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PUBLISHED DATE: - 24-12-2024
https://doi.org/10.37547/tajet/Volume06Issue12-17
PAGE NO.: - 181-189
MOISTURE ABSORPTION CHARACTERISTICS
OF YARNS IN VARIOUS ENVIRONMENTS
B.B. Mirzabaev
Namangan Engineering Construction Institute, Uzbekistan
N.Yu. Sharibaev
Namangan Institute of Engineering Technology, Uzbekistan
S.S. Sharipbaev
Namangan Institute of Engineering Technology, Uzbekistan
INTRODUCTION
Moisture absorption indicators of fabrics are one
of the important factors determining the quality of
materials. These indicators directly affect the
comfort, durability and functionality of the fabric.
Depending on the type of thread, its structure and
environmental conditions, such as temperature
and humidity, the moisture absorption properties
can vary significantly. Modern research is focused
on the deeper study of the mechanisms of moisture
absorption, with the aim of creating innovative
fabrics.
This
article
analyzes
important
information on moisture absorption properties
using scientific papers on the subject.
In the study, comfort properties of fibers were
studied under standard atmospheric conditions.
Properties of "rapid moisture absorption and
evaporation" are noted [1]. The importance of
structural changes to improve these indicators is
emphasized. Studying the modification of
polyester fibers with alkaline and surfactants, he
noted "significant improvement in moisture
absorption performance" [2]. This approach is
promising for creating fabrics resistant to wet
environments. Considering the methods of
extracting nanofibers from agricultural waste
using environmentally friendly methods, it was
noted that these fibers are "sensitive to moisture
and require special processing methods" [3].
studied the properties of "moisture absorption and
wetting" of silk fibers and noted that they have
high functionality and aesthetic advantages [4].
studied ultrahigh molecular polyethylene fibers
RESEARCH ARTICLE
Open Access
Abstract
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under different temperature and humidity
conditions and found "significant changes in
moisture absorption properties" [5]. analyzed the
structure and properties of silk fibers and showed
"significant influence of external temperature and
humidity on moisture absorption and mechanical
properties" [6]. studied fabrics intended for
medical clothing and concluded that their "good air
permeability and moisture absorption properties
ensure long-term comfort" [7]. analyzed textile
ropes and emphasized the importance of their
"moisture absorption properties for flexibility and
functionality in various conditions" [8]. studied
membranes based on fibers and concluded that
they "enable evaporation of moisture and passive
cooling" [9]. studied woven fabrics for sportswear
and found that they "effectively wick away
moisture and provide comfort for athletes" [10].
Theoretical part
The following model can be proposed to represent
the process of moisture absorption for pile fabrics
made of cotton fiber in the form of a time
differential equation taking into account
temperature, relative humidity and pressure.
Markings:
•
M(t)
—
amount of moisture in the tissue at
time ttt (% or kg water/kg dry matter).
•
Meq(T,RH,P)
—
equilibrium
moisture
content under given temperature (T),
relative humidity (RH) and pressure (P)
conditions.
•
k(T,RH,P)
—
moisture absorption rate
constant, depending on temperature,
relative humidity and pressure (1/s).
Rate constant k(T,RH,P):
The rate constant depends on temperature,
relative humidity, and pressure, and is usually
expressed as a function of temperature using the
Arrhenius equation:
𝑘(𝑇) = 𝑘
0
𝑒
−
𝐸𝑎
𝑅𝑇
(1)
Here:
•
k0 is a pre-exponential factor (1/s).
•
Ea - activation energy (J/mol).
•
R is the universal gas constant (8.314
J/mol·K).
•
T is absolute temperature (K).
Pressure and relative humidity
to take into
account k can be determined experimentally and
empirically related functions can be added to it.
Equilibrium moisture content Meq(T,RH,P):
GAB
model
(Guggenheim-Anderson-de
Boer
model) is a widely used physicochemical model for
describing moisture sorption isotherms. It was
developed on the basis of the BET model
(Brunauer-Emmett-Teller), which allows for a
more accurate description of the moisture
absorption properties of materials.
Limitations of the BET model:
Although the BET model takes into account the
monolayer and multilayer processes of adsorption,
it does not perform well under conditions of high
relative humidity (>0.5). To overcome these
limitations, the GAB model was developed.
Basics of the GAB model:
The GAB model is based on the following key
assumptions:
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1.
Monolayer adsorption:
On the surface of
the adsorbent, the molecules form the first
layer, the energy of this layer is the lowest.
2.
Multilayer adsorption:
After the first layer,
high-energy layers are formed, in which
adsorbate molecules interact with each
other and with the adsorbent.
3.
The relationship between water activity
and equilibrium moisture content:
The
adsorption process depends on the water
activity aw.
The GAB model thus provides a deeper analysis of
the physico-chemical basis of adsorption and
allows for a more accurate description of moisture
sorption isotherms.
Equilibrium moisture content is represented by
sorption isotherms. For example, the GAB
(Guggenheim-Anderson-de Boer) model:
𝑀
𝑒𝑞
=
𝑀
0
𝐶𝐾
𝑎𝑤
𝑎
𝜔
(1−𝐾
𝑎𝑤
𝑎
𝜔
)(1−𝐾
𝑎𝑤
𝑎
𝜔
+𝐶𝐾
𝑎𝑤
𝑎
𝜔
)
(2)
Here:
•
M0, C, Kaw are empirical constants.
•
awa - water activity,
𝑎
𝑤
=
𝑃
𝐻2𝑜
𝑃
𝐻2𝑜
0
, where is the partial pressure of
water vapor, and is the saturated vapor
pressure of water.
𝑃
𝐻
2
𝑜
𝑃
𝐻
2
𝑜
0
•
RH is relative humidity (%), and
=RH/100.
𝑎
𝑤
Changes in humidity over time, taking into
account temperature, relative humidity and
pressure:
𝑑𝑀(𝑡)
𝑑𝑡
= 𝑘
0
𝑒
−
𝐸𝑎
𝑅𝑇
[M
𝑒𝑞
(T, RH, P) − M(t)]
(3)
Pressure affects the boiling point of water and the
partial pressure of water vapor. The Antoine
equation is used to express the effect of pressure:
For it, we determine the partial pressure of water:
𝑃
𝐻
2
𝑜
=
𝑅𝐻
100
𝑃
𝑠𝑎𝑡
(4)
The activity of water is determined
depending on the pressure:
𝑎
𝜔
=
𝑃
𝐻20
𝑃
(5)
From these equations we get the following
equation.
𝑙𝑜𝑔
10
𝑃
𝐻
2
0
0
= 𝐴 −
𝐵
𝐶+𝑇
(6)
Here A, B, C are Antoine's constants, T is
temperature (°C or K). The saturated pressure of
water vapor is determined by this equation and
varies depending on the pressure.
𝑃
𝐻
2
0
0
The rate constant k(T,RH,P) looks like this:
The rate constant may also depend on the
pressure. We write it taking into account the
Arrhenius equation and the effect of pressure:
𝑘(𝑇, 𝑅𝐻, 𝑃) = 𝑘
0
(
𝑃
𝑃
0
)
𝛾
𝑒
−
𝐸𝑎
𝑅𝑇
(7)
Here:
•
k0 is a pre-exponential factor (1/s).
•
P0 - standard pressure (Pa).
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•
g is a pressure-dependent indicator
(determined empirically).
•
Ea - activation energy (J/mol).
•
R is the universal gas constant (8.314
J/mol·K).
•
T is absolute temperature (K).
As pressure increases, the kinetic energy of
molecules and the rate of diffusion can change,
which affects
𝑘(𝑇, 𝑅𝐻, 𝑃)
The basic differential equation for moisture
absorption taking pressure into account looks like
this:
𝑑𝑀(𝑡)
𝑑𝑡
= 𝑘
0
(
𝑃
𝑃
0
)
𝛾
𝑒
−
𝐸𝑎
𝑅𝑇
[
𝑀
0
𝐶𝐾
𝑎𝑤
𝑎
𝜔
(1−𝐾
𝑎𝑤
𝑎
𝜔
)(1−𝐾
𝑎𝑤
𝑎
𝜔
+𝐶𝐾
𝑎𝑤
𝑎
𝜔
)
− 𝑀(𝑡)]
(8)
This equation describes the process of moisture
absorption of pile fabrics made of cotton fiber as a
function of temperature, relative humidity and
pressure.
The GAB model describes moisture sorption
isotherms on a physicochemical basis and has a
convenient mathematical expression to account
for the effect of pressure. The basic differential
equation of moisture absorption written in terms
of pressure provides a more accurate modeling of
the moisture absorption process for pile fabrics
made of cotton fibers.
This equation can be solved analytically.
First of all, we remember the last created
differential equation and write it in a simplified
form.
The basic differential equation is:
𝑑𝑀(𝑡)
𝑑𝑡
= 𝑘(𝑇, 𝑅𝐻, 𝑃)[M
𝑒𝑞
(T, RH, P) − M(t)]
(9)
According to the GAB model:
𝑀
𝑒𝑞
=
𝑀
0
𝐶𝐾
𝑎𝑤
𝑎
𝜔
(1−𝐾
𝑎𝑤
𝑎
𝜔
)(1−𝐾
𝑎𝑤
𝑎
𝜔
+𝐶𝐾
𝑎𝑤
𝑎
𝜔
)
(10)
Rate constant k(T,RH,P):
𝑘(𝑇, 𝑅𝐻, 𝑃) = 𝑘
0
(
𝑃
𝑃
0
)
𝛾
𝑒
−
𝐸𝑎
𝑅𝑇
(11)
However, to simplify the analysis, we simplify the
differential equation as follows:
1.
kand Meq as constants (assuming that
temperature, relative humidity, and
pressure do not change over time).
2.
We write the equation as follows:
𝑑𝑀(𝑡)
𝑑𝑡
= 𝑘[M
𝑒𝑞
− M(t)]
(12)
This differential equation is a first-order linear differential equation that can be solved analytically.
We write the equation:
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𝑑𝑀(𝑡)
𝑑𝑡
+ 𝑘𝑀(𝑡) = 𝑘𝑀
𝑒𝑞
(13)
Let's make it simple to integrate.
This equation is a linear differential equation, the general solution of which is found as follows:
We determine the integration factor m(t):
𝜇(𝑡) = 𝑒
∫ 𝑘𝑑𝑡
= 𝑒
𝑘𝑡
(14)
We multiply the equation by the integration factor:
𝑒
𝑘𝑡 𝑑𝑀(𝑡)
𝑑𝑡
+ 𝑘𝑒
𝑘𝑡
𝑀(𝑡) = 𝑘𝑀
𝑒𝑞
𝑒
𝑘𝑡
(15)
We write the left side as a complete derivative:
𝑑
𝑑𝑡
[𝑒
𝑘𝑡
𝑀(𝑡)] = 𝑘𝑀
𝑒𝑞
𝑒
𝑘𝑡
(16)
Let's integrate both sides over time:
∫
𝑑
𝑑𝑡
[𝑒
𝑘𝑡
𝑀(𝑡)] = ∫ 𝑘𝑀
𝑒𝑞
𝑒
𝑘𝑡
(17)
Let's simplify
𝑒
𝑘𝑡
𝑀(𝑡) = 𝑘𝑀
𝑒𝑞
∫ 𝑒
𝑘𝑡
𝑑𝑡 + 𝐶
(18)
Here C is the integration constant.
Let's integrate the right side:
𝑒
𝑘𝑡
𝑀(𝑡) = 𝑘𝑀
𝑒𝑞
(
𝑒
𝑘𝑡
𝑘
) + 𝐶
(19)
Let's simplify:
𝑒
𝑘𝑡
𝑀(𝑡) = 𝑀
𝑒𝑞
𝑒
𝑘𝑡
+ 𝐶
(20)
We subtract from both sides:
𝑒
𝑘𝑡
𝑀(𝑡) = 𝑀
𝑒𝑞
+ 𝐶𝑒
−𝑘𝑡
(21)
We use the initial condition: moisture content at time t=0 (here - initial moisture content).
𝑀(0) =
𝑀
0
′
𝑀
0
′
We put the initial condition in the equation:
𝑀(0) = 𝑀
𝑒𝑞
+ 𝐶𝑒
−𝑘0
= 𝑀
𝑒𝑞
+ 𝐶
(22)
From this:
𝐶 = 𝑀(0) − 𝑀
𝑒𝑞
= 𝑀
0
′
− 𝑀
𝑒𝑞
(23)
The final analytical solution will look like this:
𝑀(𝑡) = 𝑀
𝑒𝑞
+ (𝑀
0
′
− 𝑀
𝑒𝑞
)𝑒
−𝑘𝑡
(24)
•
M(t)
—
amount of moisture in the tissue at time t.
•
Meq
—
equilibrium moisture content, moisture content tends to this value over time.
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•
𝑀
0
′
—
initial moisture content.
•
k
—
moisture absorption rate constant; the larger, the faster the moisture absorption process.
Analysis of results and conclusion
As you can see from my solution:
•
The value decreases exponentially over time.
𝑒
−𝑘𝑡
•
If t→∞, then and M(t)→Meq
.
𝑒
−𝑘𝑡
→ 0
•
The moisture content approaches the equilibrium value over time.
Picture 1.The rate of moisture absorption with temperature changes
In the graph above (Picture 1) at different time
points (10, 20, 30, 40, 50, and 60 minutes) depicted
the rate of moisture absorption with temperature
changes. Each line shows the change in moisture
content as a function of temperature at a specific
time point.
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Figure 2. Changes in relative humidity.
In the graph above (Figure 2)shows how the
moisture absorption rate of the yarn changes (10,
20, 30, 40, 50 and 60 minutes) with the change of
relative air humidity from 25% to 75%. Each line
shows the change in moisture content relative to
relative humidity at a specific time point.
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Figure 3. The degree of moisture absorption of threads with changes in air
pressure
The graph above (Figure 3) shows how the
moisture absorption rate of the yarn changes (10,
20, 30, 40, 50 and 60 minutes) as the air pressure
changes from 90,000 Pa to 110,000 Pa. Each line
shows the change in moisture content as a function
of air pressure at a specific time point.
As the pressure increases, the rate constant kkk
also changes, which affects the moisture
absorption process.
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Karabulut, AB (2024). Comfort Properties of
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Kodrić, M., et al. (2023). Modification of
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15th
Symposium
Proceedings.
3.
Zainul, R., et al (2024). Eco-friendly
Nanocellulose. Express Polymer Letters.
4.
Sharipov, K. (2024). Fine Structure of Silk.
Namangan Institute of Textile Journal.
5.
Shuo, Z., et al. (2024). Properties of
Polyethylene Fibers. Journal of Advanced
Textiles.
6.
Mao, Y., et al (2024). Properties of Silk Fibers.
MDPI Journal.
7.
Elbelbesi, MM, et al (2024). High-Performance
Fabrics. International Design Journal.
8.
Neha, K., et al (2024). Review of Ropes.
Research Journal of Textiles.
9.
Hu, M., et al (2024). Fibrous Membrane
Properties. SSRN Journal.
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10.
Priyalatha, S. (2024). Wicking Characteristics.
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