INSTRUCTOR: I'm gonna briefly describe
the idea behind reverse osmosis.
Which is used on a fairly large scale
for water purification.
And the idea is.
So first off in order to understand it,
let's look at osmosis.
And so suppose I'm looking at the cross section
of a container.
And this is a membrane
that divides two halves of the container.
And this membrane will allow water to permeate,
but will not allow salt.
So let's start out,
suppose we put water on both sides at equilibrium,
the heights of the water will be the same.
Chemical potentials water is the same
on both sides of the membrane.
Now what I'm gonna do is add salt to the right side
and then let it go to equilibrium again.
So what is it gonna look like
when we're again at equilibrium?
Well, the water on the left side
is now going to permeate through the membrane
to the right side
until the chemical potentials are again equal.
So the water level here will go down
and the water level here,
remember this is water plus salt,
this level will go up until this pressure difference,
this is a pressure difference,
due to the fact that heights liquid or not the same,
so the density of the water times the height
times the gravitational constant.
That pressure is the osmotic pressure,
sometimes represented by pi.
And so now we again at equilibrium,
there's no water permeation through the membrane.
So let's now start with this condition.
So starting with the same condition and suppose,
now I exert pressure
and push down the right side.
What that's going to is,
cause water to flow this way,
and now again let's look at equilibrium.
The water level on the left is going to rise,
of course the water level on the right is going to decrease.
So this is water plus salt, on the right side.
Again this is at equilibrium
there's no longer flow
and that's because the chemical potential of water
on the left side is equal
to the chemical potential of water on the right side.
So this is referred to then as reverse osmosis
where we've forced water through the membrane
by exerting pressure.
So the idea would be if we started here with salt water
we could make more pure water,
because we have a membrane
that will now allow the salt to permeate.
Let's look at a diagram,
then that represents its behavior.
So, if we're not at equilibrium
then we'll have flow through the membrane continuously
and here's the idea that we feed into our system,
salt water, so we're continuously feeding.
So we don't allow the system to get to equilibrium.
You'll notice that the salt concentration leaving,
is higher than at entering,
because we're getting pure water here, the outlet.
And how much water we get out,
is a function of this pressure difference,
the feed pressure 41,
atmosphere's in the outlet pressure,
permeate pressure is one atmosphere.
So the figure then on the right,
shows the water flux as a function of pressure drop
across the membrane.
So, what I've indicated here
is that osmotic pressure
that I just mentioned previously.
If we're below the osmotic pressure
then this is osmosis.
Meaning water's gonna go from the pure water side
to the salt water trying to make chemical potentials equal.
If we're above the osmotic pressure,
as I shown in the diagram on the left,
then we'll get water flowing to the pure water side
and we'll be concentrating the salt,
so this retentate leaving has a higher salt concentration.
And what this green line looks like
is a function of how well we stir this system,
because of the fact there's concentration polarization
near the membrane surface.
And so what that means,
if we look at this membrane surface,
and we have on this side water,
and here on this side water plus salt,
just like in the figure immediately above this,
then very near the surface,
the salt concentration will be higher
than out here in the bulk.
So out here we have for example,
.0445 is the mole fraction,
but right near the surface,
it'll be higher which means the concentration of water
will be lower than the bulk.
And that means the driving force,
for water to permeate will be lower
then it would be without concentration polarization.
And that's due to the fact
we have boundary layer near the surface,
and so we're relying on diffusion for water
to move through that boundary layer,
and of course the salt
has to move away from the membrane surface
and that boundary layer can be decreased
if we have better mixing.
So this is one of the reasons
we show that we're stirring this
trying to mix and decrease that boundary layer.
And therefore, this green line will look different,
it'll be up higher, if I have a higher rate of mixing.
So this is just brief idea of what reverse osmosis is.
Again the point is that's used,
very large scale to purify water
and it's relying on chemical potential differences
as driving forces for water to permeate through a membrane.