2. Rate Of Absorption Of Moisture
• Textile materials take a long time to come
into equilibrium with their surrounding e.g
Drying after Washing.
• Rate depends on temperature, air
humidity, wind velocity, surroundings,
thickness of material, density of material,
nature of fibre etc.
3. • Slowness of Conditioning – May be a
technical nuisance, because textiles
have to be conditioned before
processing or sale.
• Advantageous – Valuable stabilizing
influence : absorbent fibrous materials
in a room will prevent rapid changes in
humidity or temperature.
• Study – Factors that play a part in
change of conditions in textiles.
4. DIFFUSION OF MOISTURE
• Slow Conditioning – Slowness with which
water molecules diffuse through the fibre
or through the air to the fibre.
• If concentration of H2O molecules ( or of
any other substance with which one is
concerned ) varies from place to place in a
given medium ( e.g – air or fibre
substance ), the molecules will diffuse
from regions of high concentration to
regions of low concentration until their
distribution becomes uniform.
5. Fick’s Equation – (First Law)
• Rate of transport of diffusing substance passing
through a cross-section ‘A’ is proportional to the
concentration gradient of moisture.
• Units – cm square/sec.
• D = Diffusion coefficient
• D ~ cm 2/sec
• Determined experimentally and in tables.
A = Unit cross sectional area
J= Mass of moisture passing
throu’ unit cross section
7. Fick’s first law has limited use.
• Practical problem, which can be solved ---
Membrane problem
• Flux ‘J’ Mass of moisture passing through
a unit cross-section :
• Problem – A membrane separates two
flowing streams of gases that have
different concentration of an impurity.
8. • Steady State Flux of impurity through
membrane is
D = Diffusion coefficient of an impurity through the
membrane.
J = Flux of impurity through the membrane per
unit area of membrane
9. • Fick’s first law is useful here because
concentration gradient is constant & at
steady state ‘D’ is constant
Most Problems in Diffusion, i.e, Textile
fibres –
Region where ‘c’ changes with time
Fibre experiences an increase in moisture
content with absorption.
In such cases, we cannot use Fick’s first
law
11. DIFFUSION OF AN IMPURITY THROUGH A
SOLID BAR
• Flux through this bar of unit cross-
sectional area at x coordinate 1.
Since J1 is not equal to J2, the concentration
of species ‘c’ in the volume changes with
time
Fick’s Second Law – Flux that
corresponds to experimental conditions
12. • Law of Mass Conservation,
Substituting the expression for J from Fick’s
First Law,
This is Fick’s Second Law.
Simpler form where D is a constant & not a function of x
or c.
13. • Problem – To determine about how long it
will take for a fibre to absorb or desorb
moisture.
• Complications arise in fibres where
diffusion coefficient may vary with time.
• ( Absorption – Molecules removed from
diffusion process )
cannot be solved unless some relation
between D & c can substituted.
14. Diffusion Into A Receiver From An
Infinite Source Of Concentration Co
On integrating & assuming as initial
conditions c = 0 at t = 0,
C0
C
c=0
at
t=0
15. Time ,t
Change of relative conc c/c0 , in receiver following
diffusion from an infinite source, C0
16.
17. M = Mass needed to bring the adsorbent to
equilibrium.
18. where
• C1 = Initial concentration at surface of
adsorbent.
• Co = Concentration at surface of
conditioning solution.
19. • For a homogeneous cylinder of length ‘l’
& radius ‘r’ in which there is a change of
conditions at surface such as to cause a
change in the equilibrium concentration in
the cylinder from C2 to Co, the mass
observed is given by product of the
volume of the cylinder and change in
concentration.