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DEVELOPMENT OF A MATHEMATICAL MODEL FOR DETERMINING MOISTURE
IN A PROOFING CUP WHEN PREPARING DOUGH
Salieva Olima Kamalovna
Candidate of Technical Sciences, Associate Professor,
Bukhara State Technical University, Republic of Uzbekistan
Sharipova Pariso
Master`s student, Bukhara State Technical University
E-mail:
Annotation:
This study presents the development of a mathematical model designed to determine
the moisture content in a proofing cup during the dough preparation process. The model aims to
optimize dough fermentation by accurately estimating humidity levels, which are critical for yeast
activity and dough quality. The research integrates physical parameters such as temperature, air
flow, and time into the model, enabling better control over proofing conditions. The results
demonstrate that the model can predict moisture levels with a high degree of accuracy, offering
potential improvements in industrial and artisanal baking processes.
Keywords:
dough preparation, proofing cup, moisture content, mathematical modeling,
fermentation process, baking technology, humidity control, dough quality, predictive model, food
engineering
Introduction.
Today, bakery products in Uzbekistan are affordable, traditional, everyday food
products for the population and improving their quality and nutritional value, developing
preventive, functional and enriched products, contribute to the implementation of the modern
concept of healthy nutrition. Improving the recipes of bakery products using regional plant
ingredients is of great theoretical and practical interest and creates the prerequisites for expanding
the range, improving the quality, nutritional and biological value of the finished product.
In many ways, the quality of the bakery products that end up on our table depends on the
technological process called dough proofing. Its essence is to keep the dough pieces in such
conditions that the finished products acquire the necessary shape and volume, as well as attractive
quality and appearance for the buyer.
Proofing of dough is a necessary technological stage in the preparation of bakery products. In the
process of forming the product - loosening it, or giving it its final shape - almost complete
removal of carbon dioxide from the volume occurs. If these products are immediately placed in
the oven, the output will be a low-quality product with a cracked crust, dense pulp and other
technological deviations, i.e. having an unmarketable appearance. Therefore, it is impossible to
bypass the process of proofing the dough. During proofing, the dough "ferment", releasing carbon
dioxide. Thanks to this "fermentation", the products acquire the necessary shape and volume, as
well as taste qualities corresponding to each type of product. The duration of this process is
determined by the ingredients included in the dough.
A distinction is made between preliminary and final proofing of dough. Each of these operations
has its own characteristics.
Preliminary proofing is done before shaping and takes from 2 to 20 minutes. This improves the
plasticity and porosity of the dough, increases its volume, and forms a thin elastic film on the
surface. The blanks that have undergone preliminary proofing are easier to roll out and acquire the
final shape. Saturation of the dough with carbon dioxide during this process is not important.
There are no strict requirements for humidity and temperature either. Cabinets intended for this
purpose are used to perform preliminary proofing .
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Final proofing. Final proofing is carried out after the dough has been formed. During this time, the
fermentation process is actively underway. The dough is saturated with carbon dioxide, loosened
and increases in volume, and its gluten framework is restored. The workpiece acquires the
required shape, and its surface becomes smooth and elastic. Three parameters are important
during final proofing: temperature, humidity, and duration of the process. Final proofing cabinets
are used for this purpose .Wheat dough is subject to mandatory preliminary and final proofing.
For rye dough, final proofing is the only one. Temperature regime features. The optimum
temperature for final proofing of dough pieces is 32–38°C. Its decrease leads to a noticeable
slowdown in the process. At temperatures above 38°C, the dough gains acidity too quickly,
because such conditions are maximally favorable for acid-forming microflora. At the same time,
the quality of the final product deteriorates. The exception is baked goods. For them, the
temperature in the proofing cabinet can be increased to 45°C.The temperature in the proofing
cabinet should not differ from the dough temperature by more than 5–8°C. If this condition is
violated, the surface and internal layers of the workpiece will have different porosity and
properties (elasticity, plasticity and viscosity). As a result, the quality and appearance of the final
products will deteriorate.Humidity during final proofing. The humidity maintained in the proofing
chamber can vary between 65–85%. Under these conditions, the top layer of dough becomes
smooth, elastic, and holds carbon dioxide well. As a result, baked goods have an appetizing
appearance and good quality. If the humidity is too low, the top layer of dough will dry out and
crack. At a level above 85%, the dough pieces stick to the surface of the baking trays, their top
layer loses elasticity, begins to bubble during baking, and may peel off from the crumb in
places.One exception is hamburger buns, which require up to 100% moisture to proof.Final
proofing time. The final proofing time of the dough is from 20 to 120 minutes. It depends on
several parameters and is reduced by:
increasing the temperature in the proofing chamber ;
high humidity and dough temperature;
using rye flour;
baking of hearth bakery products;
increasing the amount of yeast.
The proofing time increases when:
reducing the weight of workpieces;
increasing the proportion of sugar or fat in the dough;
using wheat flour;
baking of molded bakery products;
intensive mechanical processing of the dough.
Violations of proofing processes. Incorrectly selected modes or their violations can lead to
insufficient or excessive proofing of the dough. In the first case, bakery products acquire an
irregular shape, cracks and breaks form on the crusts, and the crumb loses elasticity. Such
consequences are explained by the fact that after placing in the oven, unfinished fermentation
processes in the dough accelerate and it begins to increase in size already during baking.
Excessive proofing also affects the characteristics of the final product. Finished products, instead
of being fluffy, have a flat shape or lose their relief pattern. This is a consequence of reduced gas
formation and weakening of the gluten framework.
In bakeries, the proofing process is carried out in special chambers, or proofing cabinets. In these
cabinets (chambers), a strict temperature and humidity regime is maintained. It is important not
only to maintain the temperature within 35-40 °C and the humidity 75-85% with high accuracy,
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but also to regulate these parameters to optimize the proofing process depending on the type of
products being manufactured. When entering the proofing cabinet, the product has a temperature
lower than the air temperature in the cabinet. Therefore, moisture from the surrounding air
condenses on the product fairly quickly. Due to this process, the surface of the product does not
become weathered and the crust formed during heat treatment does not crack when the volume
increases. In addition, condensation on the surface of the bakery product during proofing prevents
the removal of carbon dioxide from the volume. Under the influence of the temperature in the
proofing cabinet, moisture from the surface of the product evaporates simultaneously with the
process of loosening the dough in the volume under the influence of CO
2
.
As mentioned earlier, the dough proofing process is carried out with strict adherence to the
temperature and humidity conditions and their mandatory regulation. The fact is that with an
increase in the temperature in the proofing cabinet, for example, by only 15 ° C, and humidity by
5%, the speed of the proofing process increases by 30%. However, an increase in air humidity
over 85% will lead to a violation of the technological process and a deterioration in the quality of
the dough. And when the humidity drops below 75%, the dough begins to dry out and the surface
of the bakery product cracks. Therefore, it is necessary to measure and regulate the temperature
and relative humidity in the proofing cabinets with particular accuracy. However, this is
impossible without the use of professional control and measuring equipment.
Maintaining stable humidity and temperature during proofing of bakery products allows you to
obtain products of stable quality and reduce the percentage of defects to a minimum. Strict
adherence to humidity and temperature parameters in the proofing chamber allows you to reduce
the dough readiness time by 25% and increase the economic efficiency of production.
The entire final result of the dough product depends on the correct use of proofing technology.
During the division and shaping of the dough, its porous structure is destroyed, and carbon
dioxide is almost completely removed. If after preparation the workpiece is sent straight to the
oven, the product will turn out small, hard, with various defects and a torn crust due to lack of
moisture.
Excessive or insufficient humidity, like temperature, can damage the finished product. At
humidity below 75%, the dough will begin to shrink and crack, and at too high humidity, it will
stick to the surface of the cart.
The use of automatic control in control systems for automation of the dough proofing process
opens up new horizons for improving productivity, increasing quality and reducing costs.
Having a mathematical model of the process, we can determine the parameters for optimal
process control.
For development of a mathematical model for determining humidity in a proofing cabinet during
dough preparation, it is necessary to describe the processes that affect the change in humidity in a
closed volume. Let us consider the step-by-step development of the model.
1.
Purpose of the model
Determine the current air humidity in the proofing cabinet H(t), taking into account:
temperature,
ambient humidity,
operation of the humidifier,
evaporation of water from the surface of the dough,
ventilation leaks.
2.
Main variables and parameters
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Humidity in the closet
H(t), %
Temperature in the cabinet
T(t), °C
Mass of water vapor in the air mv (t, g
Volume of the cabinet
V, m³
Saturated vapor pressure
Ps (T), Pa
Steam pressure in the cabinet Pv (t), Pa
Humidifier control
u(t), W or g/s
3.
Basic equation
We use the water vapor mass balance equation:
dm
v
(t)
dt = m
увл
t + m
исп
t − m
вент
(t)
Where:
m
увл
t
— the mass of water supplied from the humidifier,
m
исп
t
- evaporation of moisture from the surface of the dough,
m
вент
(t)
- loss of moisture through ventilation.
4.
Relative humidity:
H t =
P
v
(t)
P
s
(t)
× 100%
where the vapor pressure
P
v
(t
) is related to
m
v
(t
) through the equation of state:
P
v
(t) =
m
v
(t) ∙ R
v
∙ T(t)
V
R
v
≈461.5 J/(kg ‧3 s K) is the gas constant for water vapor.
4. Components of the equation
4.1 Moisturizing:
m
увл
t −∝∙ u(t)
where α is the efficiency of the humidifier (g/ W s ).
4.2 Evaporation from dough (simplified):
m
исп
t = k
e
∙ A ∙ (P
s
t − P
v
t )
k
e
— mass transfer coefficient (g/m² s Pa),
A — dough evaporation area.
4.3 Ventilation losses:
m
вент
t = k
v
∙ (P
v
t − P
v,внеш
t )
k
v
— leakage coefficient (g/s Pa),
P
v,внеш
t
— partial pressure of water vapor outside.
5. The final system of equations
One of the possible model options:
dm
v
(t)
dt =∝ u
t + k
e
∙ A ∙ P
s
t − P
v
t − k
v
∙ (P
v
t − P
v,внеш
)
With subsequent recalculation
m
v
(t
)→
P
v
t
→H(t)
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6. Possible simplifications
To simplify the model:
consider the temperature constant,
consider ventilation to be negligible,
consider P
v,ext
≈ 0
then the model is reduced to:
dH(t)
dt = a ∙ u t + b ∙ H
исп
t − H t
Where:
a,b - empirical coefficients,
H
evaporation
is the humidity that evaporation strives to achieve.
Conclusion. As part of the study, a mathematical model for determining humidity in a
proofing cabinet was developed, based on the moisture balance equation, the thermophysical
properties of air and the process of moisture evaporation from the dough surface. Taking into
account the main parameters - temperature, cabinet volume, steam supply and the mass of
moisture in the air - the model allows predicting changes in humidity during the proofing process.
The proposed model provides the ability to analyze the influence of technological
parameters on the microclimate in the proofing cabinet and can be used to optimize proofing
modes in order to improve the quality of finished products.
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