Most confectionery consists of sugar or other sweet substances (honey, xylitol, sorbitol), as well as molasses, various fruits and berries, milk, butter, cocoa beans, nut kernels, flour and other components. These are mainly sweet products that have a pleasant taste and aroma, good appearance, high nutritional value, calories and good digestibility.

In the work of Tamova, Shchikarev and Basyuk (2015) and Kozlova (2014) it is noted that the choice of process parameters involves comprehensive research to identify the nature of changes in the structure and properties of both individual components of raw materials and raw materials as a complex. Therefore, the participation of scientists in the implementation of technology is to deepen the understanding of the importance of nutrition in human life, taking into account national traditions, transformations of individual food components in the body structure, their impact on organs and systems. Preservation of valuable nutrients and BAS, the formation of habitual consumer characteristics, high bioavailability and product safety is based on the development of production technologies with the necessary physiological properties by improving recipes, methods and modes of processing raw materials, technological parameters of production.

Developed technologies of marzipan pastes (Apet and Pashuk, 2004; Pat. No. 2015152421, 2017) the authors aim to find and study the physiological and technological properties of non-traditional raw materials, which in terms of biologically active substances (BAS) can be attributed to the so-called functional ingredients, studying their influence on the course of preparation and formation of product quality. The recipe mainly included walnuts, hazelnuts, cashews, pecans, peanuts, chestnuts, cherry stones, apricots and pumpkin seeds. Replacement of almonds with peach or apricot pits (Chorrna et al., 2015) was accompanied by the name of the made persipan paste. In the works (Chorrna et al., 2015; Tamova et al., 2015) it is noted that the optimal quality of marzipan mass can be obtained from sweet almonds with the addition of 1 – 2% bitter. Its limitation is due to the danger of the formation of hydrocyanic acid from amygdalin.

In works (Apet and Pashuk, 2004; Pat. No. 2015152421 (2017) the ways of strengthening of taste and aromatic indicators of marzipan pastes are noted. Their prescription composition may include a variety of nontraditional raw materials, such as coffee meal, chicory powder, bunduk seeds. This approach gives marzipan pastes the smell of coffee and the taste of hot chocolate. At the same time, other works (Apet, 2004; Pat. No. 20150211, 2016) noted that the use of pear and amaranth seed powders not only enhances the taste and aromatic qualities of marzipan pastes but also improves rheological characteristics due to the high oil content. This creates the conditions for increased viscosity and adhesion stress, which improves the formation of these confectionery masses.

Reducing the caloric and glycemic content of finishing semi-finished products in their production happens by using different technological properties, origin, composition, caloric content and sweetness of sugar substitutes and sweeteners. Technologies of marzipan paste with low sugar content (Pat. No. 20150141, 2016; Pat. No. 2016127117, 2017) are represented by model compositions of sodium or potassium acesulfame, aspartame. The use of synthetic sweeteners indicates the lack of such compositions. Studies by the authors (Fernandez and Santos, 2018; Zeynep and Sifa, 2014) confirm their negative impact on human health.

The use of natural sweeteners in the technology of marzipan pastes, namely: agave syrup, erythrol, stevioside, palatinosis can significantly reduce the high caloric content (Pat. No 20150211, 2016). Known technologies of marzipan masses (Pat. No. 20150211, 2016; Pat. No. 20150141, 2016) in which various types of flax, barley, buckwheat, corn, lentil, rice are used as fillers as well as pea flour, increase the internal forces of adhesion of the components of marzipan masses. Such fillers bind moisture better and promote the formation of a more homogeneous and plastic structure of the mixture during molding. However, despite the positive attitude, these compositions reduce the organoleptic characteristics due to the presence of a sharp cereal taste and aroma. Baby foods that are part of the diet of children need special care as objects of enrichment. Their bodies are more sensitive to non-traditional ingredients because children's metabolic systems are not yet sufficiently formed and are not able to withstand high loads, to respond adequately to them.

Dried chokeberry berries and medlar leaf powder are used as a functional additive in marzipan paste technologies. This allows not only to increase the nutritional and biological value but also to achieve the maximum possible preventive effect with a relatively small content of marzipan pastes. As an antioxidant use the drug "Cyclorar". This biologically active substance improves the nutritional value of marzipan masses and improves its molding properties.

The main disadvantage of marzipan pastes with these additives is reduced sensory characteristics. The use of additives to enrich the nutritional composition has a significant effect on changes in the color and taste of this product. As a result, there are problems with the toning of marzipan paste and obtaining the appropriate color scheme. This makes this type of finishing semi-finished product unsuitable for confectionery coating and modeling of figured finishing semi-finished products. The raw material for the production of marzipan pastes due to biological, physical, and mechanical factors changes its properties and acquires characteristic of this type of paste. The process of production of pastes can be considered as a set of processes of change of rheological characteristics of the formed semi-finished product according to a compounding under the influence of biological, physical, and mechanical factors. On the other hand, changes in rheological characteristics affect the choice of design and modes of operation of equipment. Therefore, the complex of rheological (structural and mechanical) properties of marzipan pastes are the most important, which predict their state in a variety of technological processes and characterize the physical state, dispersion, structure, structure, and type of interaction.

It is established that methods and means of determining the rheological characteristics of different types of deformation affect product quality (Stadnyk et al., 2019). In our opinion, the works by Kravchenko et al. (2019) give some examples of calculations of technological processes and equipment aimed at studying the physical and mechanical properties of the environment. This approach allows to improve and intensify the technological process, to develop scientifically sound methods for calculating the technology of forming marzipan pastes.

Developed technologies of marzipan and praline masses (Sirohman and Lozova, 2008; Pat. No 2008121837, 2009) in the prescription composition of which included milk powder, in our opinion allowed to improve consumer properties and reduce production costs. It is known that DDW is used in the manufacture of confectionery as a substitute for condensed or powdered milk in the production of creamy caramel, iris, fondant, icing, chocolate (Kravchenko et al., 2020).

As a result of the analysis of literature and patent sources, the wide use of glycerin in the prescription composition of paste-like finishing semi-finished products was revealed. Glycerin in the technology of sugar pastes is used to reduce the stickiness (adhesion) of the food system, it gives softness to the pastes, improves the molding properties, makes them more pliable in the manufacturing process of finishing semi-finished products (Gulenko, Sibileva, and Zhyvotkevych, 2013). This determines the relevance of research on the feasibility of using glycerin in the technology of marzipan pastes with DDW.

The creation of a new technology of marzipan pastes with DDW, the feasibility of using glycerin in their composition requires in-depth studies of rheological and sensory characteristics of finished products to justify rational technological processes, which largely determine the consumer and functional properties of marzipan pastes. The relevance of the search for new recipe ingredients for marzipan masses in the partial replacement of almond flour, the use of which can simultaneously solve several technical problems to ensure the specified organoleptic and rheological properties, is quite high.

When calculating the recipe, the main difficulties arise due to the instability of the movement of the paste, and, accordingly, shear deformations, the impact of quality indicators. At the same time, the improvement of the technological process requires the establishment of a relationship between the characteristics of the components that affect marzipan pastes in the formation of products.

Therefore, the main approach to the choice of marzipan paste formulation is to establish rheological connections, which are the most realistic for solving the problem in the formation of semi-finished products and products. Accordingly, the study of the developed marzipan pastes requires in-depth knowledge of all the intricacies of the process, its mathematical description.

Creation and determination in the prescription composition of marzipan pastes of rational concentration of glycerol with dry demineralized whey to ensure the specified (desired) rheological, surface characteristics, which will help to some extent in ensuring the technological feasibility of use.

Dry demineralized whey made from cottage cheese with 90% level of demineralization under TU U 15.5- 00413890-089:2014 (Table 1); marzipan paste, made by traditional technology; model systems of marzipan paste with the addition of DDW in concentrations of 10 – 40% (Table 2), and food glycerin TU U 10.8-40570177- 001:2016: 1 – 6% (Table 3) of the total mass of dry components of marzipan mass (almond kernel and powdered sugar).

Sensory properties of model systems of marzipan pastes were determined according to the developed scales of organoleptic descriptors. Marzipan pastes with DDW were differentiated depending on sensory features of a consistence: marzipan pastes for a covering of confectionery; as a layer for flour and confectionery (LFC); marzipan pastes for making candies, bars, tiles; for modeling of figured products (MFP).

The study of the rheological properties of control and experimental samples was carried out using a planeparallel plastomer of the Tolstoy modification, which is based on determining the shear deformation related to the thickness of the sample at constant stress (Figure 1).

During the study of the rheological characteristics of the model systems, a fixed load was selected for all variants (65 g), provided the same temperature (+6 °C) and sample height (7 mm).

The study of the surface characteristics of the control and test samples was performed on a dynamometer connected to the MIG-1.3 measuring instrument. It allows characterizing the degree of adhesion of materials of a different structure at their surface contact. The adhesion strength was determined by the method of normal separation of the steel plate from the structured body (marzipan paste). The search for the obtained data of the results of the experimental array of the optimal mass fraction of DDW and glycerin in marzipan pastes was carried out according to known methods and methods of statistical processing using the known method of correlation and regression analysis of experimental results using differential operators qualitatively and quantitatively evaluate the characteristics in the selection of matrix ingredients.

This work is aimed at creating and studying the prospects of using marzipan paste based on a rational concentration of glycerol with dry demineralized whey. Estimation of the basic regularity of change of compounding structure and properties of marzipan paste is based on optimum parameters and modes at its rheological properties. The prescription composition establishes the probability of the obtained results of structure formation, necessary for the description of consumer properties. Features of the effect of glycerin and whey dry demineralized in the formation of the structure of marzipan paste and the conditions for achieving rational rheological parameters, it is possible to predict the adhesion of the paste.

A whole complex of rheological studies was carried out during the development of the prescription composition of marzipan pastes. To clarify the role of glycerol and dry demineralized whey, the planning and formulation of computational experiments were performed to obtain the appropriate regression equations. The dependence of the structural and mechanical properties of the pastes on the content of DDW and glycerin were constructed by the method of an arbitrary experimental design.

According to the results of rheological studies, it is not recommended to increase the concentration of glycerin by over 5%. These results are confirmed by the results of sensory analysis. The zones of rational concentrations of DDW and glycerin in the composition of marzipan pastes were determined by the method of compromise solutions. Accordingly, the variables, optimization criteria, as well as the area of the definition of factors were identified.

The determined mathematical dependences of the main structural and mechanical parameters of marzipan pastes on the content of glycerin and DDW have the form:

Where:

Y_1MFV is strength of marzipan paste MFV, points; Y_2MFV is extensibility of marzipan paste MFV, points; Y_{3 MFV} is ability to form, points; X1 is content of MJ and CP,%; X2 is content of glycerin,%; X3 is MSDS content,%.

By integration, the functions were obtained and the areas of optimal parameters of glycerol and DDW content in marzipan pastes were determined (Table 4).

The optimal values are selected by rounding the optimized values within the compromise areas, to facilitate the dosing of the components of the formulation of marzipan pastes in the production environment.

Thus, the results of rheological and sensory studies confirmed the possibility of adding DDW to the prescription composition of marzipan pastes at a concentration of 10 – 20%, which allows the improvement of their sensory, technological, and functional properties.

If before the collision with the surface the paste layer had a surface Sk, and the surface of the solid workpiece was St, then in equilibrium, when the paste layer forms a drop of a certain shape on the body surface, the surface area of their collision will be Sc, and the paste surface area Sp. The total free surface energy at the initial moment is:

(7) E = S k σ n + S T σ T

Finally, after reaching equilibrium, the total free surface energy will be:

E 2   =   S n σ n   +   S TP σ TP

It is known that a necessary condition for the spontaneous process of applying the paste is that there is a decline in free surface energy (Berlin and Basik, 1974). In our case, when stopping the application (the action of shear stress), the decline occurs quite quickly:

(8) Δ E = ( E 1 − E 2 ) ≺ 0

For this condition of applying the paste, the inequality is valid:

(9) σ T − σ T   n σ n ≻ s n − s K s TII

It follows that at σт> σтп there is an increase in the surface contact of the paste with the medium (Sp> Sk). Thus, the application (wetting) is thermodynamically possible under the condition σт> σтп.

The equilibrium of the paste layer on the surface of a solid body (excluding the surface roughness and the action of gravity) is subject to the Jung equation from which it follows:

σ T = σ n T + σ n c o s θ

Where:

Ө is the edge angle or wetting angle. From which it follows:

cos θ =  σ T − σ TII σ II

Analysis of the state of equilibrium in the ternary system (solid-liquid – gas (air)) leads to the dependence of the form:

(10) σT = σII ( 10 ) σ T = σ II 1 + cosθ 1 − cosθ σ T − σ T   n σ n ≻ s n − s K s TII

Interfacial surface tension for two media is determined by Antonov's rule, according to which the surface tension is equal to the difference of surface tensions of each of the phases separately (Adamson and Gast, 1997; Rydil, 1936).

Assuming this assumption for solid-liquid systems, we can write

σ TII   =   | σ T − σ II | = | σ II − σ T |

Then, using Jung's rule (Adamson and Gast, 1997; Rydil, 1936) it is possible to receive a simple expression for the value of surface energy of a firm body:

(11) σ T = | σ n − σ T | + σ n c o s θ

(12) σ T + σ T = σ n + σ n c o s θ

(13) 2 σ T = σ n ( 1 + c o s θ )

(14) σ T = 1 2 σ n ( 1 + c o s θ )

It follows that the determination of the magnitude of the surface energy of a solid is possible by measuring the marginal wetting angle, ie the layer of paste (Figure 3).

The study of the contact angle θ was determined by the method of dynamic measurement, provided that the phase boundary moves and there is a change in the contact angle over time is the method of changing the volume of the drop (Figure 3). Among these processes, sorption and dissolution in the boundary layer of the two contacting phases promotes the diffusion of atoms (molecules) through the layer of confectionery and paste to desorb and release moisture.

The method of operative determination of the wetting angle was used to calculate the values of the derivative at the point of contact of the marzipan paste with the solid surface of the sponge blank. The surface of the marzipan paste is not described by simple analytical expressions. For an analytical description of the profile line of such a surface, you can use an approximation polynomial of the form:

y = a 0 + a 1 x + a 2 x 2 + a 3 x 3

Where:

x and y are, respectively, the vertical and horizontal coordinates of the point on the surface of the marzipan paste;

a 0 , a 1 , a 2 i a 3   are polynomial coefficients.

The value of the angle, in this case, can be found by determining the derivative at the point of three-phase contact:

y ′ = t g θ = a 1 + 2 a 2 x + 3 a 3 x 2

Obviously, at σт <σ тп and cos Ө <0, ie when the marzipan paste does not stick (wet) to the surface, the edge angle Ө must be less than 90 °. If the wetting angle is more than 90 °, partial wetting occurs. At Ө = 0, when the edge angle is not formed, there is a complete wetting, or spreading, which in our conditions does not occur.

(15) σ T > σ TT + σ TII.

Thus, the wetting edge angle Ө or cos Ө is a measure of the application of marzipan paste. In the manifestation of physicochemical hysteresis, the wetting angles of the marzipan paste depend on the contact time of the phases during application to the surface of the workpiece. The surface of the workpiece marzipan paste covers completely, without the formation of voids. Therefore, the shape of the drop corresponds to a minimum of free energy. In our case we use the formula:

θ z = | a r c t g ( a 1 + 2 a 2 x + 3 a 3 x 2 ) |

According to our research and data processing, the contact equation of applying the paste at an angle will be:

y = − 0.677 + 1.641 x + 0.013 x 2 + 2.454 ⋅ 10 − 3 x 3

The equation for determining the angle will be:

θ z = | a r c t g ( 1.641 + 0.013 x + 2.454 ⋅ 10 − 4 x 2 ) |

Therefore, to achieve high adhesion, the surface tension of the paste must be of great importance.

It is also necessary that the surface tension of the solid confectionery was greater than the surface tension of the paste in contact with it.

Under such conditions, the application of adhesive on the surface of the substrate will be provided:

(16) Σ   substrate   >   σ   adhesive

High-quality application of marzipan paste on flour confectionery allows moisture to penetrate some of its layers.

We made a section of applying the paste before and after 30 s of its contact. Photographs of the section under the microscope are presented in Figure 4.

According to the developed recipe, to determine the rate of penetration of moisture of marzipan pastes into the surface of the confectionery was used by weight method of research at a temperature of 25 °C.

The amount of moisture that penetrated through the surface of the confectionery was periodically weighed with an error of not more than 0.001 g. The change in the mass of the workpiece determines the amount of moisture that has penetrated through the test material. The experimentally established dependences of the change in the mass of the experimental samples in the time measured in min are shown in Figure 5.

From the graphs shown in Figure 5, it follows that the absorbency of the sample coated with marzipan paste with a content of 20% and 30% DDW remained stable for 15 – 20 min from the beginning of the experiment. The less-dense molecular structure of marzipan paste with glycerin causes a greater ability to pass moisture into the workpiece. It may be desirable for the active application and coating of confectionery semi-finished products.

The effectiveness of this modification can be assessed by calculating the work of adhesion (Wa), which is determined (Zimon, 1974) by the ratio of surface energies of the adhesive, substrate, as well as interfacial energy:

(17) W a = σ n g + σ T g − σ T n

Where:

σ_ng is the surface tension of the paste (adhesive) on the border with gas (Air), MJ.m^-2; σ_Tg is the surface tension of solid body (substrate) at the boundary with gas (air), MJ.m^-2; σ_Tn is interphase surface tension, MJ.m^-2.

Temperature and time dependences of wetting are investigated. Figure 6 presents the results of the experiments. It is shown that in the temperature range 293 – 308 the conditions for wetting the workpiece surface (θ >90 deg) are not created. The dependence of the wetting angle in the system of marzipan paste (sponge cake) on the temperature is nonlinear, which may indicate a chemical interaction. The calculation of temperature changes showed that the probability of such a process significantly depends on the temperature of the experiment. The process of flow at the adhesion boundaries at the contact of the paste with the workpiece is best at temperatures that are present in the production premises: 20 – 250 °C, which is an improvement in wetting in the system.

σ_ng is the surface tension of the paste (adhesive) on the border with gas (Air), MJ.m^-2; σ_Tg is the surface tension of solid body (substrate) at the boundary with gas (air), MJ.m^-2; σ_Tn is interphase surface tension, MJ.m^-2.

Taking into account Young's equation, the work of adhesion can be determined by the formula, which uses the values available for experimental determination:

(18) W a = σ n g ( 1 + c o s θ )

Taking into account the interfacial interaction, a more accurate value of the adhesion can be determined by the formula:

(19) W a = σ ng ( 2 + b ⋅ σ xr ) − b ⋅ σ kr 2

Where:

b is the coefficient of proportionality equal to the tangent of the angle of inclination, depending on cosθ = f (σn) to the abscissa.

Σkr is the critical value of the surface tension of the adhesive, which provides complete wetting, MJ.m^-2 (equal to the value of the surface tension of the substrate).

Dependence (19) is the equation of the parabola, the vertex of which is at the following value of the surface tension of the adhesive:

(20) σ n g = 1 b + 0.5 σ k r

The maximum adhesion work is determined by the dependence of the type:

(21) W a   max = 1 b + σ k r + 0.25 b σ k r 2

Figure 7 shows the dependence of the adhesion on the surface tension of marzipan paste with different compositions.

The performed calculations and constructed graphical dependences testify to an increase of work of adhesion and the use of paste with DDW of 20% and 30% and glycerin to 5%. The most effective indicators of marzipan pastes (Figure 7 item 5) with 30% DDW and 5% glycerin. Therefore, this recipe has the most significant effect compared to other recipes. This is due to the quality distribution of marzipan paste and its adhesive properties. Partial replacement of almond flour with DDW in the prescription composition of marzipan pastes leads to changes in the structural state and quantitative values of rheological and sensory characteristics.

Indicators of the total deformation with increasing concentration of glycerol do not increase in direct proportion and depend on the mass fraction of DDW in the composition of marzipan pastes. Accordingly, at a concentration of DDW of 20%, the indicators of total deformation increase depending on the glycerol content in 1.0 – 1.2 times, at a concentration of DDW of 30% increase in 1.0 – 1.3 times, respectively. Irreversible deformation at a concentration of DDW of 20% is constant and does not depend on the concentration of glycerol. At a concentration of DDW of 30% with increasing concentration of glycerol, the reverse deformation increases by 1.5 times. The inverse deformation increases in direct proportion to the total deformation