**4. Rheological properties of crystallized honey**

*η* = 14.2 ⋅ 10 3 ⋅ exp(− 0.31 ⋅ *w* − 0.085 ⋅ *t* ). (17)

*η* = 19.2 ⋅ 10 3 ⋅ exp(− 0.3 ⋅ *w* − 0.087 ⋅ *t* ). (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

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

*μ* = 1.72 ⋅ 10 22 ⋅ exp(− 38.363 ⋅ *W* − 0.1398 ⋅ *T* ) (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

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

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

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

the temperature and the water content.

126 Honey Analysis

content and temperature expressed in absolute terms [29]:

below 0°, all types of honey show high viscosity exceeding 1000 Pas.

In the case of crystallized honey, the task of determining the rheological properties is more complicated. Honey is not a homogeneous body, it does not show Newtonian properties and additionally it becomes solid after longer periods of storage. In order to analyse such a medium, cylinder-cylinder systems seem to be the most appropriate. Even the filling of the measurement system with crystallized honey can be problematic, as the block needs to be crushed, which at a temperature below 20°C can be difficult. The method used to this end can later influence the results of the experiment, so it needs to be done in a repeatable fashion. Such a problem does not occur in the case of creamed honey, which is obtained (to put in plainly) by mixing of the crystallizing mass. Rheological properties of crystallized honeys can be influenced by the mass fraction and shaping (morphology) of the crystalline phase apart from temperature and water content.

The crystalline structure of different types of honey can vary significantly, which is a result of differences in chemical composition—mainly the content of glucose, fructose and water [36]. The morphology of crystals is also significantly influenced by crystallization conditions. **Figure 6** shows images of the crystalline structure of three types of honey: rape, multifloral and buckwheat. Even a superficial quality assessment conducted based on visual data allows to identify significant differences. The results of sample measurements, which allow to quantitatively characterize the populations of crystals of the individual types of honey samples, are shown in **Figures 7**–**9**. Rape honey is characterized by the largest crystal fraction with a *d*max of <10 μm [12]. The multifloral honey has a large crystal fraction of 10 < *d*max < 30 μm in diameter [12]. Buckwheat honey has a large number of crystals with the dimensions of 30 < *d*max < 70 μm [12]. The numerical distribution of buckwheat honey crystals clearly distinguishes it from the other honeys through a characteristic local extreme for the 30 < *d*max < 35 μm fraction and is close to the results obtained by Mora-Escobedo et al. for the Mexican tajonal honey. The obtained results using the maximum diameter characterize the morphology of the crystalline structure more clearly than using the crystals' surface area [14]. Distributions characterizing the population of crystals have an exponential character and can be described unambiguously using the λ-parameter.

**Figure 6.** Images showing the morphology of the crystalline structure of honeys samples: (a) and (b) rape honey, (c) and (d) multifloral honey, (e) and (f) buckwheat honey.

The crystalline structure of different types of honey can vary significantly, which is a result of differences in chemical composition—mainly the content of glucose, fructose and water [36]. The morphology of crystals is also significantly influenced by crystallization conditions. **Figure 6** shows images of the crystalline structure of three types of honey: rape, multifloral and buckwheat. Even a superficial quality assessment conducted based on visual data allows to identify significant differences. The results of sample measurements, which allow to quantitatively characterize the populations of crystals of the individual types of honey samples, are shown in **Figures 7**–**9**. Rape honey is characterized by the largest crystal fraction with a *d*max of <10 μm [12]. The multifloral honey has a large crystal fraction of 10 < *d*max < 30 μm in diameter [12]. Buckwheat honey has a large number of crystals with the dimensions of 30 < *d*max < 70 μm [12]. The numerical distribution of buckwheat honey crystals clearly distinguishes it from the other honeys through a characteristic local extreme for the 30 < *d*max < 35 μm fraction and is close to the results obtained by Mora-Escobedo et al. for the Mexican tajonal honey. The obtained results using the maximum diameter characterize the morphology of the crystalline structure more clearly than using the crystals' surface area [14]. Distributions characterizing the population of crystals have an exponential charac-

**Figure 6.** Images showing the morphology of the crystalline structure of honeys samples: (a) and (b) rape honey, (c) and

(d) multifloral honey, (e) and (f) buckwheat honey.

ter and can be described unambiguously using the λ-parameter.

128 Honey Analysis

**Figure 7.** Numerical distribution of the population of 2000 crystals identified in rape honey samples according to maximum diameter.

**Figure 8.** Numerical distribution of the population of 2000 crystals identified in multifloral honey samples according to maximum diameter.

**Figure 9.** Numerical distribution of the population of 2000 crystals identified in buckwheat honey samples according to maximum diameter.

It is best to begin the rheological characteristic of crystallized honeys from the presentation of equilibrium flow curves (**Figure 10**). As a reminder, the equilibrium flow curve is obtained through assigning equilibrium stress values to shear rate values. The equilibrium stress values are read after stabilizing at a constant level with shearing at a constant shear rate. Next, the value of shear rate is increased in increments and the measurement is repeated.

Based on the flow curves shown in **Figure 10**, the influence of morphology of the crystalline structure on the rheological properties of the analysed suspensions can be estimated. It needs to be mentioned, however, that the content of solid phase in these media was rape 18.2%, multifloral 18.5% and buckwheat 19.2%. The rape honey curve is located the highest and the stress increases at the fastest rate in relation to the increase in shear rate despite the fact that the solid phase content is not the highest. Multifloral honey is characterized by a flow curve located below the rape honey, while the flow curve of buckwheat honey is located below the previous two [12, 36].

A large amount of small crystals causes a significant increase of the texture coefficient and causes the stress in the suspension to increase quickly with the increase of shear rate. Crystallized honeys with large and flat crystals show lower values of the texture coefficient as well as apparent viscosity [12]. The flow curves shown in **Figure 10** can have the following dependencies assigned to describe the apparent viscosity:

$$\text{rape honey} \quad \eta' = 122.07 \times \gamma^{\text{-}0.604} \tag{20}$$

$$\text{multiformal money} \quad \eta' = 56.54 \times \text{y}^{-0.468} \tag{21}$$

It is best to begin the rheological characteristic of crystallized honeys from the presentation of equilibrium flow curves (**Figure 10**). As a reminder, the equilibrium flow curve is obtained through assigning equilibrium stress values to shear rate values. The equilibrium stress values are read after stabilizing at a constant level with shearing at a constant shear rate. Next,

**Figure 9.** Numerical distribution of the population of 2000 crystals identified in buckwheat honey samples according to

Based on the flow curves shown in **Figure 10**, the influence of morphology of the crystalline structure on the rheological properties of the analysed suspensions can be estimated. It needs to be mentioned, however, that the content of solid phase in these media was rape 18.2%, multifloral 18.5% and buckwheat 19.2%. The rape honey curve is located the highest and the stress increases at the fastest rate in relation to the increase in shear rate despite the fact that the solid phase content is not the highest. Multifloral honey is characterized by a flow curve located below the rape honey, while the flow curve of buckwheat honey is located below the previous two [12, 36].

A large amount of small crystals causes a significant increase of the texture coefficient and causes the stress in the suspension to increase quickly with the increase of shear rate. Crystallized honeys with large and flat crystals show lower values of the texture coefficient as well as apparent viscosity [12]. The flow curves shown in **Figure 10** can have the following

<sup>−</sup>0.604 (20)

<sup>−</sup>0.466 (21)

dependencies assigned to describe the apparent viscosity:

maximum diameter.

130 Honey Analysis

rape honey *η*′ = 122.07 × *γ*˙

multifloral honey  *η*′ = 56.54 × *γ*˙

the value of shear rate is increased in increments and the measurement is repeated.

$$\text{buckwheel honey} \quad \eta^{\prime} = 10.39 \times \text{y}^{-0.291}.\tag{22}$$

Based on the data above, it can be stated that honeys with a fine-scaled structure are characterized by a higher value of apparent viscosity. This effect is even more noticeable in the form of a graph presenting the dependency of apparent viscosity in the function of mass fraction of the crystalline phase with low values of shear rate of *γ*˙ <sup>=</sup> 0.5 s ˙ <sup>−</sup><sup>1</sup> (**Figure 11**). It needs to be remembered that shear rate is a parameter which is strongly influencing the value of apparent viscosity.

Another characteristic effect presented by crystallized honey samples is its rheological instability. **Figure 12** shows characteristic hysteresis loops obtained in a shearing cycle with an increasing and then decreasing shear rate to a shear stress value of 500 Pa. The obtained hysteresis loops are characteristic for thixotropic fluids [19, 20]. All honeys in their crystallized state show a strong thixotropic effect, which can be measured using the hysteresis surface area. Nevertheless, it needs to be stressed that this effect is to a great extent permanent (the fluid does not fully rebuild its dormant-state properties) and is also connected with the destruction of the crystalline structure. During shearing, the breaking of small crystals occurs, which can be attributed to rheodestruction [20].

Crystallized honey samples show interesting behaviour in a dynamic rheological test. **Figure 13** shows the results of measurements of the same honey samples, which were rheologically characterized under rotational shearing conditions in **Figure 10**. The values of the viscosity modulus are a few times higher than of the elasticity modulus. As a result, the rheological properties of crystallized honeys are similar to those of viscous fluids. It is noticeable that the highest values of both the viscosity modulus and the storage modulus fall to the multifloral honey, while buckwheat honey is characterized by the lowest values. The values *G'* and *G"* for rape honey are located between the values obtained for multifloral and buckwheat honeys, respectively. This behaviour shows that in relations to measurements conducted under rotary shearing conditions (**Figure 10**), there is both a quality and quantity change in the behaviour of the media.

**Figure 11.** Dependency of apparent viscosity of crystallized honey on the mass fraction of crystallized phase for *γ*˙ = 0.5 s ˙ <sup>−</sup>1 .

**Figure 12.** Characteristic hysteresis loops obtained for the analysed honeys for shearing with an increasing and then decreasing shear rate [12].

ulus are a few times higher than of the elasticity modulus. As a result, the rheological properties of crystallized honeys are similar to those of viscous fluids. It is noticeable that the highest values of both the viscosity modulus and the storage modulus fall to the multifloral honey, while buckwheat honey is characterized by the lowest values. The values *G'* and *G"* for rape honey are located between the values obtained for multifloral and buckwheat honeys, respectively. This behaviour shows that in relations to measurements conducted under rotary shearing conditions

**Figure 12.** Characteristic hysteresis loops obtained for the analysed honeys for shearing with an increasing and then

**Figure 11.** Dependency of apparent viscosity of crystallized honey on the mass fraction of crystallized phase

decreasing shear rate [12].

for *γ*˙ = 0.5 s ˙ <sup>−</sup>1 .

132 Honey Analysis

(**Figure 10**), there is both a quality and quantity change in the behaviour of the media.

**Figure 13.** Values of the elasticity modulus and storage modulus of crystallized media in a function of angular oscillation frequency at a temperature of 30°C [12].

Differences in measurement results of rotational and oscillation measurements of crystallized honeys can be shown especially effectively by placing the values of apparent viscosity and dynamic viscosity on one graph. Such a graph is presented in **Figure 14**. Under oscillation shearing conditions, the highest values of complex viscosity were shown by crystallized multifloral honey samples, whereas under equilibrium shearing, the highest values of apparent viscosity were shown by rape honey samples (**Figure 10**). It needs to be stressed that both media were characterized by a similar water content and crystalline phase content. The parameter, which determined such behaviour, was mainly the morphology of the crystalline structure. The irregular shaping of crystals in multifloral honey samples under oscillation shearing (with constant shifts of the direction of deformation) generated higher movement resistance. It was thus noted that the manner of deformation of crystallized honey is a significant factor influencing the obtained rheological measurement results. Apparent viscosity of crystallized honeys decreases along with the increase of shear rate, whereas complex viscosity shows only slight changes with values close to constant.

**Figure 14** clearly shows that crystallized honeys do not fulfil the Cox-Merz rule Coxa-Merza [20], since

$$\left.\eta^\*\,\,\eta^\*\,\eta^\*\right|\_{\omega\omega\gamma}.\tag{23}$$

Nevertheless, there are such values of angular oscillation frequency and shear rate at which complex viscosity and apparent viscosity are equal to one another. These can be determined from **Figure 14**.

**Figure 14.** Presentation of the values of complex viscosity and apparent viscosity of crystallized honeys at a temperature of 30°C [12].

The results of rheological measurements of crystallized honey presented above do not exhaust the issue. The majority of the graphs shown in this text were obtained under specific conditions and it is hard to generalize them, as was the case with liquid honeys. Rheological studies of crystallized honey are extremely important in shaping the texture of the so-called creamed honeys. Creamed honey is obtained by the so-called direct crystallization with additional mixing during crystallization. This enables to deliberately shape the texture of crystallized honey to obtain characteristic features expected by consumers.

#### **Acknowledgements**

Studies were carried out within the framework S/ZWL/1/2014 and financed from the science funds for the Ministry of Science and Higher Education.
