INTRODUCTION
Although containing a number of nutrients in their
composition, some parts of commercial hydrobionts are
not widely used in food production, thus being wasted
while processing. These include octopus skin, which
makes up to 37% by weight of raw material and is rich
in caratinoids, collagen, taurine, selenium, high-limit
fatty acids [1–4]. Processing of Pacific herring produces
rarely used now milt (up to 12.4% by weight of raw
materials), which contains nucleoproteins, including
biologically active substances (deoxyribonucleic acid
and ribonucleic acid), and polyunsaturated fatty acids,
including ω-3 and ω-6 families [5]. Among other
insufficiently used raw materials, sources are the Pacific
squid and Japanese cucumaria [6, 7]. However, these
commercial objects provide sources of such biologically
active substances as complete protein, hexosamines,
chondroitin sulfate, triterpene glycosides, and
polyunsaturated fatty acids [3, 8–10]. Getting with food
in the human body, they slow down the aging process
and have a corrective effect on metabolic processes, thus
improving the quality of life and promoting longevity.
Cryotechnology is a promising trend in the
industrial processing of biologically highly valuable raw
materials. The method allows obtaining concentrates
with highly preserved natural properties and biological
activity [11–13]. Since the resulting cryopowders,
as a rule, have the properties of biologically active
additives, they are often used as biological correctors
in the production of various food products and
30
Bogdanov V.D. et al. Foods and Raw Materials, 2019, vol. 7, no. 2, pp. Х–Х
cosmetic materials, also being included in formulation
compositions [14–18].
There are three main processes in cryogenic
processing of raw materials of animal and plant origin:
cryopreservation, cryogenic grindingб and freeze
drying. Cryopreservation consists in rapid freezing
of raw materials to a much lower than cryoscopic
temperature, when most of the water turns into ice.
It not only suppresses the activity of enzymes and
the vital activity of microorganisms, but also creates
favorable conditions for easier destruction of tissues
during subsequent cryogenic grinding [11, 19]. By now,
the process of freezing fish as a method of preservation
has been widely studied, but there is lack of data on lowtemperature
processing of non-fish commercial objects.
Also lacking are data on seafood thermal properties in
the course of low-temperature processing. However, this
knowledge is necessary when performing engineering
calculations of processes and equipment related to
cryogenic processing.
In this regard, the aim of the paper was to study the
changes in thermal properties in the process of freezing
raw materials of marine origin. Total specific heat
capacity, thermal conductivity coefficient and density
were calculated for the selected objects of study.
STUDY OBJECTS AND METHODS
The study objects were the skin of giant octopus
(Octopus dofleini), pallium of Pacific squid (Todarodes
pacificus), milt of Pacific herring (Clupea pallasii),
and muscle tissue of Japanese cucumaria (Cucumaria
japonica).
The amount of water in the samples, being the main
factor of the freezing process, was determined by the
standard method according to State Standard 7636-85 [20].
The standard software package of Microsoft Office
2007 and CurveExpert 1.4 were used for statistical data
processing and graphs plotting with formula derivation.
Total specific heat capacity determination.
The specific heat capacity of food products as
multicomponent substances is calculated according to
the law of additivity [21]:
n n с  g c  g c  g c ... g c 1 1 2 2 3 3
dt
dq L W d f

 
   fr 0
   
 

 




 
 2
2
( ) 2
1
p p
i fr
fr i
i p i fr
f  
 
 
   





 

 

  

w
i
w
i
i
p
m W
W








1
 
3
1
2
2
1
1 1
1


 


frm g g g
 


2751.19 4 4888.57 3 2159.33 2 9.05 4.26
s с          (11)
where c1, c2 , c3 ,..., cn are specific heat capacities of
components, kJ/kg·K;
g1, g2 , g3 ,...gn are mass fractions of the components.
Consider the body of the study object as a twocomponent
mixture containing W parts of water and
(1–W) parts of dry substances with corresponding
specific heat capacities for each component cw and cd.s.
Heat capacity of the product in the temperature range
before 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 raw
materials [22].
Since at negative temperatures part of the water
ω in the object under study transforms into ice, whose
heat capacity is ci , the heat capacity of the frozen raw
material 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 be
removed 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 3
dt
dq L W d f

 
   fr 0
   
 

 




 
 2
2
( ) 2
1
p p
i fr
fr i
i p i fr
f  
 
 
   





 

 

  

w
i
w
i
i
p
m W
W








1
 
3
1
2
2
1
1 1
1


 


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 3.95
cu 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 in
the expression (3), the amount of heat will receive the
dimension and meaning of the component of the specific
total heat capacity and be recorded as:
qω = LfW(ω2 – ω1) (4)
where 1 ω
is the amount of frozen out water at the initial
temperature;
and ω2 is the amount of frozen out water at the final
temperature.
The sum of calculated heat capacity of the frozen raw
material cfrm and the heat of ice formation qω will give
the total specific heat capacity:
ctot = cfrm + qω (5)
Thermal conductivity coefficient determination.
When the temperature drops below the cryoscopic
value and the product is in the process of ice formation,
its thermal conductivity increases significantly, since
thermal conductivity of ice is four times greater than
that of water.
The increase in thermal conductivity of the product
with decrease in temperature almost ceases with the end
of water freezing out, granted that further insignificant
change in the thermal conductivity of ice and other
components of the product is neglected. The thermal
conductivity coefficient of products in the range of
negative temperatures
n n с  g c  g c  g c ... g c 1 1 2 2 3 3
dt
dq L W d f

 
   fr 0
    




 
 2
2
( ) 2
1
p p
i fr
fr i
i p i fr
f  
 
 
   





 

 

  

w
i
w
i
i
p
m W
W








1
 
3
1
2
2
1
1 1
1


 


frm g g g
 


2751.19 4 4888.57 3 2159.33 s с       depends on the amount of
frozen out water and approximates to the equation [23]:
n n с  g c  g c  g c ... g c 1 1 2 2 3 3
dt
dq L W d f

 
   fr 0
   
 

 




 
 2
2
( ) 2
1
p p
i fr
fr i
i p i fr
f  
 
 
   





 

 

  

w
i
w
i
i
p
m W
W








1
 
3
1
2
2
1
1 1
1


 


frm g g g
 


(6)
where 0 λ
is the coefficient of thermal conductivity of the
product before freezing, W/m·°C;
Δλ is the change in thermal conductivity of the
product in the temperature range from the start of
freezing ts to tc corresponding to completion of ice
formation.
31
Bogdanov V.D. et al. Foods and Raw Materials, 2019, vol. 7, no. 2, pp. Х–Х
Considering raw materials as a two-component
mixture containing parts of water W and (1–W) parts
of dry substances with respective thermal conductivity
coefficients of λw and d.s λ , the heat capacity of the
product in the temperature range before ice formation is
determined by the expression:
W ( W) m w d s = + 1− . λ λ λ
where w λ = 0,597W/m2·K is the coefficient of water
thermal conductivity;
d.s λ – thermal conductivity coefficient of dry
substances [6].
The coefficient of thermal conductivity can be
calculated by the formula based on the models of
Krisher [5]:
n n с  g c  g c  g c ... g c 1 1 2 2 3 3
dt
dq L W d f

 
   fr 0
   
 

 




 
 2
2
( ) 2
1
p p
i fr
fr i
i p i fr
f  
 
 
   





 

 

  

w
i
w
i
i
p
m W
W








1
 
3
1
2
2
1
1 1
1


 


frm g g g
 


2751.19 4 4888.57 3 2159.33 2 9.05 4.26
s с          (11)
1786.77 4 3293.67 3 1410.95 2 95.48 3.58
m с          (12)
2511.06 4 4238.40 3 1611.53 2 149.47 3.66
os с          (13)
1140.6 4 2110.32 3 669.94 2 291.58 3.95
cu 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 λ
is thermal conductivity of ice coefficient within
the temperature range 273–208 K (2,22 W/m·K);
p ε – porosity coefficient which depends on the amount
of frozen out water and chemical composition.
The structure of the frozen product can be
considered as a dispersed system consisting of ice pores
with coefficient of thermal conductivity i λ
and a matter
containing unfrozen water and dry substances with a
coefficient of thermal conductivity approximately equal
to 0 λ
before freezing.
Porosity coefficient of the assumed structure will be
determined by the expression:




 

 

+ + −
=
w
i
w
i
i
p
m W
W
ρ
ρ
ω
ρ
ρ
ρ
ω
ε
1 (8)
where i ρ
is 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 of
dry substances in the process of freezing, and practically
unvarying density m ρ
m w
m W
ρ ρ
= 1 −
(9)
Frozen raw material density determination.
Consider the body of the object under study as a threecomponent
mixture consisting of unfrozen water, ice,
and dry matter. Density of the samples can thus be
presented as the equation [6]:
( )
3
1
2
2
1
1 1
1
ρ
ω
ρ ρ
ω
ρ
frm g g g
+ +
−
=
(10)
where 1 g is the mass fraction of water contained in the
sample body;
2 g is the mass fraction of solids contained in the
sample body;
1 ρ
is 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 DISCUSSION
Data on water content determination in the tissues of
the studied hydrobionts are given in Table 1.
The objects under study have a high water content
ranging from 77.4% (in the milt of Pacific herring) to
88.9% (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 specific
heat capacity of the samples. To do this, it is necessary
to determine the amount of frozen out water at different
temperatures using Ryutov’s formula [25]. Then
we apply formulae (2) and (4) to determine the heat
capacity for the selected raw material and the heat of ice
formation. The resulting values of the total specific heat
capacity of the raw material are depicted as graphs in
Figure 1.
Presented in Figure 1 graphs show the relation
between total specific heat capacity and the amount of
frozen out water for the four studied objects. As can be
seen, they are of the same type and have two distinct
areas. The first one demonstrates an increase in the
total specific heat capacity of seafood samples, which is
associated with intensive ice formation in their tissues
with a decrease in temperature and accompanying
heat release. The second area is characterized by a
gradual decrease in the total specific heat capacity of
seafood samples. This is associated with a significant
decrease in the amount of liquid aqueous phase and,
accordingly, a decrease in the intensity of its transition
to the crystalline form with the release of heat caused
by ice formation. At the final stage, when most water
is frozen out, the total specific heat capacity of the
samples under study tends to the heat capacity of ice
becoming one of the main factors of the further freezing
process. The transition point of the total specific heat
capacity from increase to decrease is reached when
the amount of frozen out water gets close to 50%.
The obtained values of total specific heat capacity of
commercial hydrobionts’ tissues are consistent with the
data available in the academic literature on aquatic raw
materials [25].
Approximating the curves shown in Fig. 1 with
Curve Expert Professional 2.3, we get the formulae:
Table 1 Water content in the tissues of hydrobionts
Sample Water content,%
Milt of Pacific herring 77.4
Pallium of Pacific squid 78.6
Skin of octopus 84.8
Japanese cucumaria 88.9
32
Bogdanov V.D. et al. Foods and Raw Materials, 2019, vol. 7, no. 2, pp. Х–Х
These formulae can be used to calculate the relation
between total specific heat capacity and the amount
of frozen out water for the studied raw materials with
a correlation coefficient of 0.99. The free term in the
obtained formulae determines the value of total heat
capacity of the raw material with the amount of frozen
water equal to 0. Therefore, total specific heat capacity
of 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 capacity
of non-frozen raw materials calculated, based on the
standard formula (1) were as follows (kJ/kg·K): 4.06 for
squid; 3.52 for milt; 4.05 for octopus skin; and 3.93 for
cucumaria. The difference between the data obtained
according 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 derived
mathematical relationships.
Using formula (7), we calculated the coefficient of
thermal conductivity of the selected raw material and
plotted the relation to the amount of frozen out water
(Fig. 2).
Analysing the graphs in Figure 2, we see that the
dependence of the change in the thermal conductivity
of the studied samples is close to linear. The thermal
conductivity of the studied seafood in the process
of freezing increases with the proportion of frozen
out water, tending to the thermal conductivity of ice,
which is almost four times greater than the thermal
conductivity of water. Approximating the chart data
using Curve Expert Professional 2.3, we obtain the
formulae:
for squid:
n n с  g c  g c  g c ... g c 1 1 2 2 3 3
dt
dq L W d f

 
   fr 0
   
 

 




 
 2
2
( ) 2
1
p p
i fr
fr i
i p i fr
f  
 

   





 

 

  

w
i
w
i
i
p
m W
W








1
 
3
1
2
2
1
1 1
1


 


frm g g g
 


2751.19 4 4888.57 3 2159.33 2 9.05 4.26
s с          1786.77 4 3293.67 3 1410.95 2 95.48 3.58
m с          2511.06 4 4238.40 3 1611.53 2 149.47 3.66
os с          1140.6 4 2110.32 3 669.94 2 291.58 3.95
cu 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 3
dt
dq L W d f

 
   fr 0
   
 

 




 
 2
2
( ) 2
1
p p
i fr
fr i
i p i fr
f  
 
 
   





 

  
  

w
i
w
i
i
p
m W
W








1
 
3
1
2
2
1
1 1
1


 


frm g g g
 


2751.19 4 4888.57 3 2159.33 2 9.05 4.26
s с          1786.77 4 3293.67 3 1410.95 2 95.48 3.58
m с          2511.06 4 4238.40 3 1611.53 2 149.47 3.66
os с          1140.6 4 2110.32 3 669.94 2 291.58 3.95
cu 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 3
dt
dq L W d f

 
   fr 0
   
 

 




 
 2
2
( ) 2
1
p p
i fr
fr i
i p i fr
f  
 
 
   





 

  
  

w
i
w
i
i
p
m W
W








1
 
3
1
2
2
1
1 1
1


 


frm g g g
 


2751.19 4 4888.57 3 2159.33 2 9.05 4.26
s с          1786.77 4 3293.67 3 1410.95 2 95.48 3.58
m с          2511.06 4 4238.40 3 1611.53 2 149.47 3.66
os с          1140.6 4 2110.32 3 669.94 2 291.58 3.95
cu 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 3
dt
dq L W d f

 
   fr 0
   
 

 




 
 2
2
( ) 2
1
p p
i fr
fr i
i p i fr
f  
 
 
   





 

  
  

w
i
w
i
i
p
m W
W








1
 
3
1
2
2
1
1 1
1


 


frm g g g
 


2751.19 4 4888.57 3 2159.33 2 9.05 4.26
s с          1786.77 4 3293.67 3 1410.95 2 95.48 3.58
m с          2511.06 4 4238.40 3 1611.53 2 149.47 3.66
os с          1140.6 4 2110.32 3 669.94 2 291.58 3.95
cu 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 the
thermal conductivity of the studied objects with a
correlation coefficient of 0.99. They also allow us
to determine the thermal conductivity of the test
(a) (b)
Total specific heat
capacity, kJ/kg·K
Amount of frozen out water, kg/kg
Total specific heat
capacity, kJ/kg·K
Amount 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 of
Pacific herring; (C) octopus skin; (D) Japanese cucumaria.
Total specific heat
capacity, kJ/kg·K
Amount of frozen out water, kg/kg
Total specific heat
capacity, kJ/kg·K
Amount of frozen out water, kg/kg
n n с  g c  g c  g c ... g c 1 1 2 2 3 3
dt
dq L W d f

 
   fr 0
   
 

 




 
 2
2
( ) 2
1
p p
i fr
fr i
i p i fr
f  
 
 
   





 

 

  

w
i
w
i
i
p
m W
W








1
 
3
1
2
2
1
1 1
1


 


frm g g g
 


2751.19 4 4888.57 3 2159.33 2 9.05 4.26
s с          (11)
1786.77 4 3293.67 3 1410.95 2 95.48 3.58
m с          (12)
2511.06 4 4238.40 3 1611.53 2 149.47 3.66
os с          (13)
1140.6 4 2110.32 3 669.94 2 291.58 3.95
cu 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 3
dt
dq L W d f

 
   fr 0
   
 

 




 
 2
2
( ) 2
1
p p
i fr
fr i
i p i fr
f  
 
 
   





 

 

  

w
i
w
i
i
p
m W
W








1
 
3
1
2
2
1
1 1
1


 


frm g g g
 


2751.19 4 4888.57 3 2159.33 2 9.05 4.26
s с          (11)
1786.77 4 3293.67 3 1410.95 2 95.48 3.58
m с         (12)
2511.06 4 4238.40 3 1611.53 2 149.47 3.66
os с          (13)
1140.6 4 2110.32 3 669.94 2 291.58 3.95
cu 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 3
dt
dq L W d f

 
   fr 0
   
 

 




 
 2
2
( ) 2
1
p p
i fr
fr i
i p i fr
f  
 
 
   





 

 

  

w
i
w
i
i
p
m W
W







1
 
3
1
2
2
1
1 1
1


 


frm g g g
 


2751.19 4 4888.57 3 2159.33 2 9.05 4.26
s с          (11)
1786.77 4 3293.67 3 1410.95 2 95.48 3.58
m с          (12)
2511.06 4 4238.40 3 1611.53 2 149.47 3.66
os с          (13)
1140.6 4 2110.32 3 669.94 2 291.58 3.95
cu 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 3
dt
dq L W d f

 
   fr 0
   
 

 




 
 2
2
( ) 2
1
p p
i fr
fr i
i p i fr
f  
 
 
   




 

 

  

w
i
w
i
i
p
m W
W








1
 
3
1
2
2
1
1 1
1


 


frm g g g
 


2751.19 4 4888.57 3 2159.33 2 9.05 4.26
s с          (11)
1786.77 4 3293.67 3 1410.95 2 95.48 3.58
m с          (12)
2511.06 4 4238.40 3 1611.53 2 149.47 3.66
os с          (13)
1140.6 4 2110.32 3 669.94 2 291.58 3.95
cu 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)
33
Bogdanov V.D. et al. Foods and Raw Materials, 2019, vol. 7, no. 2, pp. Х–Х
samples before freezing, when the amount of frozen
out water ω = 0. The thermal conductivity coefficient
of 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 of
thermal conductivity coefficients obtained correlate well
with the data available in academic literature for fish raw
materials: big-eyed tuna, Pacific cod, tilapia [26–28].
Formulae (15–18) correspond to the equation (6),
which allows to conclude that for the studied samples
Δλ 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 to
experimental data for food containing 70–80% of water
varies within 0.928–1.16 W/m·K [23]. This range exceeds
Δλ of cucumaria, which can be explained by the peculiar
structure and higher water content (88.9%) in its muscle
tissue.
Formula (10) helps calculate the density of raw
materials in the process of freezing and construct graphs
of the relation between density and the amount of frozen
out water (Fig. 3).
Analysing the graphs in Figure 3 it should be noted
that the considered relations are of the same type
and close to linear. Density of frozen raw materials
is reduced with the increase in the amount of frozen
water. This happens due to the high water content in the
studied objects. Water turns into ice which has a lower
density index. Approximating data curves with the help
of 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 3
dt
dq L W d f

 
   fr 0
   
 

 




 
 2
2
( ) 2
1
p p
i fr
fr i
i p i fr
f  
 
 
   





 

 

  

w
i
w
i
i
p
m W
W








1
 
3
1
2
2
1
1 1
1


 


frm g g g
 


2751.19 4 4888.57 3 2159.33 2 9.05 4.26
s с          1786.77 4 3293.67 3 1410.95 2 95.48 3.58
m с          2511.06 4 4238.40 3 1611.53 2 149.47 3.66
os с          1140.6 4 2110.32 3 669.94 2 291.58 3.95
cu 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 3
dt
dq L W d f

 
   fr 0
   
 

 




 
 2
2
( ) 2
1
p p
i fr
fr i
i p i fr
f  
 
 
   





 

 

  

w
i
w
i
i
p
m W
W








1
 
3
1
2
2
1
1 1
1


 


frm g g g
 


2751.19 4 4888.57 3 2159.33 2 9.05 4.26
s с          1786.77 4 3293.67 3 1410.95 2 95.48 3.58
m с          2511.06 4 4238.40 3 1611.53 2 149.47 3.66
os с          1140.6 4 2110.32 3 669.94 2 291.58 3.95
cu 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 3
dt
dq L W d f

 
   fr 0
   
 

 




 
 2
2
( ) 2
1
p p
i fr
fr i
i p i fr
f  
 
 
   





 

 

  

w
i
w
i
i
p
m W
W








1
 
3
1
2
2
1
1 1
1


 


frm g g g
 


2751.19 4 4888.57 3 2159.33 2 9.05 4.26
s с          1786.77 4 3293.67 3 1410.95 2 95.48 3.58
m с          2511.06 4 4238.40 3 1611.53 2 149.47 3.66
os с          1140.6 4 2110.32 3 669.94 2 291.58 3.95
cu 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 3
dt
dq L W d f

 
   fr 0
   
 

 




 
 2
2
( ) 2
1
p p
i fr
fr i
i p i fr
f  
 
 
   





 

 

  

w
i
w
i
i
p
m W
W








1
 
3
1
2
2
1
1 1
1


 


frm g g g
 


2751.19 4 4888.57 3 2159.33 2 9.05 4.26
s с          1786.77 4 3293.67 3 1410.95 2 95.48 3.58
m с          2511.06 4 4238.40 3 1611.53 2 149.47 3.66
os с          1140.6 4 2110.32 3 669.94 2 291.58 3.95
cu 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 density
of the samples before freezing, with the amount of
frozen water equals 0. Then the density of chilled milt
of Pacific herring can be set to 0 ρ = 1209.60 kg/m3, 0 ρ
squid = 1226.74 kg/m3, 0 ρ octopus skin = 1128.55 kg/m3,
and 0 ρ cucumaria shell = 1031.26 kg/m3. These data
correlate well with the calculated values of the density of
unfrozen objects under study obtained by formula (10).
The derived formulae (19–22) can be used to
calculate the relation between the density of herring
milk of the Pacific, squid trunk, octopus skin, cucumaria
shell and the amount of frozen out water with a
correlation coefficient of 0.99. The results of calculations
show that the decrease in the density of the studied
hydrobionts’ tissues during freezing, when the amount
of frozen out water reaches, for example, 90% makes
up for squid – 11.9%, milt – 9.0%, octopus – 11.0%, and
cucumaria – 8.4%. It is known that during freezing the
(a) (b)
Thermal conductivity
coefficient, W/m3·K
Amount of frozen out water, kg/kg
Thermal conductivity
coefficient, W/m3·K
Amount of frozen out water, kg/kg
Thermal conductivity
coefficient, W/m3·K
Amount of frozen out water, kg/kg
Thermal conductivity
coefficient, W/m3·K
Amount 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 of
herring; (C) octopus skin; (D) cucumaria
34
Bogdanov V.D. et al. Foods and Raw Materials, 2019, vol. 7, no. 2, pp. Х–Х
density of Atlantic mackerel muscle tissue decreases by
9.3% [23].
Thus, studies of changes in thermal properties in the
process of freezing Pacific squid, milt of Pacific herring,
giant octopus, and muscle tissue of Japanese cucumaria
were undertaken.
CONCLUSION
It was found that during freezing the change in total
specific heat capacity of all the objects under study is
of the same type: first, this figure increases due to the
intensive ice formation in the tissues of

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