INTRODUCTIONAlthough containing a number of nutrients in theircomposition, some parts of commercial hydrobionts arenot widely used in food production, thus being wastedwhile processing. These include octopus skin, whichmakes up to 37% by weight of raw material and is richin caratinoids, collagen, taurine, selenium, high-limitfatty acids [1–4]. Processing of Pacific herring producesrarely used now milt (up to 12.4% by weight of rawmaterials), which contains nucleoproteins, includingbiologically active substances (deoxyribonucleic acidand ribonucleic acid), and polyunsaturated fatty acids,including ω-3 and ω-6 families [5]. Among otherinsufficiently used raw materials, sources are the Pacificsquid and Japanese cucumaria [6, 7]. However, thesecommercial objects provide sources of such biologicallyactive substances as complete protein, hexosamines,chondroitin sulfate, triterpene glycosides, andpolyunsaturated fatty acids [3, 8–10]. Getting with foodin the human body, they slow down the aging processand have a corrective effect on metabolic processes, thusimproving the quality of life and promoting longevity.Cryotechnology is a promising trend in theindustrial processing of biologically highly valuable rawmaterials. The method allows obtaining concentrateswith highly preserved natural properties and biologicalactivity [11–13]. Since the resulting cryopowders,as a rule, have the properties of biologically activeadditives, they are often used as biological correctorsin the production of various food products and30Bogdanov V.D. et al. Foods and Raw Materials, 2019, vol. 7, no. 2, pp. Х–Хcosmetic materials, also being included in formulationcompositions [14–18].There are three main processes in cryogenicprocessing of raw materials of animal and plant origin:cryopreservation, cryogenic grindingб and freezedrying. Cryopreservation consists in rapid freezingof raw materials to a much lower than cryoscopictemperature, when most of the water turns into ice.It not only suppresses the activity of enzymes andthe vital activity of microorganisms, but also createsfavorable conditions for easier destruction of tissuesduring subsequent cryogenic grinding [11, 19]. By now,the process of freezing fish as a method of preservationhas been widely studied, but there is lack of data on lowtemperatureprocessing of non-fish commercial objects.Also lacking are data on seafood thermal properties inthe course of low-temperature processing. However, thisknowledge is necessary when performing engineeringcalculations of processes and equipment related tocryogenic processing.In this regard, the aim of the paper was to study thechanges in thermal properties in the process of freezingraw materials of marine origin. Total specific heatcapacity, thermal conductivity coefficient and densitywere calculated for the selected objects of study.STUDY OBJECTS AND METHODSThe study objects were the skin of giant octopus(Octopus dofleini), pallium of Pacific squid (Todarodespacificus), milt of Pacific herring (Clupea pallasii),and muscle tissue of Japanese cucumaria (Cucumariajaponica).The amount of water in the samples, being the mainfactor of the freezing process, was determined by thestandard method according to State Standard 7636-85 [20].The standard software package of Microsoft Office2007 and CurveExpert 1.4 were used for statistical dataprocessing and graphs plotting with formula derivation.Total specific heat capacity determination.The specific heat capacity of food products asmulticomponent substances is calculated according tothe law of additivity [21]:n n с  g c  g c  g c ... g c 1 1 2 2 3 3dtdq L W d f    fr 0       22( ) 21p pi frfr ii p i frf           wiwiipm WW1 312211 11 frm g g g 2751.19 4 4888.57 3 2159.33 2 9.05 4.26s с          (11)where c1, c2 , c3 ,..., cn are specific heat capacities ofcomponents, kJ/kg·K;g1, g2 , g3 ,...gn are mass fractions of the components.Consider the body of the study object as a twocomponentmixture containing W parts of water and(1–W) parts of dry substances with correspondingspecific heat capacities for each component cw and cd.s.Heat capacity of the product in the temperature rangebefore ice formation is determined by the expression:c = cwW + c d.s(1–W) ( 1)where cw = 4 .19 k J/kg·K i s w ater h eat c apacity(4.19 kJ/kg·K);cd.s is specific heat capacity of dry substances in rawmaterials [22].Since at negative temperatures part of the waterω in the object under study transforms into ice, whoseheat capacity is ci , the heat capacity of the frozen rawmaterial cfrm is calculated by the formula:cfrm = cwW(1 – ω) + ciW ω + cd.s(1–W) (2)where ci is the heat capacity of ice (2.1 kJ/kg·K).When freezing, the heat of ice formation will beremoved from the mass unit at a lower temperature,which is defined a n n с  g c  g c  g c ... g c 1 1 2 2 3 3dtdq L W d f    fr 0       22( ) 21p pi frfr ii p i frf           wiwiipm WW1 312211 11 frm g g g 2751.19 4 4888.57 3 2159.33 2 9.05 s с        1786.77 4 3293.67 3 1410.95 2 95.48 m с        2511.06 4 4238.40 3 1611.53 2 149.47 os с        1140.6 4 2110.32 3 669.94 2 291.58 3.95cu с         for squid:  0.52 1.02 s   for milt of herring:  0.47 1.01 m   for octopus skin:  0.631.07 os for cucumaria:   0.531.54 cu  1209.6 142.89 .   f m  1226.74 149.08 .   f s  1128.55 138.24 .   f os  1031.26 100.42 .   f cu (3)where Lf is the specific heat capacity of ice formation(334.2 + 2.12t + 0.0042t2 kJ/kg);W – total water content of the sample, kg/kg.t – temperature of frozen raw materials, °C.If temperature change of one degree is adopted inthe expression (3), the amount of heat will receive thedimension and meaning of the component of the specifictotal heat capacity and be recorded as:qω = LfW(ω2 – ω1) (4)where 1 ωis the amount of frozen out water at the initialtemperature;and ω2 is the amount of frozen out water at the finaltemperature.The sum of calculated heat capacity of the frozen rawmaterial cfrm and the heat of ice formation qω will givethe total specific heat capacity:ctot = cfrm + qω (5)Thermal conductivity coefficient determination.When the temperature drops below the cryoscopicvalue and the product is in the process of ice formation,its thermal conductivity increases significantly, sincethermal conductivity of ice is four times greater thanthat of water.The increase in thermal conductivity of the productwith decrease in temperature almost ceases with the endof water freezing out, granted that further insignificantchange in the thermal conductivity of ice and othercomponents of the product is neglected. The thermalconductivity coefficient of products in the range ofnegative temperaturesn n с  g c  g c  g c ... g c 1 1 2 2 3 3dtdq L W d f    fr 0      22( ) 21p pi frfr ii p i frf           wiwiipm WW1 312211 11 frm g g g 2751.19 4 4888.57 3 2159.33 s с       depends on the amount offrozen out water and approximates to the equation [23]:n n с  g c  g c  g c ... g c 1 1 2 2 3 3dtdq L W d f    fr 0       22( ) 21p pi frfr ii p i frf           wiwiipm WW1 312211 11 frm g g g (6)where 0 λis the coefficient of thermal conductivity of theproduct before freezing, W/m·°C;Δλ is the change in thermal conductivity of theproduct in the temperature range from the start offreezing ts to tc corresponding to completion of iceformation.31Bogdanov V.D. et al. Foods and Raw Materials, 2019, vol. 7, no. 2, pp. Х–ХConsidering raw materials as a two-componentmixture containing parts of water W and (1–W) partsof dry substances with respective thermal conductivitycoefficients of λw and d.s λ , the heat capacity of theproduct in the temperature range before ice formation isdetermined by the expression:W ( W) m w d s = + 1− . λ λ λwhere w λ = 0,597W/m2·K is the coefficient of waterthermal conductivity;d.s λ – thermal conductivity coefficient of drysubstances [6].The coefficient of thermal conductivity can becalculated by the formula based on the models ofKrisher [5]:n n с  g c  g c  g c ... g c 1 1 2 2 3 3dtdq L W d f    fr 0       22( ) 21p pi frfr ii p i frf           wiwiipm WW1 312211 11 frm g g g 2751.19 4 4888.57 3 2159.33 2 9.05 4.26s с          (11)1786.77 4 3293.67 3 1410.95 2 95.48 3.58m с          (12)2511.06 4 4238.40 3 1611.53 2 149.47 3.66os с          (13)1140.6 4 2110.32 3 669.94 2 291.58 3.95cu с         for squid:  0.52 1.02 s   (15)for milt of herring:  0.47 1.01 m   (16)for octopus skin:  0.631.07 os (17)for cucumaria:   0.531.54 cu (18) 1209.6 142.89 .   f m (19) 1226.74 149.08 .   f s (20) 1128.55 138.24 .   f os (21) 1031.26 100.42 .   f cu (22)(7)where i λis thermal conductivity of ice coefficient withinthe temperature range 273–208 K (2,22 W/m·K);p ε – porosity coefficient which depends on the amountof frozen out water and chemical composition.The structure of the frozen product can beconsidered as a dispersed system consisting of ice poreswith coefficient of thermal conductivity i λand a mattercontaining unfrozen water and dry substances with acoefficient of thermal conductivity approximately equalto 0 λbefore freezing.Porosity coefficient of the assumed structure will bedetermined by the expression:  + + −=wiwiipm WWρρωρρρωε1 (8)where i ρis ice density, kg/m3;w ρ is product density before freezing, kg/m3;m is mass fraction of dry substances in raw materials.Taking into consideration stable weight fraction ofdry substances in the process of freezing, and practicallyunvarying density m ρm wm Wρ ρ= 1 −(9)Frozen raw material density determination.Consider the body of the object under study as a threecomponentmixture consisting of unfrozen water, ice,and dry matter. Density of the samples can thus bepresented as the equation [6]:( )312211 11ρωρ ρωρfrm g g g+ +−=(10)where 1 g is the mass fraction of water contained in thesample body;2 g is the mass fraction of solids contained in thesample body;1 ρis water density (1000 kg/m3);2 ρ is dry matter density of raw materials, kg/m3 [21];3 ρ is ice density (917 kg/m3);ω is the amount of frozen out water.RESULTS AND DISCUSSIONData on water content determination in the tissues ofthe studied hydrobionts are given in Table 1.The objects under study have a high water contentranging from 77.4% (in the milt of Pacific herring) to88.9% (in the muscle tissue of the Japanese cucumaria),which corresponds to the known data [2, 3, 7, 24].Using formula (5), we calculate the total specificheat capacity of the samples. To do this, it is necessaryto determine the amount of frozen out water at differenttemperatures using Ryutov’s formula [25]. Thenwe apply formulae (2) and (4) to determine the heatcapacity for the selected raw material and the heat of iceformation. The resulting values of the total specific heatcapacity of the raw material are depicted as graphs inFigure 1.Presented in Figure 1 graphs show the relationbetween total specific heat capacity and the amount offrozen out water for the four studied objects. As can beseen, they are of the same type and have two distinctareas. The first one demonstrates an increase in thetotal specific heat capacity of seafood samples, which isassociated with intensive ice formation in their tissueswith a decrease in temperature and accompanyingheat release. The second area is characterized by agradual decrease in the total specific heat capacity ofseafood samples. This is associated with a significantdecrease in the amount of liquid aqueous phase and,accordingly, a decrease in the intensity of its transitionto the crystalline form with the release of heat causedby ice formation. At the final stage, when most wateris frozen out, the total specific heat capacity of thesamples under study tends to the heat capacity of icebecoming one of the main factors of the further freezingprocess. The transition point of the total specific heatcapacity from increase to decrease is reached whenthe amount of frozen out water gets close to 50%.The obtained values of total specific heat capacity ofcommercial hydrobionts’ tissues are consistent with thedata available in the academic literature on aquatic rawmaterials [25].Approximating the curves shown in Fig. 1 withCurve Expert Professional 2.3, we get the formulae:Table 1 Water content in the tissues of hydrobiontsSample Water content,%Milt of Pacific herring 77.4Pallium of Pacific squid 78.6Skin of octopus 84.8Japanese cucumaria 88.932Bogdanov V.D. et al. Foods and Raw Materials, 2019, vol. 7, no. 2, pp. Х–ХThese formulae can be used to calculate the relationbetween total specific heat capacity and the amountof frozen out water for the studied raw materials witha correlation coefficient of 0.99. The free term in theobtained formulae determines the value of total heatcapacity of the raw material with the amount of frozenwater equal to 0. Therefore, total specific heat capacityof non-frozen seafood equals (kJ/kg·K): 4.26 for squid,3.58 for milt of Pacific herring, 3.66 for octopus skin,and 3.95 for cucumaria shell. The values of heat capacityof non-frozen raw materials calculated, based on thestandard formula (1) were as follows (kJ/kg·K): 4.06 forsquid; 3.52 for milt; 4.05 for octopus skin; and 3.93 forcucumaria. The difference between the data obtainedaccording to formulae (11–14) and (1) is 4.9, 1.7, 9.6,and 0.5% for squid, milt, octopus skin, and cucumaria,respectively. This indicates the adequacy of the derivedmathematical relationships.Using formula (7), we calculated the coefficient ofthermal conductivity of the selected raw material andplotted the relation to the amount of frozen out water(Fig. 2).Analysing the graphs in Figure 2, we see that thedependence of the change in the thermal conductivityof the studied samples is close to linear. The thermalconductivity of the studied seafood in the processof freezing increases with the proportion of frozenout water, tending to the thermal conductivity of ice,which is almost four times greater than the thermalconductivity of water. Approximating the chart datausing Curve Expert Professional 2.3, we obtain theformulae:for squid:n n с  g c  g c  g c ... g c 1 1 2 2 3 3dtdq L W d f    fr 0       22( ) 21p pi frfr ii p i frf          wiwiipm WW1 312211 11 frm g g g 2751.19 4 4888.57 3 2159.33 2 9.05 4.26s с          1786.77 4 3293.67 3 1410.95 2 95.48 3.58m с          2511.06 4 4238.40 3 1611.53 2 149.47 3.66os с          1140.6 4 2110.32 3 669.94 2 291.58 3.95cu с         squid:  0.52 1.02 s   for milt of herring:  0.47 1.01 m   for octopus skin:  0.631.07 os for cucumaria:   0.531.54 cu  1209.6 142.89 .   f m  1226.74 149.08 .   f s  1128.55 138.24 .   f os  1031.26 100.42 .   f cu (15)for milt of herring:n n с  g c  g c  g c ... g c 1 1 2 2 3 3dtdq L W d f    fr 0       22( ) 21p pi frfr ii p i frf            wiwiipm WW1 312211 11 frm g g g 2751.19 4 4888.57 3 2159.33 2 9.05 4.26s с          1786.77 4 3293.67 3 1410.95 2 95.48 3.58m с          2511.06 4 4238.40 3 1611.53 2 149.47 3.66os с          1140.6 4 2110.32 3 669.94 2 291.58 3.95cu с         for squid:  0.52 1.02 s   for milt of herring:  0.47 1.01 m   for octopus skin:  0.631.07 os for cucumaria:   0.531.54 cu  1209.6 142.89 .   f m  1226.74 149.08 .   f s  1128.55 138.24 .   f os  1031.26 100.42 .   f cu (16)for octopus skin:n n с  g c  g c  g c ... g c 1 1 2 2 3 3dtdq L W d f    fr 0       22( ) 21p pi frfr ii p i frf            wiwiipm WW1 312211 11 frm g g g 2751.19 4 4888.57 3 2159.33 2 9.05 4.26s с          1786.77 4 3293.67 3 1410.95 2 95.48 3.58m с          2511.06 4 4238.40 3 1611.53 2 149.47 3.66os с          1140.6 4 2110.32 3 669.94 2 291.58 3.95cu с         for squid:  0.52 1.02 s   for milt of herring:  0.47 1.01 m   for octopus skin:  0.631.07 os for cucumaria:   0.531.54 cu  1209.6 142.89 .   f m  1226.74 149.08 .   f s  1128.55 138.24 .   f os  1031.26 100.42 .   f cu (17)for cucumaria:n n с  g c  g c  g c ... g c 1 1 2 2 3 3dtdq L W d f    fr 0       22( ) 21p pi frfr ii p i frf            wiwiipm WW1 312211 11 frm g g g 2751.19 4 4888.57 3 2159.33 2 9.05 4.26s с          1786.77 4 3293.67 3 1410.95 2 95.48 3.58m с          2511.06 4 4238.40 3 1611.53 2 149.47 3.66os с          1140.6 4 2110.32 3 669.94 2 291.58 3.95cu с         for squid:  0.52 1.02 s   for milt of herring:  0.47 1.01 m   for octopus skin:  0.631.07 os for cucumaria:   0.531.54 cu  1209.6 142.89 .   f m  1226.74 149.08 .   f s  1128.55 138.24 .   f os  1031.26 100.42 .   f cu (18)Formulae (15–18) can be used to calculate thethermal conductivity of the studied objects with acorrelation coefficient of 0.99. They also allow usto determine the thermal conductivity of the test(a) (b)Total specific heatcapacity, kJ/kg·KAmount of frozen out water, kg/kgTotal specific heatcapacity, kJ/kg·KAmount of frozen out water, kg/kg(c) (d)Figure 1 Relation between total specific heat capacity and the amount of frozen out water: (A) pallium of Pacific squid; (B) milt ofPacific herring; (C) octopus skin; (D) Japanese cucumaria.Total specific heatcapacity, kJ/kg·KAmount of frozen out water, kg/kgTotal specific heatcapacity, kJ/kg·KAmount of frozen out water, kg/kgn n с  g c  g c  g c ... g c 1 1 2 2 3 3dtdq L W d f    fr 0       22( ) 21p pi frfr ii p i frf           wiwiipm WW1 312211 11 frm g g g 2751.19 4 4888.57 3 2159.33 2 9.05 4.26s с          (11)1786.77 4 3293.67 3 1410.95 2 95.48 3.58m с          (12)2511.06 4 4238.40 3 1611.53 2 149.47 3.66os с          (13)1140.6 4 2110.32 3 669.94 2 291.58 3.95cu с         for squid:  0.52 1.02 s   (15)for milt of herring:  0.47 1.01 m   (16)for octopus skin:  0.631.07 os (17)for cucumaria:   0.531.54 cu (18) 1209.6 142.89 .   f m (19) 1226.74 149.08 .   f s (20) 1128.55 138.24 .   f os (21) 1031.26 100.42 .   f cu (22)(11)n n с  g c  g c  g c ... g c 1 1 2 2 3 3dtdq L W d f    fr 0       22( ) 21p pi frfr ii p i frf           wiwiipm WW1 312211 11 frm g g g 2751.19 4 4888.57 3 2159.33 2 9.05 4.26s с          (11)1786.77 4 3293.67 3 1410.95 2 95.48 3.58m с         (12)2511.06 4 4238.40 3 1611.53 2 149.47 3.66os с          (13)1140.6 4 2110.32 3 669.94 2 291.58 3.95cu с         for squid:  0.52 1.02 s   (15)for milt of herring:  0.47 1.01 m   (16)for octopus skin:  0.631.07 os (17)for cucumaria:   0.531.54 cu (18) 1209.6 142.89 .   f m (19) 1226.74 149.08 .   f s (20) 1128.55 138.24 .   f os (21) 1031.26 100.42 .   f cu (22)(12)n n с  g c  g c  g c ... g c 1 1 2 2 3 3dtdq L W d f    fr 0       22( ) 21p pi frfr ii p i frf           wiwiipm WW1 312211 11 frm g g g 2751.19 4 4888.57 3 2159.33 2 9.05 4.26s с          (11)1786.77 4 3293.67 3 1410.95 2 95.48 3.58m с          (12)2511.06 4 4238.40 3 1611.53 2 149.47 3.66os с          (13)1140.6 4 2110.32 3 669.94 2 291.58 3.95cu с         for squid:  0.52 1.02 s   (15)for milt of herring:  0.47 1.01 m   (16)for octopus skin:  0.631.07 os (17)for cucumaria:   0.531.54 cu (18) 1209.6 142.89 .   f m (19) 1226.74 149.08 .   f s (20) 1128.55 138.24 .   f os (21) 1031.26 100.42 .   f cu (22)(13)n n с  g c  g c  g c ... g c 1 1 2 2 3 3dtdq L W d f    fr 0       22( ) 21p pi frfr ii p i frf           wiwiipm WW1 312211 11 frm g g g 2751.19 4 4888.57 3 2159.33 2 9.05 4.26s с          (11)1786.77 4 3293.67 3 1410.95 2 95.48 3.58m с          (12)2511.06 4 4238.40 3 1611.53 2 149.47 3.66os с          (13)1140.6 4 2110.32 3 669.94 2 291.58 3.95cu с         for squid:  0.52 1.02 s   (15)for milt of herring:  0.47 1.01 m   (16)for octopus skin:  0.631.07 os (17)for cucumaria:   0.531.54 cu (18) 1209.6 142.89 .   f m (19) 1226.74 149.08 .   f s (20) 1128.55 138.24 .   f os (21) 1031.26 100.42 .   f cu (22)(14)33Bogdanov V.D. et al. Foods and Raw Materials, 2019, vol. 7, no. 2, pp. Х–Хsamples before freezing, when the amount of frozenout water ω = 0. The thermal conductivity coefficientof non-frozen seafood equals: squid – 0.52 W/m·K,milt of Pacific herring – 0.47 W/m·K, octopus skin –0.63 W/m·K, cucumaria – 0.53 W/m·K. The values ofthermal conductivity coefficients obtained correlate wellwith the data available in academic literature for fish rawmaterials: big-eyed tuna, Pacific cod, tilapia [26–28].Formulae (15–18) correspond to the equation (6),which allows to conclude that for the studied samplesΔλ equals the following values, W/(m·K): squid – 1.02;milt of herring – 1.01; octopus skin – 1.07; cucumaria– 1.54. It is known that the value of Δλ according toexperimental data for food containing 70–80% of watervaries within 0.928–1.16 W/m·K [23]. This range exceedsΔλ of cucumaria, which can be explained by the peculiarstructure and higher water content (88.9%) in its muscletissue.Formula (10) helps calculate the density of rawmaterials in the process of freezing and construct graphsof the relation between density and the amount of frozenout water (Fig. 3).Analysing the graphs in Figure 3 it should be notedthat the considered relations are of the same typeand close to linear. Density of frozen raw materialsis reduced with the increase in the amount of frozenwater. This happens due to the high water content in thestudied objects. Water turns into ice which has a lowerdensity index. Approximating data curves with the helpof Curve Expert Professional 2.3, we get the formulae:n n с  g c  g c  g c ... g c 1 1 2 2 3 3dtdq L W d f    fr 0       22( ) 21p pi frfr ii p i frf           wiwiipm WW1 312211 11 frm g g g 2751.19 4 4888.57 3 2159.33 2 9.05 4.26s с          1786.77 4 3293.67 3 1410.95 2 95.48 3.58m с          2511.06 4 4238.40 3 1611.53 2 149.47 3.66os с          1140.6 4 2110.32 3 669.94 2 291.58 3.95cu с         for squid:  0.52 1.02 s   for milt of herring:  0.47 1.01 m   for octopus skin:  0.631.07 os for cucumaria:   0.531.54 cu  1209.6 142.89 .   f m  1226.74 149.08 .   f s  1128.55 138.24 .   f os  1031.26 100.42 .   f cu (19)n n с  g c  g c  g c ... g c 1 1 2 2 3 3dtdq L W d f    fr 0       22( ) 21p pi frfr ii p i frf           wiwiipm WW1 312211 11 frm g g g 2751.19 4 4888.57 3 2159.33 2 9.05 4.26s с          1786.77 4 3293.67 3 1410.95 2 95.48 3.58m с          2511.06 4 4238.40 3 1611.53 2 149.47 3.66os с          1140.6 4 2110.32 3 669.94 2 291.58 3.95cu с         for squid:  0.52 1.02 s   for milt of herring:  0.47 1.01 m   for octopus skin:  0.631.07 os for cucumaria:   0.531.54 cu  1209.6 142.89 .   f m  1226.74 149.08 .   f s  1128.55 138.24 .   f os  1031.26 100.42 .   f cu (20)n n с  g c  g c  g c ... g c 1 1 2 2 3 3dtdq L W d f    fr 0       22( ) 21p pi frfr ii p i frf           wiwiipm WW1 312211 11 frm g g g 2751.19 4 4888.57 3 2159.33 2 9.05 4.26s с          1786.77 4 3293.67 3 1410.95 2 95.48 3.58m с          2511.06 4 4238.40 3 1611.53 2 149.47 3.66os с          1140.6 4 2110.32 3 669.94 2 291.58 3.95cu с         for squid:  0.52 1.02 s   for milt of herring:  0.47 1.01 m   for octopus skin:  0.631.07 os for cucumaria:   0.531.54 cu  1209.6 142.89 .   f m  1226.74 149.08 .   f s  1128.55 138.24 .   f os  1031.26 100.42 .   f cu (21)n n с  g c  g c  g c ... g c 1 1 2 2 3 3dtdq L W d f    fr 0       22( ) 21p pi frfr ii p i frf           wiwiipm WW1 312211 11 frm g g g 2751.19 4 4888.57 3 2159.33 2 9.05 4.26s с          1786.77 4 3293.67 3 1410.95 2 95.48 3.58m с          2511.06 4 4238.40 3 1611.53 2 149.47 3.66os с          1140.6 4 2110.32 3 669.94 2 291.58 3.95cu с         for squid:  0.52 1.02 s   for milt of herring:  0.47 1.01 m   for octopus skin:  0.631.07 os for cucumaria:   0.531.54 cu  1209.6 142.89 .   f m  1226.74 149.08 .   f s  1128.55 138.24 .   f os  1031.26 100.42 .   f cu (22)These equations can be used to determine the densityof the samples before freezing, with the amount offrozen water equals 0. Then the density of chilled miltof Pacific herring can be set to 0 ρ = 1209.60 kg/m3, 0 ρsquid = 1226.74 kg/m3, 0 ρ octopus skin = 1128.55 kg/m3,and 0 ρ cucumaria shell = 1031.26 kg/m3. These datacorrelate well with the calculated values of the density ofunfrozen objects under study obtained by formula (10).The derived formulae (19–22) can be used tocalculate the relation between the density of herringmilk of the Pacific, squid trunk, octopus skin, cucumariashell and the amount of frozen out water with acorrelation coefficient of 0.99. The results of calculationsshow that the decrease in the density of the studiedhydrobionts’ tissues during freezing, when the amountof frozen out water reaches, for example, 90% makesup for squid – 11.9%, milt – 9.0%, octopus – 11.0%, andcucumaria – 8.4%. It is known that during freezing the(a) (b)Thermal conductivitycoefficient, W/m3·KAmount of frozen out water, kg/kgThermal conductivitycoefficient, W/m3·KAmount of frozen out water, kg/kgThermal conductivitycoefficient, W/m3·KAmount of frozen out water, kg/kgThermal conductivitycoefficient, W/m3·KAmount of frozen out water, kg/kg(c) (d)Figure 2 Relation between thermal conductivity coefficient and the amount of frozen out water for: (A) squid trunk; (B) milt ofherring; (C) octopus skin; (D) cucumaria34Bogdanov V.D. et al. Foods and Raw Materials, 2019, vol. 7, no. 2, pp. Х–Хdensity of Atlantic mackerel muscle tissue decreases by9.3% [23].Thus, studies of changes in thermal properties in theprocess of freezing Pacific squid, milt of Pacific herring,giant octopus, and muscle tissue of Japanese cucumariawere undertaken.CONCLUSIONIt was found that during freezing the change in totalspecific heat capacity of all the objects under study isof the same type: first, this figure increases due to theintensive ice formation in the tissues of