WEBVTT
Kind: captions
Language: en
00:00:01.520 --> 00:00:14.539
.
In
00:00:14.539 --> 00:00:21.080
the previous lecture, we were discussing
about some of the basics of electrical double
00:00:21.080 --> 00:00:30.160
layer theory. And in the process we
came in the context of the Gauss law and
00:00:30.160 --> 00:00:46.579
based on that we derived the Poisson equation.
So, the Poisson equation ,
00:00:46.579 --> 00:00:56.190
this is the Poisson equation with which
we finished our previous lecture. And we concluded
00:00:56.190 --> 00:01:01.079
that you know this equation has to be combined
with a Boltzmann distribution to solve the
00:01:01.079 --> 00:01:04.420
potential distribution within the electrical
double layer.
00:01:04.420 --> 00:01:12.459
How that can be done we will get into that
now. So, let us say psi be the potential in
00:01:12.459 --> 00:01:25.689
the electrical double layer across the electrical
double layer . So, E is equal to minus of
00:01:25.689 --> 00:01:31.819
grad psi this is the definition of electric
field. It is the by definition minus of gradient
00:01:31.819 --> 00:01:49.020
of the electrical potential. So, it becomes
;
00:01:49.020 --> 00:01:58.430
now this being a general problem , we can
consider a special case where the electric
00:01:58.430 --> 00:02:04.060
field distribution is one dimensional; that
means, the electrical field only varies along
00:02:04.060 --> 00:02:11.320
the y direction where y is the direction perpendicular
to the solid boundary .
00:02:11.320 --> 00:02:19.900
So, we can write not only that we also assume
that; we have a solution for which epsilon
00:02:19.900 --> 00:02:25.490
is a constant epsilon is the permittivity
of the solution. Typically for an aqueous
00:02:25.490 --> 00:02:34.630
solution it is around 80 times that of
epsilon naught, which is the permittivity
00:02:34.630 --> 00:02:49.200
of the free space. So, with that we can write
the Laplacian becomes the second derivative
00:02:49.200 --> 00:03:04.460
with respect to y ,
next the charge density . So, let us say that
00:03:04.460 --> 00:03:19.710
n plus is the number density of positive ions
and n minus is the number density of negative
00:03:19.710 --> 00:03:33.290
ions .
For example, this may be Na plus number density
00:03:33.290 --> 00:03:41.470
this may be Cl minus number density. So, Boltzmann
distribution which we derived in the previous
00:03:41.470 --> 00:03:56.760
lecture , it tells that n plus is equal to
n 0 where n 0 is the bulk concentration , where
00:03:56.760 --> 00:04:14.280
Z is the valency of the positive ions you
can write Z plus . And n minus is n 0 e to
00:04:14.280 --> 00:04:26.849
the power minus Z minus e psi by kBT.
Now, as a special example let us consider
00:04:26.849 --> 00:04:39.710
a Z is to Z symmetric electrolyte ,
00:04:39.710 --> 00:04:49.830
what does it mean? If you take NaCl in NaCl
when it breaks up into Na plus and Cl minus,
00:04:49.830 --> 00:04:59.389
then Z plus is one and Z minus is minus 1
ok. So, Z is to Z means whatever is the valency
00:04:59.389 --> 00:05:04.000
of the positive ion the same is the valency
of the negative ion, but you have to give
00:05:04.000 --> 00:05:12.110
a minus sign to take into account that the
others ion has opposite charge. So, if you
00:05:12.110 --> 00:05:36.729
have Z is to Z then n plus is equal to n 0
e to the power minus Ze ok.
00:05:36.729 --> 00:05:55.509
So, here we have substitute plus Z here we
have substitute minus Z ok. So, then this
00:05:55.509 --> 00:06:17.569
equation will boil down to ;
00:06:17.569 --> 00:06:43.919
ok now before that ok. So, this is the
charge density, this we have written as the
00:06:43.919 --> 00:06:50.949
net charge density is what the difference
between the positive and the negative charges.
00:06:50.949 --> 00:07:05.860
So, technically rho e is defined as this one.
Now here Z plus is Z and Z minus is minus
00:07:05.860 --> 00:07:12.639
z. So, if you take Z common it becomes e Z
e into n plus minus n minus that is what is
00:07:12.639 --> 00:07:45.559
written here.
So, then this can be written as ; ok so now
00:07:45.559 --> 00:07:54.869
let me rub the this part of the board so that
we can write better is clearer.
00:07:54.869 --> 00:08:41.919
So, epsilon d 2 psi dy 2 . So, this by definition
is sin hyperbolic x is e to the power x minus
00:08:41.919 --> 00:08:47.020
e to the power minus x by 2. So, e to the
power minus e to the power x minus e to the
00:08:47.020 --> 00:09:02.690
power minus x is 2 sin hyperbolic x; that
is what is written. So, this equation is thus
00:09:02.690 --> 00:09:25.640
so called Poisson Boltzmann equation .
Now, this equation is a non-linear equation
00:09:25.640 --> 00:09:33.370
and although there are techniques for solving
this equation, but just for the sake of convenience
00:09:33.370 --> 00:09:39.560
we will work out the solution for a special
case, when this becomes a linear equation
00:09:39.560 --> 00:09:47.910
and that; is there see the non-linearity is
because of this term . So, this term can be
00:09:47.910 --> 00:09:58.320
linearized when this is small when Ze psi
by kBT is small is much, much less than one
00:09:58.320 --> 00:10:16.630
then sin h is as good as Ze psi by kBT. This
is this you can easily do by expanding sin
00:10:16.630 --> 00:10:23.140
h in terms of exponential series and retaining
only up to the linear term in the exponential
00:10:23.140 --> 00:10:41.520
series. So, this is known as Debye Huckel
linearization .
00:10:41.520 --> 00:10:46.860
So and so typically now you can argue that
what is the typical physical value of the
00:10:46.860 --> 00:10:51.890
potential. The typical physical value of the
potential that keeps this within this limit
00:10:51.890 --> 00:10:59.820
is around 25 millivolt. So, if the zeta potential
the maximum psi is zeta potential, so if the
00:10:59.820 --> 00:11:17.210
zeta potential magnitude is less than 25 millivolt
you can safely apply this linearization. So,
00:11:17.210 --> 00:11:34.400
under that case ; so now before solving this
equation this equation can be solved very
00:11:34.400 --> 00:11:42.090
easily, but even before solving this equation
we can make an estimation of how thick the
00:11:42.090 --> 00:11:46.250
electrical double layer is.
So, to do that we will do an order of magnitude
00:11:46.250 --> 00:11:56.790
analysis . So, order of magnitude of these
is epsilon zeta by lambda square. Where lambda
00:11:56.790 --> 00:12:03.800
is a characteristic length of the edl ok.
And zeta is maximum psi so d 2 psi dy 2 is
00:12:03.800 --> 00:12:11.930
what ddy of d psi dy. So, it is some characteristic
psi divided by square of some characteristic
00:12:11.930 --> 00:12:17.390
length. So, the characteristic length lambda
this is called as Debye length . This is the
00:12:17.390 --> 00:12:23.670
characteristic length of edl this is not actually
the length of edl this is the length scale
00:12:23.670 --> 00:12:30.990
you know the order of magnitude of the edl.
So, this and this is of the order of 2 n 0
00:12:30.990 --> 00:12:43.600
Z square e square zeta by kBT . So, from here
since these 2 terms are equated we can write
00:12:43.600 --> 00:12:58.250
1 by lambda square is of the order of 2 n
0 Z square e square by epsilon kBT ok. So,
00:12:58.250 --> 00:13:04.750
I will show you that if you do some calculations
based on what is so in these what you can
00:13:04.750 --> 00:13:11.660
vary this n 0 you can vary which is the concentration
of the salt solution. Z also you can vary,
00:13:11.660 --> 00:13:18.250
but normally you know it will be one 2 like
that monovalent bivalent, e is the protonic
00:13:18.250 --> 00:13:23.340
charge it is a constant epsilon is the
permittivity of the solution, which is also
00:13:23.340 --> 00:13:29.260
not varying that much kB is Boltzmann constant
and T mostly we are doing in the room temperature.
00:13:29.260 --> 00:13:37.590
So, n 0 is the parameter and you can see here
that lambda will be varying with 1 by square
00:13:37.590 --> 00:13:44.160
root of n 0 given all other parameters are
constant. So now, I will show you a slide
00:13:44.160 --> 00:13:55.720
where I will show you what are the typical
values of lambda based on the concentration.
00:13:55.720 --> 00:14:02.900
So, you can see the concentration of the solution
capital M is molar, that is moles per liter.
00:14:02.900 --> 00:14:10.730
So, if it is 10 to the power minus 6 which
is micro molar this kind of solution we normally
00:14:10.730 --> 00:14:16.050
do not use, but in that case it is around
300 nanometer.
00:14:16.050 --> 00:14:23.920
But typically it is around milli molar to
so milli molar to molar. So, milli molar that
00:14:23.920 --> 00:14:30.290
is 10 to the power minus 3 the Debye length
is around 10 nanometer. So, this is the very
00:14:30.290 --> 00:14:36.340
typical rough idea you know as a biomicrofluidics
engineer it is very important that you have
00:14:36.340 --> 00:14:42.620
a rough feel of these numbers. So, for a typical
milli molar solution the Debye length will
00:14:42.620 --> 00:14:50.300
be around 10 nanometer. So, if you imagine
that the channel the micro channel is 10 micron
00:14:50.300 --> 00:14:56.910
then only a small portion close to the wall
will be having this Debye layer outside that
00:14:56.910 --> 00:15:02.260
the surface charging effect will not be felt
ok.
00:15:02.260 --> 00:15:10.470
Now, how do you solve this equation; the
solution of this equation is quite simple.
00:15:10.470 --> 00:15:21.750
And I will of course, give you the idea
of how to solve this equation, but I will
00:15:21.750 --> 00:15:28.820
not go get into the solution for all general
cases because it takes time.
00:15:28.820 --> 00:15:39.360
So, let us say psi equal to e to the power
my be the trial solution this is this equation
00:15:39.360 --> 00:15:44.970
is basically a second order homogeneous ordinary
differential equation.
00:15:44.970 --> 00:16:15.530
So, m square epsilon e to the power my is
d 2 psi dy 2 . So, m square minus so this
00:16:15.530 --> 00:16:30.250
is 1 by lambda square so; that means, m is
equal to plus minus lambda. So, the solution
00:16:30.250 --> 00:16:44.680
is psi is equal to c 1 e to the power lambda
y sorry, plus minus 1 by lambda. So, minus
00:16:44.680 --> 00:16:56.340
c sorry plus c 2 e to the power minus 1
by lambda y ok . This c 1 and c 2 you can
00:16:56.340 --> 00:17:02.540
calculate from the boundary conditions.
So, for example if you have a open surface
00:17:02.540 --> 00:17:13.240
like this then at open open surface means
fluid is open in this direction. So, here
00:17:13.240 --> 00:17:20.800
you can write that at y equal to 0 psi is
zeta potential . This is an example at y equal
00:17:20.800 --> 00:17:31.730
to 0 psi is zeta and at y tends to infinity
psi will be 0 . So, at y tends to infinity
00:17:31.730 --> 00:17:47.140
psi equal to 0 ; this will give you c 1 equal
to 0 . So, psi is equal to c 2 e to the power
00:17:47.140 --> 00:17:57.260
minus y by lambda . And at y equal to 0 psi
equal to lambda zeta; that means, psi equal
00:17:57.260 --> 00:18:05.630
to zeta into e to the power minus y by lambda.
So, it is a exponential decay of the potential,
00:18:05.630 --> 00:18:10.120
but if it is a channel you know the boundary
conditions will be different if it is a closed
00:18:10.120 --> 00:18:14.610
channel and accordingly the solutions will
be different. So, if you look into this
00:18:14.610 --> 00:18:23.040
slide here I have given a solution for psi
with the condition that psi is equal to
00:18:23.040 --> 00:18:29.390
zeta at y equal to 0 and y equal to 2 h, which
are the boundaries of the bottom plate and
00:18:29.390 --> 00:18:33.540
the top plate. And accordingly the solution
will be given by this cos hyperbolic function,
00:18:33.540 --> 00:18:39.110
which is a combination of e to the power x
and e to the power minus x. Sin hyperbolic
00:18:39.110 --> 00:18:44.430
was e to the power x minus e to the power
minus x by 2 cos hyperbolic is e to the power
00:18:44.430 --> 00:18:52.670
x plus e to the power minus x by t ok .
So, the next concept so what we will do with
00:18:52.670 --> 00:18:58.060
this electrical double layer concept, how
can we use this to drive the flow . So, to
00:18:58.060 --> 00:19:08.870
understand that we will consider a mechanism
called as a electro osmosis . So, what is
00:19:08.870 --> 00:19:17.910
the electro osmosis ?
Let us say that you have a channel with negative
00:19:17.910 --> 00:19:26.210
surface charge . So, bulk will have more positive
charge and then you apply a bias here positive
00:19:26.210 --> 00:19:32.790
bias and you have a negative bias .
So, when you apply this bias this negative
00:19:32.790 --> 00:19:39.780
ions will be driven towards this, I am sorry
positive ions will be driven toward this negative
00:19:39.780 --> 00:19:46.160
electrode. So, when this is done these ions
are not alone right these are hydrated by
00:19:46.160 --> 00:19:51.380
water. So, because of the viscous interaction
between the iron and the water, water will
00:19:51.380 --> 00:19:56.710
also be dragged in this direction and that
is how a flow will be created. So, this is
00:19:56.710 --> 00:20:03.320
the physics of electro osmosis. Now we will
try to see try to understand that how we can
00:20:03.320 --> 00:20:09.590
translate this physics into mathematics how
can we write an expression for the corresponding
00:20:09.590 --> 00:20:14.160
velocity profile.
So, to do that let us assume that you have
00:20:14.160 --> 00:20:20.100
a parallel plate channel that is a rectangular
channel, with the width much much higher than
00:20:20.100 --> 00:20:32.870
the height . Ah Let us say this height is
2 H . And at a section y we take a strip of
00:20:32.870 --> 00:20:43.380
width dy . If there is no pressure gradient
which is a acting on this fluid; that means,
00:20:43.380 --> 00:20:51.160
the pressure here and pressure here are the
same and the zeta potential is uniform, then
00:20:51.160 --> 00:20:58.040
the only forces are the resisting viscous
forces and the driving electrical forces.
00:20:58.040 --> 00:21:11.250
So, the resisting viscous forces so here the
viscous force is So, let us say that this
00:21:11.250 --> 00:21:18.680
boundary , whatever is the fluid below it
that is moving at a faster rate because it
00:21:18.680 --> 00:21:24.270
is closer to the center line. So, it is trying
to pull the fluid in the forward direction.
00:21:24.270 --> 00:21:31.309
So, this is the force exerted by the bottom
fluid on this element. Similarly, the top
00:21:31.309 --> 00:21:37.130
fluid is closer to the wall so it is try to
create a drag which we which will try to slow
00:21:37.130 --> 00:21:41.610
down. So, if we call it as tau this we call
as tau plus d tau .
00:21:41.610 --> 00:21:50.679
So, let us say this length of the element
is dx so this is tau into dx let us say width
00:21:50.679 --> 00:21:59.500
of the channel is a one. So, this is tau plus
d tau into dx into 1 . There is also a body
00:21:59.500 --> 00:22:06.100
force, what is the body force? Which is pulling
this let us say Ex is the electric field along
00:22:06.100 --> 00:22:13.450
the x direction . So, this is not the induced
electric field this is the applied electric
00:22:13.450 --> 00:22:18.020
field. So, here there are 2 types of electric
field one is induced in this direction due
00:22:18.020 --> 00:22:23.220
to electrical double layer, another is a applied
along the x direction to make the fluid flow
00:22:23.220 --> 00:22:27.340
a combination of these 2 is actually making
the fluid flow.
00:22:27.340 --> 00:22:39.360
So, if you have now Ex as the electric field
the body force due to that is rho e into Ex
00:22:39.360 --> 00:22:48.100
per unit volume. So now, if you multiply this
with the volume this is dy into dx into 1
00:22:48.100 --> 00:22:55.470
this is the total force. Now if the flow is
fully developed all forces are balanced so;
00:22:55.470 --> 00:23:13.180
that means, d tau tau plus d tau into dx minus
plus tau dx plus rho e into Ex into dy dx
00:23:13.180 --> 00:23:26.880
this is 0.
So, you can write
00:23:26.880 --> 00:23:48.130
that this 1 minus d tau dy plus rho e into
Ex equal to 0 ok. Now what is this tau? Tau
00:23:48.130 --> 00:24:00.750
is equal to minus mu du dy where u is the
velocity along the x direction . So, why minus
00:24:00.750 --> 00:24:12.740
mu du dy because if you write tau is equal
to mu du into d of dd say of some coordinate
00:24:12.740 --> 00:24:20.460
y without the minus sign then that coordinate
has to be outward normal to the wall. Here
00:24:20.460 --> 00:24:27.429
the y direction is like this which is a opposite
to this so that is why the minus sign here
00:24:27.429 --> 00:24:43.280
ok . So, you have this is our governing equation
.
00:24:43.280 --> 00:25:03.290
Now, what is rho e ? This is from the Poisson
equation d 2 psi dy 2 is equal to minus rho
00:25:03.290 --> 00:25:49.990
e by epsilon ok. So, we can write ok so now
let us make an order of magnitude analysis.
00:25:49.990 --> 00:25:56.679
And see what is the velocity so this is of
the order of let us call it a u characteristic
00:25:56.679 --> 00:26:04.360
velocity, which is also known as Helmholtz
Smoluchowski velocity. So, uhs by lambda square
00:26:04.360 --> 00:26:17.740
this is of the order of minus epsilon zeta
Ex by mu . Forget about minus just order of
00:26:17.740 --> 00:26:24.179
magnitude wise this plus or minus we will
see later on.
00:26:24.179 --> 00:26:38.440
So, uhs is of the order of epsilon zeta Ex
by mu . And normally we give it a minus sign,
00:26:38.440 --> 00:26:46.130
why minus sign; because see if you have a
positive bias here and a negative bias here,
00:26:46.130 --> 00:26:54.070
then what is the electric field? Electric
field is minus of the gradient of the potential.
00:26:54.070 --> 00:27:00.920
So, the electric field is positive E the surface
charge if it is negative then zeta potential
00:27:00.920 --> 00:27:04.700
is negative and it is driving a flow in the
positive direction.
00:27:04.700 --> 00:27:14.059
So, minus E sorry plus of E and minus of
zeta is driving a positive u to adjust for
00:27:14.059 --> 00:27:21.919
that you have a minus sign here ok . So, with
this conceptual understanding let us solve
00:27:21.919 --> 00:27:41.971
this . So, du dy if you draw the channel like
this at the centerline of the channel you
00:27:41.971 --> 00:27:48.660
have both du dy and d psi dy 0; that means,
c 1 equal to 0 . And then if you integrate
00:27:48.660 --> 00:28:06.970
it u minus epsilon Ex by mu psi is equal to
c 2. At the wall u is 0 at the wall this is
00:28:06.970 --> 00:28:16.870
no slip and psi is zeta.
So, you have c 2 is equal to minus epsilon
00:28:16.870 --> 00:28:50.490
zeta Ex by mu . So, u ok from this equation
by putting c 2. So, u this is nothing but
00:28:50.490 --> 00:29:02.380
this uHS . So, u by uHS is equal to 1 minus
psi by zeta. So, what kind of velocity profile
00:29:02.380 --> 00:29:10.660
it is psi will be 0 outside the electrical
double layer , and let us say this is the
00:29:10.660 --> 00:29:17.040
channel . The electrical double layer this
say this is micron electrical double layer
00:29:17.040 --> 00:29:21.890
is say within 10 nanometer. So, within 10
nanometer only you have this variation outside
00:29:21.890 --> 00:29:27.350
that is psi is 0 so u is uHS.
So, the velocity profile is something like
00:29:27.350 --> 00:29:42.020
this, almost uniform . So, this is a great
advantage for bio biological applications
00:29:42.020 --> 00:29:47.450
because for the pressure driven flow you have
a parabolic velocity profile. So, if you have
00:29:47.450 --> 00:29:54.030
a reaction site at the wall the sample which
is flowing the sample will have a tendency
00:29:54.030 --> 00:29:58.250
to go along the center line, but it will not
come easily to the wall. But if you have a
00:29:58.250 --> 00:30:04.630
uniform velocity profile the biological sample
will come easily to the wall and do the biological
00:30:04.630 --> 00:30:08.429
reaction.
So, these are the advantage, but any advantage
00:30:08.429 --> 00:30:15.730
is also associated with a limitation the limitation
is that you in this situation you can have
00:30:15.730 --> 00:30:20.530
a joule effect, because there is a current
flowing to the system there is a heating effect,
00:30:20.530 --> 00:30:27.080
because of these some biological samples which
are thermally labile, they can be disintegrated
00:30:27.080 --> 00:30:32.090
and that cannot that may be a detrimental
thing in a biological application . So, one
00:30:32.090 --> 00:30:40.340
cannot use very large electric field .
So, with this um so I will go through
00:30:40.340 --> 00:30:46.020
this slide to give you a basic idea of what
are the typical values . So, zeta potential
00:30:46.020 --> 00:30:53.710
is 25 millivolt epsilon is 80 into the permittivity
of free space. Mu is 10 to the power minus
00:30:53.710 --> 00:30:59.950
3 Pascal second, electrical field is typically
along x is typically 10 to the power 4 volt
00:30:59.950 --> 00:31:05.170
per meter. So, the velocity that you get out
of this is of the order of 10 to the power
00:31:05.170 --> 00:31:10.260
minus 4 meter per second.
So, this is what is typically, what you
00:31:10.260 --> 00:31:17.780
get and this is the velocity profile, how
it looks if you draw it almost uniform
00:31:17.780 --> 00:31:23.970
except in a thin region close to the wall.
So, this is the comparison between electro
00:31:23.970 --> 00:31:29.350
osmotic and pressure driven flow. So, you
can see here that if the pressure driven flow
00:31:29.350 --> 00:31:33.930
is having a parabolic velocity profile and
electro osmotic flow is almost a uniform velocity
00:31:33.930 --> 00:31:40.270
profile provided the zeta potential is constant
and therefore it has several advantages.
00:31:40.270 --> 00:31:49.000
So, pros and cons of the the Electro Osmotic
Flow; advantages velocity does not depend
00:31:49.000 --> 00:31:55.570
on geometrical dimensions it is minus epsilon
zeta e by mu does not depend on the channel
00:31:55.570 --> 00:31:58.240
dimensions.
There are no moving components involved. And
00:31:58.240 --> 00:32:03.970
you can integrate this easily with an electronic
or electrical circuitry, but the disadvantage
00:32:03.970 --> 00:32:10.940
is that the zeta potential is a strong function
of the chemistry. So, there is a strong dependence
00:32:10.940 --> 00:32:16.080
on surface chemistry and properties of the
solution. Not only that the uniform velocity
00:32:16.080 --> 00:32:21.020
profile will become non uniform as soon as
the zeta potential becomes non uniform, and
00:32:21.020 --> 00:32:27.910
that may be the case if the the the surface
is inhomogeneous and the third point is the
00:32:27.910 --> 00:32:35.010
joule heating which I have already mentioned.
Next in the next couple of minutes I will
00:32:35.010 --> 00:32:40.929
try to go through some other electro kinetic
effects very briefly one is streaming potential.
00:32:40.929 --> 00:32:47.049
So, stream streaming potential what you do
is instead of applying an electric field you
00:32:47.049 --> 00:32:53.789
apply a fluid flow. So, when you apply a fluid
flow through a pressure gradient, then because
00:32:53.789 --> 00:32:57.770
of the electrical double layer effect there
are ions in the solution these ions will be
00:32:57.770 --> 00:33:03.669
migrating in a particular direction and a
potential will be created across the channel.
00:33:03.669 --> 00:33:10.419
So, here in electro osmosis the input is a
axial potential and output is flow in streaming
00:33:10.419 --> 00:33:15.570
potential the input is a flow due to pressure
gradient and a output is a potential. And
00:33:15.570 --> 00:33:22.390
you can tap that potential to harness power.
And we will discuss later on in one of our
00:33:22.390 --> 00:33:28.090
lectures in microfluidics for healthcare that;
how can this be used to energize point of
00:33:28.090 --> 00:33:36.970
care diagnostic devices . Electrophoresis
it is a it is a very fundamental process which
00:33:36.970 --> 00:33:40.980
is basically the movement of a charge due
to electric field.
00:33:40.980 --> 00:33:49.340
So, if you have an electric field you you
can drive the charge Q by applying a force
00:33:49.340 --> 00:33:56.780
which is Q into the electric field. So, you
can in biomicrofluidics it is important because
00:33:56.780 --> 00:34:02.350
DNA has negative charge. So, you can apply
electric field to move DNA and that is known
00:34:02.350 --> 00:34:11.179
as DNA electrophoresis . there is also a terminology
called as di electrophoresis, where the difference
00:34:11.179 --> 00:34:16.419
in polarizability between a particle and a
solution in a non-uniform electric field give
00:34:16.419 --> 00:34:23.290
rise give rise to a net force on a particle.
So, the 2 things are required one is non uniform
00:34:23.290 --> 00:34:28.580
electric field, second is the difference in
polarizability of the particle and the solution.
00:34:28.580 --> 00:34:39.270
So, in by using this you can actually apply
a force and make a particle move. AC Electroosmosis,
00:34:39.270 --> 00:34:47.280
so with the DC electroosmosis which I have
a explained earlier it is associated with
00:34:47.280 --> 00:34:51.870
overheating problem and bubble formation due
to local electrolysis at the electrode. So,
00:34:51.870 --> 00:34:59.840
this can be prevented by using a AC bias instead
of a DC bias. And if you have an AC electric
00:34:59.840 --> 00:35:06.770
field on a surface then the surface charge
also changes with time and the force and
00:35:06.770 --> 00:35:11.620
the electric field also changes with time.
Combination of charge and electric field which
00:35:11.620 --> 00:35:16.240
is shown in the diagram here is such that;
that is always acting in a particular direction
00:35:16.240 --> 00:35:21.970
the charge in a cycle changes the electric
field in a cycle changes, but their product
00:35:21.970 --> 00:35:29.800
does not change in the direction.
So, AC electroosmosis is a very important
00:35:29.800 --> 00:35:35.030
process and finally, I will talk about another
electrokinetic effect called as electro thermal
00:35:35.030 --> 00:35:42.550
flows. So, in electro thermal flows if you
create a thermal field in the sample or a
00:35:42.550 --> 00:35:47.970
thermal field is already there in the sample
that can give rise to gradients in electrical
00:35:47.970 --> 00:35:52.550
properties.
So, you can see here that there is a property
00:35:52.550 --> 00:35:58.700
permittivity and there is a gradient in permittivity
which can give rise to an additional body
00:35:58.700 --> 00:36:04.010
force beyond the charge density times the
electric field. So, this additional body force
00:36:04.010 --> 00:36:11.960
is because of the variation of permittivity
with temperature. And that therefore, is created
00:36:11.960 --> 00:36:16.770
where you have a temperature gradient in the
fluid. So, this may be very important for
00:36:16.770 --> 00:36:22.910
many biological applications this has not
yet been harnessed so far for many biological
00:36:22.910 --> 00:36:26.510
applications.
But using the natural property gradient due
00:36:26.510 --> 00:36:34.340
to temperature gradient you can actually modulate
and control a flow. And that flow can be utilized
00:36:34.340 --> 00:36:41.410
for microfluidic purposes with biological
applications as at specific example. So, to
00:36:41.410 --> 00:36:48.290
summarize in this lecture we have discussed
some basic electrokinetic effects. We have
00:36:48.290 --> 00:36:54.619
primarily focused on electroosmosis, but we
have also discussed on several other effects.
00:36:54.619 --> 00:37:01.020
And till now we have therefore, studied
the pressure driven flow, the surface tension
00:37:01.020 --> 00:37:06.140
driven flow, the rotational microfluidics
and electro kinetically driven flow. Now how
00:37:06.140 --> 00:37:13.250
do you actually use these for healthcare applications.
We will see this later on towards the end
00:37:13.250 --> 00:37:14.829
of this course.
Thank you very much .