Steady & Non Steady State Diffusion Video Lecture | Mass Transfer - Chemical Engineering

welcome back to the course on
introduction to material science and
engineering offered by era period world
previous lecture we started the
discussion on diffusion we saw the
different mechanisms by which diffusion
takes place the fundamentals of
diffusion today we will discuss about
the two types of diffusion which can be
steady state diffusion or non steady
state diffusion will understand what
they are when do each of the type occur
and what are the concerning factors
affecting the steady state or the non
steady state diffusion now as I have
discussed diffusion is basically flow of
matter from one region to another region
right so obviously it is going to take
some time to occur the process of
diffusion therefore is a time dependent
phenomena diffusion is a time dependent
process okay and since diffusion is a
time dependent process that is it is
going to take certain amount of time for
certain amount of material to move from
one location to another location
therefore the rate of diffusion is a
very important practical parameter rate
of diffusion will define how much
material is actually being transported
and this is practically important
because in different heat treatments
which we'll discuss about later the
important phenomena occurring is
actually diffusion so how much diffusion
is taking place will determine how much
time the material needs to be heat
treated at a particular temperature or
how much time should a particular
process be carried out for the relevant
action to be implemented now how do we
define the rate of diffusion obviously
there has to be a factor of time there
has to be amount of matter being
transported but the thing is that you
might have a small diameter bar or you
can have a very very thick diameter bar
so if we do not take into account a
cross section
then we will assume that this is having
a smaller rate of diffusion than this
but if we take per unit area we'll
understand that under similar condition
for same material the rate of diffusion
is same so there is has to be another
factor concerning that area now to
define the rate of diffusion we have
something known as diffusional flux or
diffusion flux which is denoted by J and
what exactly is a diffusion flux states
the amount of matter the amount of
matter which is transported per unit
cross section per unit area per unit
time
okay so diffusion flux is basically the
amount of matter flowing through a unit
area in unit time in differential form
we can write it as 1 upon a the area
concerned and del M upon del T that is
the amount of mass flowing per unit time
okay so now we understand the idea about
diffusion flux and diffusion flux is a
very very important criteria as I said
it is the practical parameter based on
which many decisions for heat treatment
processes will be taking place now these
diffusion flux if this remains constant
with time if the diffusion flux at the
start of a process after 10 minutes
after 20 minutes after T minutes remains
the same then we say that the process is
a steady state diffusion it's a steady
state diffusion when the diffusional
flux remains constant with time it is
not changing with time this is possible
when we have a reservoir of one material
and that is diffusing into another
material which has very small
concentration of this material ok there
is a sea of material over here a large
amount of material there by any number
of atoms coming to this
material over here will not change the
amount of material significantly also
this material the other material over
here in which the first material let's
call this the first and this the second
material the second material in which
the first materials atoms are diffusing
in is also large enough so that the
concentration of the first material
atoms remains almost constant in the
second material after any amount of time
thereby what will happen that the
concentration difference will be
maintained continued to be maintained
and once the concentration difference
continue to be maintained for any amount
of time then the diffusion flux will
continue to remain same at any time we
will see why that is so why is the
concentration gradient very important
this is because basically what happens
is that the diffusion process the
driving force for it is concentration
gradient the amount of gradient between
region one and region two defines how
fast the diffusion will take place what
is concentration gradient concentration
gradient is rate of change of
concentration per unit change of
position okay so suppose we have a
concentration of C one here for a
particular atom and C 2 here for the
same atom let's call C 1 a and C 2 a
where we are talking about a kind of
atom and let's say this is length L
right
so the concentration gradient for this
atom a in this material will be C 1 a
minus C 2 a that is the change in
concentration upon the total length
along which the change is taking place
so this will be my concentration
gradient for this particular case okay
so now higher the concentration gradient
which means that smaller the length or
more the
in concentration across the same length
faster will be the diffusion right
because there will be more driving force
more change is taking place in smaller
lengths more driving force faster
diffusion now this exact idea that the
concentration gradient defines the rate
of diffusion was given by ficks first
law
what does ficks first law say ficks
first law says that the diffusional flux
is equal to negative gradient
concentration gradient times factor
constant factor which is known as
diffusion coefficient so let me write it
down here diffusion flux is minus D del
C upon del X this is the concentration
gradient and the negative sign is
because the diffusion is taking place
from higher concentration to lower
concentration to take that into account
we have to put a negative sign D is a
diffusion coefficient this depends on
several factors including what is the
specimen that is diffusing what is the
temperature at which the diffusion is
taking place for higher temperatures D
will be large for lower temperatures D
will be small there will be some
materials which are smaller in size
diffusion D will be large diffusion
coefficient will be large
there will be atoms which will be larger
in size hence diffusion should be slow
for them they will be small okay so this
ficks first law which relates the
diffusion flux with the concentration
gradient is possible in the steady state
diffusion process why so because here we
have assumed that the concentration
gradient does not depend on time this
does not have any factor of time no e
factor so this relation holds in case of
steady state diffusion now let us see
what happens when the concentration
gradient is itself a function of time
that is the concentration gradient does
not remain constant
when that happens what we have is known
as non steady state diffusion before I
jump let me show you something for a
steady state diffusion we can assume
something like this that either there is
a concentration jump like this C 1 a and
C 2 a and this remains constant over
time or we have a constant constant
concentration gradient C 1 a C 2 a and
this gradient remains constant with time
ok but in the case of non steady state
diffusion the concentration gradient
itself is continuously changing with
time and for most practical application
concentration gradient keeps changing
with time the previous case which we
studied the steady state case happens
very very rarely practical cases are non
steady state cases and in non steady
state diffusion cases the diffusion flux
therefore itself is a function of time
and then in such circumstances ficks
second law holds true what does ficks
second law states ficks second law
basically relates the change of
concentration with time to the change of
concentration with position okay so
ficks second law C is the change of
concentration with time is the diffusion
coefficient D second derivative of
concentration with respect to position
this is ficks second law now how does
this implement itself how can we show
this in form of a graph here we are
plotting the concentration against the
distance so initially let's suppose we
have a material here and another
material here this the concerned atom
which we are discussing has a
concentration C s in this particular
material whereas it has C o in this
material this is a big material which
remains C s always
so here we are Axios but in the next
material at initial time at t0 initial
time concentration remains C naught
throughout the material but with
increasing time what is happening there
is a concentration buildup of that let
us say we are focusing on a atom type a
so there is a buildup of atom a close to
the interface and with increasing time
that keeps on moving further right so
concentration buildup takes place and
that buildup keeps getting further into
the material with increasing time so now
the concentration gradient no longer is
the sharp concentration gradient like
this rather after some time we have
something like this then we have
something like this and it keeps on
changing so at the same location at the
same location right if we are
considering at this distance X naught at
T naught the concentration was C naught
after some time the concentration is
increased with time it keeps on
increasing at the same location this is
what is non steady state diffusion there
is a concentration build-up within the
material and these are the real
scenarios which happens during different
processes like carburizing nitro
carburizing carbonate riding different
elements are being added for different
purposes this is exactly how that takes
place
okay so if we continue understanding
this problem this is example of a
semi-infinite solid right which means
that we have a constant concentration C
s over here whereas this end the
material in which the EI type of atoms
is diffusing in is semi infinite it is
large enough so as to say and the
initial concentration in that large
enough material was C naught as shown
here and the surface concentration here
remains CS this remains constant
using this initial condition parameters
if we solve the ficks second law then
what we get is this relation this is the
relation relating the concentration at
any position X so any position X the
concentration is C X C naught was the
initial concentration in the semi
infinite solid material CS is this
boundary
concentration and C naught again is the
same thing and that is found to be equal
to 1 minus e RF this is error called as
error function this has standard values
like logarithmic function error function
has standard values there are available
charts where you can find the value and
the most important thing is what are the
parameters within the error function
what will define the value of the error
function those parameters are X that is
the distance how far into the material
you want to find out the concentration
at what time do we want to find out the
concentration and what is the diffusion
coefficient so further into the material
you go lesser will be the concentration
more time we give more will be the
concentration more the diffusion
coefficient more will be the
concentration at position X so this
error function basically will define
what will be the concentration at any
position X in the material ok with these
relations and with this fundamental
understanding that steady state
diffusion means the concentration
gradient remains constant non steady
state diffusion means that the
concentration gradient is continuously
changing you have a glimpse into the
idea of diffusion and this idea will be
handy to understanding the different
heat treatment processes which we'll
discuss further down the line ok this
brings us to the conclusion of today's
lecture next lecture we'll see some of
the dominant factors which affect the
rate of diffusion till then have a great
day goodbye
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