Fick's Law of Diffusion Video Lecture | Mass Transfer - Chemical Engineering

let's look at the ficks law of molecular
diffusion note that we are concerned
here with the transport of matter only
due to molecular diffusion and not due
to convection so in a binary mixture
that means a mixture that has got two
fluids the rate of mass flux of
component a is proportional to its
concentration gradient this is what was
observed by fake and then expressed as m
dot a divided by a and this represents
the flux of component a that it's
proportional to the concentration
gradient DCA divided by DX so let's see
what these terms mean m dot a is the
rate of mass flow of component a and we
will use the units kilograms per second
a is the cross-sectional area as square
meters and C a is the concentration of
the component so that would be kilogram
per cubic meters and X is the distance
or the space coordinate so we can remove
the proportionality by introducing a
constant in this expression and we will
use the constant D and we will write the
expression as m dot a divided by a
equals minus D a B times D CA over DX
where the coefficient or the constant
d and we signify that as a B is the
diffusion coefficient sometime also
called diffusivity of a in B in other
words of component a in fluid B and the
units are meter square per second well
let's check out the units on the left
hand side for m dot a we have kilograms
per second a is in square meters and on
the right hand side the diffusivity has
the unit's meter square per second times
the concentration is kilograms per cubic
meters and forex the units are meters so
meter square will cancel out and we will
have kilograms per second meter square
on the right hand side same as on the
left hand side now if B is a liquid then
the molecules in liquid will be closer
to each other instead of if it was a gas
where the molecules are separated by
larger distances so that means it will
take longer time for the component a to
move from region one to region two and
we can see that in this schematic that
the molecules of B are much closer to
each other and a has to collide with a
number of these molecules of B as it
finds its path through the liquid B and
getting it to the other side so that
conceptually tells us that the
diffusivity values in liquid are smaller
than in gases and also if instead of
liquid
we had a solid that had some porous
structure then the diffusivity in solids
is even smaller than in liquids in fact
if we look at the numbers diffusivity in
a gas is about 10 raised to power five
times greater than in a liquid and
diffusivity in liquids vary with the
concentration of the diffusing component
just a couple of other values for you to
get an appreciation of this the
diffusivity of air in ammonia the value
is zero point one nine eight times 10
raised to power minus 4 meter square per
second whereas the diffusivity of
ammonia in water so a gas in a liquid
the diffusivity value is one point six
four times 10 raised to power minus 9
meter square per second again note that
the molecular diffusion process is very
slow and it is much slower in a solid
compared to the movement of molecules in
a gas