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Special application ofwetting knowledge
Wicking into fibrous materialsCONTACT ANGLE ESTIMATION
TNT
Eva Kuželová Košťáková
KCH, FP, TUL
THEORY OF NONWOVENS
-Determining (estimating) the contact angle for porous (fibrous) materials
-Determining (estimating) the contact angle of fibrous swelling materials
- Wicking into structured textiles
THEORY OF NONWOVENS
How to determine the contact angle of
nonwovens (or porous materials in general) for
contact angles of less than 90 °?
Washburn method Washburn theory suggests that if a porous
solid (eg, a nonwoven fabric) comes into contact with a liquid
so that the solid is not immersed in the liquid but rather
touches only the surface of the liquid, then the rise of liquid
into the pores of the solids will result controlled by the
following equation:
Determining (estimating) the contact angle for
porous (fibrous) materials
THEORY OF NONWOVENS
.8
2
h
Pr
dt
dh e
Lucas – Washburn equation
The fiber wetting theory was built
in the 1920s independently by
Lucas and Washburn.
Their approach is based on a
strong simplification of the
multifunctional structure of the fiber
mass into a single capillary.
Inside the capillary fluid is
transported due to surface tension.
The experimental results show that
this highly simplified model gives
qualitatively comparable results
with the fabric transport behavior.
.
8
4
21
h
rpp
dt
dV
pr
r r1 2
2 2
cos cos.
p gh2 cos .
.8
cos
4
cos 2
gr
h
r
dt
dh
bh
a
dt
dh
Determining (estimating) the contact angle for
porous (fibrous) materials
THEORY OF NONWOVENS
.8
2
h
Pr
dt
dh e
.8
cos
4
cos 2
gr
h
r
dt
dh b
h
a
dt
dh
Wicking(0°,90°
bhab
a
b
ht ln
2
The limit t is found from equation. Then ln(a-bh) and thus a-bh=0. Finally the limit, i.e. the maximal h value is …
Relation can be solved in different ways under the assumption that the second term on the right side can be neglected. (i) gravitation is neglected, g=0; or (ii) a height in a capillary is small, so a notation (h→0) can be accepted
2
1
2
cosKtt
rh
OR
Lucas – Washburn equationDetermining (estimating) the contact angle for
porous (fibrous) materials
THEORY OF NONWOVENS
https://www.lpdlabservices.co.uk/application_note_list/powder_wetting.php
2
1
2
cosKtt
rh
What does c mean? So the material
constant?
c represents: pore structure, pore size and pore number
in a solid porous material, for example, in a nonwoven
fabric
How to determine the value of c?
Correctly, when plotting a square of mass m2 against time t, it shows a linear region whose slope for known liquid properties
(, ρ and η) contains only two unknown c and θ.
Since the contact angle depends on the slope of the curve in the above data, the selected portion of the measurement data
may affect the contact angle value calculated from this slope. If the data were analyzed closer to the start of the experiment,
the slope would be greater than if the data near the end of the experiment were used. This would provide a lower contact
angle for the data selected at the start of the experiment than at the end of the experiment.
h to mto contact angle
Determining (estimating) the contact angle for
porous (fibrous) materials
THEORY OF NONWOVENS
c represents: pore structure, pore size and pore number in a solid porous material, for example, in a
nonwoven fabric
What does c mean? How to calculate value c?
First, another liquid of known contact angle with solid is used.
Typically, N-hexane is used which has a very low surface tension of 18.4mN / m and
usually has a 0 ° contact angle with solids.
Subsequently, the constant c of the nonwoven fabric to be tested is calculated. In a
further measurement, with the known constant c, a measurement is then made with the
desired liquid which does not have a zero contact angle.
The nonwoven fabric under study must be as uniform as possible, which may be a
problem at lower basis weights. Detailed statistical evaluation of acquired data is
necessary.
Determining (estimating) the contact angle for
porous (fibrous) materials
THEORY OF NONWOVENS
c represents: pore structure, pore size and pore number in a solid porous material, for example, in a nonwoven fabric
How to calculate value c?
N-hexane (contact angle 0°)
𝑚2 =𝑐𝜌2𝛾 𝑐𝑜𝑠𝜃
𝑡
y = ax; 𝑚2 = 𝑦; 𝑡 = 𝑥; 𝑎 =𝑐 𝜌2𝛾 𝑐𝑜𝑠𝜃
voda
cos 𝜃 =𝑎
𝒄 𝜌2𝛾
Determining (estimating) the contact angle for porous (fibrous) materials
THEORY OF NONWOVENS
𝒄 =𝑎ℎ𝑒𝑥𝑎𝑛𝑒
𝜌2𝛾 cos 𝜃=
0,08. 0,00033
429025 . 0,0184 . 1= 3,34 ∗ 10
− 9
N-hexane (contact angle 0°)
voda
HexaneViscosity 0,33mPasSurface tension 18,4mN/mDensity 655 kg/m3
𝑐𝑜𝑠𝜃 =0,0666 .0,001
3,34∗10−9 .1000 000 . 0,072= 0,274
Arccos 0,274 = 74,1°
cos 𝜃 =𝑎𝑤𝑎𝑡𝑒𝑟𝒄 𝜌2𝛾
WaterViscosity 1 mPasSurface tension72 mN/mDensity 1000 kg/m3
Example
THEORY OF NONWOVENS
THEORY OF NONWOVENS
https://www.sciencedirect.com/science/article/pii/S0021979713000714http://iopscience.iop.org/article/10.1088/0957-0233/24/12/125902https://www.sciencedirect.com/science/article/pii/S0927775717311512
The same procedure can be used
for powdered materials. For Kruss it
is necessary to use a special
container in which the powder is
poured.
Contact angles are calculated from
the linear parts of the graphs at the
beginning of the measurement
(for very small h, respectively for
small m).
Contact angles greater than 90 °
cannot be determined in this way -
no wetting occurs.
Determining (estimating) the contact angle
for porous (fibrous) materials
THEORY OF NONWOVENS
Static x dynamic contact angle
Advancing x receding contact angle
http://www.weistron.com/products/contact-angle-meter/
1. Static contact angleStatic contact angles are
measured when a droplet is placed on the
surface and the three-phase boundary does not
move. A drop is placed on the solid surface and
the drop image is recorded. The static contact
angle is then defined by placing a Young-Laplace
equation around the droplet, although other
methods such as a circle and a polynomial may
be used. Static contact angles are used in quality
control, research and product development.
2. Dynamic contact angleWhen the three-phase
boundary moves, dynamic contact angles can be
measured. Contact angle hysteresis is the
difference between advancing and receding
contact angles. Contact angle hysteresis is based
on chemical and topographic surface
heterogeneity, surface impurities absorbed on the
surface, or swelling, rearrangement, or solvent
surface changes. Dynamic contact angles
indicate maximum and minimum static contact
values. Dynamic contact angles can be
measured using two different approaches:
changing the drop volume or using a tilting plane.
2. (1) Volume change method:In short, a small drop is
first created and placed on the surface. The needle is
then applied to the surface and the droplet volume is
gradually increased while recording the image. This
will provide a advancing contact angle. The receding
angle is measured in the same way, but this time the
droplet volume gradually decreases.
2. (2) The principle of the tilting plane method:The
drop is placed on the substrate, which is gradually
tilted. The advancing angle is measured on the front of
the drop just before the drop begins to move. The
receding contact angle is measured at the back of the
droplet at the same time point.
Determining (estimating) the contact angle for
porous (fibrous) materials
THEORY OF NONWOVENS
http://www.face-kyowa.co.jp/english/en_science/en_theory/en_what_contact_angle/
A generalized contact angle plot showing the advancing (qAdv) and receding (qRec) contact angleshttps://www.uweb.engr.washington.edu/research/tutorials/contact.html
https://www.youtube.com/watch?v=Qxe2gp3e1u8
Contact Angle Hysteresis is
due to:
Surface roughness
Chemical surface
heterogeneity
…
Velikost kapky
Determining (estimating) the contact angle for
porous (fibrous) materials
THEORY OF NONWOVENS
Determination of contactangle on swelling fiber
materials
A variety of experimental methods are availableto determine the contact angle of liquids on
solids. However, standard optical or Wilhelmy methods become difficult to apply when the
sample swells during wetting.
THEORY OF NONWOVENS
(a) Schematic of the swelling process of collagen structure consisting of fibers and fibrils. (b) SEM images of the collagen fiber before and after swelling due to water.
https://www.nature.com/articles/srep20563#f5
Fig. 1: Pulp fiber with swollen areas marked by
the circles and the corresponding degree of
swelling, i.e. the percentage of swollen fiber
length.
https://www.researchgate.net/figure/Pulp-fiber-with-swollen-areas-marked-by-the-circles-and-the-corresponding-degree-of_fig1_267694157
THEORY OF NONWOVENS
Determining (estimating) the contact angle of porous (fibrous) materials
Swelling of viscose hollow fibers in water
Botnání viskózových dutých vláken ve vodě Different types of fiber swelling according to geometric changes
- Fiber Diameter Increase ( D / D)
- Dial Fiber surface area increase ( A / A)
- Fiber length increase ( L / L)
- Axial Fiber volume increase ( V / V)
http://textilelearner.blogspot.com/2016/06/swelling-of-textile-fibers.html
THEORY OF NONWOVENS
http://textilelearner.blogspot.com/2016/06/swelling-of-textile-fibers.html
Determining (estimating) the contact angle of porous (fibrous) materials
THEORY OF NONWOVENS
An experiment with determining the contact angle
of water on a nonwoven that has been used to
produce feminine hygiene products.
When the fibers swell during wetting, the resulting
curve in the Washburn method is not linear even
at the beginning of the measurement.
It is necessary to proceed to indirectly determine
(estimate) the contact angle. Viscose nonwoven
+ water = not measurable directly === swelling
=== curve not linear. Indirect measurement of
contact angle.
1) Find liquids that can be directly measured, the
fibrous material in contact with them is not. For
example, organic solvents such as benzyl alcohol
(benzene methanol), diodomethane = viscose
fibers do not swell.
Determining (estimating) the contact angle of porous (fibrous) materials
THEORY OF NONWOVENS
Indirect Contact Angle Measurement Procedure:
1) Finding liquids that can be directly measured
does not swell the fiber material in contact with
them. For example, organic solvents such as
benzyl alcohol (benzenemethanol),
diodomethane = viscose fibers do not swell.
2) Washburn method - direct dependence of the
m2/t curve on wetting with these organic solvents
3) Using Fowkes analysis - diodomethane is an
ideal candidate because it has a polar surface
tension component of zero.Tabulated values of polar and dispersion
components of surface tension.
Determining (estimating) the contact angle of porous (fibrous) materials
THEORY OF NONWOVENS
Polar and dispersion components of surface tension
Fowkes equation
https://www.accudynetest.com/surface_tension_table.html
Determining (estimating) the contact angle of porous (fibrous) materials
THEORY OF NONWOVENS
Polar and dispersion components of surface tension Fowkes equationhttps://www.accudynetest.com/surface_tension_table.html
Determining (estimating) the contact angle of porous (fibrous) materials
THEORY OF NONWOVENS
Polar and dispersion components of surface tension Fowkes equation
There are several approaches that are used to calculate the surface tension, or surface energy, of solids
developed by a number of scientists.
Total surface energy of solids and liquids depends on various types of molecular
interactions such as dispersion (van der Waals), polar, and acid-base interactions.
The methods differ in the number of components or parameters they are equipped with. The most commonly used
theories are:
Zisman's theory
Fowkes method
Owens-Wendt-Rabel-Kaelble (OWRK) method
Wu theory
Acido-basic Van Oss method
Neumann Method
.
Determining (estimating) the contact angle of porous (fibrous) materials
THEORY OF NONWOVENS
FOWKES'S THEORY
When two arbitrary phases contact each other, the Lifshitz-van der Waals force is applied;
1) Coulomb forces (molecules with distinct dipole - water, alcohols.
2) Inductive forces - inductively induced or strengthened dipoles are bound by electrostatic forces,
3) Dispersion forces - these forces correspond to the surface energy dispersion component
In fact, free surface energy is only divided into two parts: disperse and non-dispersive (including all
non-dispersive components).
Determining (estimating) the contact angle of porous (fibrous) materials
THEORY OF NONWOVENS
FOWKES'S THEORY
The absence of a polar component in diiodomethane leads to
a simplification of the Fowkes equation
Calculation of disperse surface energy component
Subsequently, the polar surface energy component can be
calculated using benzyl alcohol in which both the polar and
dispersion components are known.
P
Determining (estimating) the contact angle of porous (fibrous) materials
THEORY OF NONWOVENS
FOWKES'S THEORY
The absence of a polar component in diiodomethane leads to
a simplification of the Fowkes equation
If the surface energy of both solids components
has been calculated, the WATER contact angle
can be easily resolved by following the Fowkes
equation adjustment using standard WATER
surface tension values.
Determining (estimating) the contact angle of porous (fibrous) materials
THEORY OF NONWOVENS
Swelling of hollow viscose fibers
Sometimes, the contact angle of the fluid due to swelling,
solubility, or any other similar problem cannot be directly
measured in the sample.
However, there is a method to determine this angle.
First, determine a set of solvents with different polar and
dispersion components (one of the components is zero in
one of the liquids) their surface tension, which does not
create a problem with the sample (do not swell, dissolve
the sample, etc.). (benzyl alcohol, diiodomethane)
Then calculate the surface energy of the sample using the
Fowkes method.
Once the surface energy (solids) of the sample is known,
these values, together with the surface tension values of
the problem fluid or solvent, can be used in the rearranged
Fowkes equation to indirectly determine the contact angle.
c c
c
Determining (estimating) the contact angle of porous (fibrous) materials
THEORY OF NONWOVENS
Thank you for your attention!
THEORY OF NONWOVENS