamic viscosity of liquid honeys.

ln(

possible based on rheological measurements.

be chosen.

118 Honey Analysis

[23, 24].

As a matter of fact, measurements of the rheological properties of crystallized honey samples should be conducted solely by the use of rotational rheometers, additionally with a cylindercylinder measurement system. This is due to the fact that systems characterized by narrow openings generate significant errors in research because of the dimensions of the crystals. It is believed that the openings should have a linear dimension of at least three times the size of the largest crystal.

An additional effect, which needs to be taken into account in rheological studies of suspensions with a high concentration of solid phase such as honeys, is the unstable behaviour during shearing [19]. In the case when this influence is reversible, the fluids are thixotropic or antithixotropic [19, 20]. Irreversible changes in rheological properties of fluid are called rheodestruction or rheomalaxis [20]. This is connected with the destruction of the crystalline structure during shearing. The characteristic of rheologically unstable fluids requires the use of different research methods and additional rheological parameters. An additional and important aspect is the method of preparation and placement of the analysed medium in the measurement system, as the activities connected with filling the measurement cylinders significantly influence the results of the analyses.

In the case of suspensions with a high-weight concentration of solid body, which present non-Newtonic behaviour, apparent viscosity is commonly used for rheological characteristic [20]. The apparent viscosity *η*′ is defined as a relation between the value of shear stress and shear rate:

$$
\eta^{+} = \frac{\pi}{\dot{\gamma}^{\prime}}.\tag{6}
$$

Apparent viscosity is the simplest and often used parameter of rheological characteristic of crystalline suspensions as well as other non-Newtonian fluids [19]. A graphic representation of changes in the apparent viscosity in the function of shear rate allows also to create a precise rheological characteristic of rheologically stable fluids.

In the studies of rheological properties of suspensions, which are in most cases rheologically unstable, equilibrium viscosity *η*eq is used [19]. This parameter can be identified as the relation of equilibrium stress *τ*eq obtained during shearing at a constant rate *γ*˙ for a period of time long enough for equilibrium in the deformed system to occur:

$$
\eta\_{\alpha q} = \frac{\pi\_{\alpha q}}{j^\*}.\tag{7}
$$

The representation of equilibrium viscosity or equilibrium stress in the function of shear rate is commonly used for rheological characteristic of suspensions [19]. Experiments are usually conducted with shear speed increasing in increments [20]. Equilibrium stress in crystallized honey samples is usually described using the Ostwald-de Waele model [14]:

$$
\pi\_{\text{eq}} = \Bbbk \cdot \dot{\jmath}^{\text{eq}}.\tag{8}
$$

Another aspect of analysing the properties of semisolid sets related with their instability is the determination of behaviour in a closed cycle of shearing with increasing and then decreasing shear rate. By using a constant tempo of increase and then decrease of shear stress, characteristic changes in time are obtained in the form of a hysteresis loop [20]. This constitutes a traditional quality test for the occurrence of thixotropia [19]. By repeating an identical shear cycle after a certain amount of time of the medium remaining dormant, an answer can be obtained to the influence of time on the rebuilding of the internal structure of the crystalline suspension. Conforti et al. used such a cycle: with an increasing shear rate from 0 to 320s-1 for 1.5 min, holding for 2 min at *γ*˙ <sup>=</sup> 320 s-1 and then decreasing with an identical shear tempo, for the rheological characteristic of honey samples in their crystallized state [13]. It was proven that all analysed honey samples presented with a hysteresis loop whose shape was determined by the crystalline structure of the analysed media.

Measurements which enable us to obtain a hysteresis loop need to be performed with caution, for the cylinder slip not to occur causing the syneresis effect [19, 20]. It needs to be mentioned that the possibility to compare the hysteresis loop is available only when the loops are obtained in an identical shear cycle with a constant increase of deformation rate and its consecutive decrease. Additionally, there is a strong influence of the human factor related to the method of introducing the sample into the measurement system of the rheometer [12].

The thixotropic effect is also analysed in the microstructural context, as stress changes during shearing are related with the transformations occurring in the internal structure of the fluid. The scalar value *κ* also called the structural parameter is used for this purpose [19]. Then, the thixotropic behaviour of the substance can be described using two constitutive equations:

measurement system, as the activities connected with filling the measurement cylinders sig-

In the case of suspensions with a high-weight concentration of solid body, which present non-Newtonic behaviour, apparent viscosity is commonly used for rheological characteristic

*γ*˙

Apparent viscosity is the simplest and often used parameter of rheological characteristic of crystalline suspensions as well as other non-Newtonian fluids [19]. A graphic representation of changes in the apparent viscosity in the function of shear rate allows also to create a precise

In the studies of rheological properties of suspensions, which are in most cases rheologically unstable, equilibrium viscosity *η*eq is used [19]. This parameter can be identified as the relation of equilibrium stress *τ*eq obtained during shearing at a constant rate *γ*˙ for a period of time long

*γ*˙

*n*

The representation of equilibrium viscosity or equilibrium stress in the function of shear rate is commonly used for rheological characteristic of suspensions [19]. Experiments are usually conducted with shear speed increasing in increments [20]. Equilibrium stress in crystallized

Another aspect of analysing the properties of semisolid sets related with their instability is the determination of behaviour in a closed cycle of shearing with increasing and then decreasing shear rate. By using a constant tempo of increase and then decrease of shear stress, characteristic changes in time are obtained in the form of a hysteresis loop [20]. This constitutes a traditional quality test for the occurrence of thixotropia [19]. By repeating an identical shear cycle after a certain amount of time of the medium remaining dormant, an answer can be obtained to the influence of time on the rebuilding of the internal structure of the crystalline suspension. Conforti et al. used such a cycle: with an increasing shear rate from 0 to 320s-1 for 1.5 min, holding for 2 min at *γ*˙ <sup>=</sup> 320 s-1 and then decreasing with an identical shear tempo, for the rheological characteristic of honey samples in their crystallized state [13]. It was proven that all analysed honey samples presented with a hysteresis loop whose shape was determined by

Measurements which enable us to obtain a hysteresis loop need to be performed with caution, for the cylinder slip not to occur causing the syneresis effect [19, 20]. It needs to be mentioned that the possibility to compare the hysteresis loop is available only when the loops are obtained in an identical shear cycle with a constant increase of deformation rate and its consecutive decrease. Additionally, there is a strong influence of the human factor related to the method of introducing the sample into the measurement system of the rhe-

honey samples is usually described using the Ostwald-de Waele model [14]:

is defined as a relation between the value of shear stress and

.   (6)

. (7)

. (8)

nificantly influence the results of the analyses.

*<sup>η</sup>*′ <sup>=</sup> *<sup>τ</sup>* \_\_

rheological characteristic of rheologically stable fluids.

enough for equilibrium in the deformed system to occur:

*<sup>η</sup>*eq <sup>=</sup> *<sup>τ</sup>*eq \_\_\_

*τ*eq =*k* ⋅ *γ*˙

the crystalline structure of the analysed media.

ometer [12].

[20]. The apparent viscosity *η*′

shear rate:

120 Honey Analysis

$$
\tau = f(\mathbf{y}, \mathbf{x});\tag{9}
$$

$$\frac{d\kappa}{dt} = \mathbf{g}(\mathbf{\dot{\gamma}}, \kappa \text{ }). \tag{10}$$

When the equilibrium stresses *τeq* are reached, that is, the shear rate of the structure equalsits rebuild rate, then the growth \_\_\_ *<sup>d</sup><sup>κ</sup> dt* <sup>=</sup> 0and the structural parameter has the equilibrium value *<sup>κ</sup>* <sup>=</sup> *<sup>κ</sup>*eq(*γ*˙ ) .Eq. (**9**) has the form [19]:

$$
\pi = f\{\dot{\gamma}, \kappa\_{\alpha q}(\dot{\gamma} \text{ })\} \text{= } \pi\_{\alpha q}(\dot{\gamma} \text{ }).\tag{11}
$$

This is the equilibrium flow curve, which as mentioned above for crystallized honey samples can have the form of relation (**8**). Nevertheless, one can find reports in the literature on the usage of the structural parameter defined in a different way [4, 20].

The complement of the empirical methods of the rheological analysis of crystallized honey samples is studies conducted using a dynamic rheological test. Such techniques are very useful to measure properties of suspensions, in which complex interactions between the ingredients take place. By determining the conditions of the decay of structures forming such sets during shearing, it is possible to obtain a precise rheological characteristic [20]. A classic method in this regard is to use oscillation measurements to identify the influence of temperature and pH of the environment on the blood coagulation process [26].

The values measured in dynamic measurements are usually complex modulus *G*\* and the phase angle (Eqs. (**8**) and (**9**)). Based on these two parameters, it is possible to conduct a uniform assessment of the rheological behaviour of the medium. Viscoelastic media are additionally characterized by a parameter called complex viscosity, which is defined as the ratio of the complex modulus to the angular frequency of oscillation [20]:

$$
\eta^\* = \frac{G}{\omega} \tag{12}
$$

Attention is paid to the fact that between the complex and dynamic viscosity, there is a dependency called the Cox-Merz dependency [20]:

$$
\left.\eta^\* = \eta\right|\_{\omega \circ \gamma^\*}.\tag{13}
$$

Lazaridou et al. stated that in the case of Greek honey in liquid form, the value of dynamic viscosity is generally greater than that of complex viscosity [2]. Ferguson and Kembłowski (1991) noted that the Cox-Merz dependency has a limited range of use in the case of suspensions due to the structural differences of these fluids while dormant and while in set flow. In the case of semisolid food products, the Cox-Merz dependency is modified to the form of [20]

$$
\eta^\* = \left. C \eta^a \right|\_{\omega \omega \gamma}.\tag{14}
$$

There are, however, no data whether the above-mentioned rule can be used for crystallized honey.

#### **2.3. Research methods used to measure the amount of solid phase in crystallized honey**

Reports on the amount of solid phase formed in honey are relatively modest. Existing data point to this value being approximately 15% [12]. Meanwhile, this parameter defines, at a very basic level, the rheological properties of crystallized honey. It would seem that the answer to this question can be obtained by simply comparing the solubility of glucose in water (saturation concentration) at a given temperature with its content in the product. The result of this comparison is not, however, so obvious. Glucose can crystallize in an anhydrous form and as a monohydrate [5]. Data on the solubility of anhydrous glucose point to its saturation concentration (in an aqueous single component solution) at a temperature of 25°C being approximately 60% [27]. The solubility of glucose monohydrate is lower and in these conditions amounts to slightly above 50% [27]. Zamora and Chirife assume that the value of saturation concentration of glucose in water at 25°C is 103.3 g of glucose per 100 g of water [28]. By relating the glucose content to water content for various honeys, we can obtain a glucose concentration level of 1.5–2.5 g of glucose/g of water [28]. Glucose in almost all types of honey is present in a supersaturated state. Fructose, despite the fact that its content is higher in most honeys than that of glucose, never reaches its saturated state, which is 405.1 g per 100 g of water [5, 27, 28]. Nevertheless, there is an influence of fructose on the crystallization process of glucose and it is necessary to perceive honey as a ternary set of water, glucose and fructose. The results of studies by Lothrop and Kelley regarding the equilibrium of such sets show that they are sufficiently complex [5]. It is generally known that a high addition of fructose reduces the tendency to crystallize. Own research of model aqueous solutions of glucose and fructose allowed to make visible the significant influence of fructose on the crystallization process of glucose [29]. The increase of fructose concentration in a supersaturated glucose solution extended the time of crystallization changes the morphology of the crystals formed and reduces the amount of crystallized glucose [29]. Measurements using computer imagery analysis allowed to show that the formed crystals of glucose monohydrate in the presence of high concentration of fructose within the solution are characterized by larger size in comparison to crystals obtained from pure glucose solutions. There is, additionally, a linear increase in absorbance in the infrared spectrum of glucose suspension under the influence of an increased mass fraction of solid phase [12]. Lupano analysed changes in the absorbance of honey samples during crystallization at a wavelength of *λ* = 660 nm and stated that they depend on the crystallization temperature [30]. Conforti et al. searched for a dependency between the absorbance determined at *λ* = 660 nm, for various types of honey samples and the water content and parameters determined on the basis of chemical composition. The results of these comparisons did not yield uniform results [13].

A standard approach to determining the amount of solid phase, which melts in the mixture, is by using differential scanning calorimetry (DSC). In the case of honey, there are several reports on the use of DSC to analyse crystallized honey samples [2, 14, 17, 22, 30]. The results of these analyses show unarguably that DSC allows for a perfect identification of the glass-transition temperature together with the caramelization temperature and other changes occurring in carbohydrates in high temperatures [2, 14, 22]. Lupano reports that in the range of 20–50°C, changes occur on the DSC thermograms, which strongly depend on the conditions in which the crystallization of honey takes place and are characterized by a low value of enthalpy with a significant standard deviation of results [30].

Crystallization changes significantly the way of binding water within a product. Growth in water activity caused by the crystallization in honey samples is from approximately 0.012 even to as much as 0.12 with an average value of 0.027 [12]. Identical results obtained for 49 Argentinian honey samples yielded values from 0.014 to 0.056 with an average value of 0.034 [28]. Glieter et al. showed that the increase in water activity after crystallization depends on the origin and for nectar honey samples it has the value of approximately 0.04 and for honeydew honey samples of 0.02 [15]. Nevertheless, the literature lacks in a clear explanation of the factors determining the increase in water activity in honey samples after crystallization. Bhandari and Bareyre [31] showed on model glucose solutions that the dissolution of glucose monohydrate lowers the water activity proportionally to the weight of dissolved crystals. Basing on this, a conclusion was reached that through changes in water activity, the amount of crystallized solid phase can be determined. Own research conducted under similar conditions, but using honey samples, allowed to show that the explanation is not that obvious.

**2.3. Research methods used to measure the amount of solid phase in crystallized honey**

122 Honey Analysis

tion. The results of these comparisons did not yield uniform results [13].

enthalpy with a significant standard deviation of results [30].

A standard approach to determining the amount of solid phase, which melts in the mixture, is by using differential scanning calorimetry (DSC). In the case of honey, there are several reports on the use of DSC to analyse crystallized honey samples [2, 14, 17, 22, 30]. The results of these analyses show unarguably that DSC allows for a perfect identification of the glass-transition temperature together with the caramelization temperature and other changes occurring in carbohydrates in high temperatures [2, 14, 22]. Lupano reports that in the range of 20–50°C, changes occur on the DSC thermograms, which strongly depend on the conditions in which the crystallization of honey takes place and are characterized by a low value of

Reports on the amount of solid phase formed in honey are relatively modest. Existing data point to this value being approximately 15% [12]. Meanwhile, this parameter defines, at a very basic level, the rheological properties of crystallized honey. It would seem that the answer to this question can be obtained by simply comparing the solubility of glucose in water (saturation concentration) at a given temperature with its content in the product. The result of this comparison is not, however, so obvious. Glucose can crystallize in an anhydrous form and as a monohydrate [5]. Data on the solubility of anhydrous glucose point to its saturation concentration (in an aqueous single component solution) at a temperature of 25°C being approximately 60% [27]. The solubility of glucose monohydrate is lower and in these conditions amounts to slightly above 50% [27]. Zamora and Chirife assume that the value of saturation concentration of glucose in water at 25°C is 103.3 g of glucose per 100 g of water [28]. By relating the glucose content to water content for various honeys, we can obtain a glucose concentration level of 1.5–2.5 g of glucose/g of water [28]. Glucose in almost all types of honey is present in a supersaturated state. Fructose, despite the fact that its content is higher in most honeys than that of glucose, never reaches its saturated state, which is 405.1 g per 100 g of water [5, 27, 28]. Nevertheless, there is an influence of fructose on the crystallization process of glucose and it is necessary to perceive honey as a ternary set of water, glucose and fructose. The results of studies by Lothrop and Kelley regarding the equilibrium of such sets show that they are sufficiently complex [5]. It is generally known that a high addition of fructose reduces the tendency to crystallize. Own research of model aqueous solutions of glucose and fructose allowed to make visible the significant influence of fructose on the crystallization process of glucose [29]. The increase of fructose concentration in a supersaturated glucose solution extended the time of crystallization changes the morphology of the crystals formed and reduces the amount of crystallized glucose [29]. Measurements using computer imagery analysis allowed to show that the formed crystals of glucose monohydrate in the presence of high concentration of fructose within the solution are characterized by larger size in comparison to crystals obtained from pure glucose solutions. There is, additionally, a linear increase in absorbance in the infrared spectrum of glucose suspension under the influence of an increased mass fraction of solid phase [12]. Lupano analysed changes in the absorbance of honey samples during crystallization at a wavelength of *λ* = 660 nm and stated that they depend on the crystallization temperature [30]. Conforti et al. searched for a dependency between the absorbance determined at *λ* = 660 nm, for various types of honey samples and the water content and parameters determined on the basis of chemical composi-

The measurement of mass fraction of solid phase in crystallized honey samples is possible using near-infrared spectroscopy (NIR). Near-infrared spectroscopy is an effective measurement technique enabling the conducting of complex analyses of the crystallization process [32]. The NIR spectroscopy is especially effective in analysing food product sets, which contain water. Own research showed a linear increase in the absorbance with an increase in the mass fraction of the crystalline phase in aqueous glucose suspensions. By using NIR spectroscopy, it is possible to analyse other occurrences in honey samples during crystallization [32].

The analysis procedure for determining the mass fraction of crystallized phase in crystallized honey comprises two stages [12]. The first stage is to determine the calibration equations using preparations with a known mass fraction of crystalline phase in a given honey samples (different honey samples show different absorbance values). In the second stage, measurement is possible of the mass fraction of crystalline phase in crystallized honey. The identification of solid phase has to be conducted for a wavenumber of *ν* ≈ 4467 cm <sup>−</sup><sup>1</sup> [12]. This results from the fact that for this value of the wavenumber there is an isobestic point in glucose solutions. In an isobestic point, the absorbance values of glucose solutions have a constant value, which is the same as the absorbance of water and does not depend on the concentration of glucose in the aqueous solution. For the value of *ν* ≈ 4467 cm <sup>−</sup><sup>1</sup> , there occurs one of the local extremes on the differential spectrums of liquid and crystallized honey samples [12]. Fructose solutions do not have at this point an isobestic point. Nevertheless, the absorbance values of aqueous fructose solutions for *ν* ≈ 4467 cm <sup>−</sup><sup>1</sup> are also close to absorbance of pure water. By using this information, it is possible to state that the increase of absorbance in crystallized honey samples for a wavenumber of *ν* ≈ 4467 cm <sup>−</sup><sup>1</sup> is connected only to the presence of solid phase in the form of glucose monohydrate within the honey [12].

#### **2.4. Quantitative measurement of the morphology of a crystalline structure**

Crystals formed in honey during crystallization are most commonly presented as photographs made using ordinary optical microscopes [13, 14, 17, 30]. Unfortunately, such images are not very clear and troublesome in interpretation and in computer editing using software 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 and buckwheat honey [12].

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 maximum diameter:

**Figure 2.** Images made under birefractive interferometry showing the structure of crystallized honey samples: (a) rape honey and (b) buckwheat honey [12].

$$N(d\_{\text{max}}) = \lambda \cdot \exp(-\lambda \cdot d\_{\text{max}}) \tag{15}$$

Due to the fact that exponential distribution is characterized by one parameter, there is a possibility of quantitative characteristic of the morphological crystalline structure the analysed honeys through a comparison of the λ values [12].
