WEBVTT
Kind: captions
Language: en
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We will start our discussion on Theoretical
Biomicrofluidics with pressure driven flows.
00:00:23.180 --> 00:00:33.780
So, what do we mean by pressure driven flow
we mean that there is a fluid in a micro channel
00:00:33.780 --> 00:00:41.140
and there is a pressure gradient or difference
in pressure that is created across the fluid,
00:00:41.140 --> 00:00:48.630
so that by virtue of the pressure gradient
the fluid starts flowing this method has it
00:00:48.630 --> 00:00:54.660
is own advantages and disadvantages. But one
has to understand that this is one of the
00:00:54.660 --> 00:01:00.490
very classical methods of driving the flow,
even in your household application you see
00:01:00.490 --> 00:01:09.530
that there is a pump that is driving the fluid
from the lower level to the higher level .
00:01:09.530 --> 00:01:17.990
Similarly, you will see that in micro fluidics
there are different other types of pumps not
00:01:17.990 --> 00:01:23.590
really the type of pump that you use in the
household application, but a pump where you
00:01:23.590 --> 00:01:33.140
may have a piston driving the flow by getting
displaced inside a cylinder. So, that type
00:01:33.140 --> 00:01:39.139
of pump looks like a big injection syringe
and that is often called as a syringe pump.
00:01:39.139 --> 00:01:46.859
Syringe pump is very important for medical
applications and it is used for many applications
00:01:46.859 --> 00:01:54.109
including metering of flow and drug
delivery and so many other issues .
00:01:54.109 --> 00:02:04.079
So, it is therefore quite important that
we learn that what are the fundamental aspects
00:02:04.079 --> 00:02:13.720
of a pressure gradient driving of fluid flow,
to understand that one classical way is you
00:02:13.720 --> 00:02:21.000
know to start with the basic equations in
fluid dynamics which for certain special types
00:02:21.000 --> 00:02:29.730
of flows like Newtonian fluid and so on are
governed by well known may be a stokes equations.
00:02:29.730 --> 00:02:36.200
But here what we will do is that we will not
go through the root of the navier stokes equation
00:02:36.200 --> 00:02:43.939
and this I am doing deliberately because
I can understand that this being an interdisciplinary
00:02:43.939 --> 00:02:50.670
course there are many participants in this
course who have who may not have done a very
00:02:50.670 --> 00:02:56.260
rich basic course in fluid mechanics.
So, if you have not done that then it will
00:02:56.260 --> 00:03:02.230
be difficult to follow if we start as such
with the navier stokes equation, so what I
00:03:02.230 --> 00:03:09.319
will do is that I will start with a basic
force balance in the fluid to explain how
00:03:09.319 --> 00:03:12.200
the fluid flow takes place using pressure
gradient .
00:03:12.200 --> 00:03:26.170
So, to understand that
let us consider a circular channel which in
00:03:26.170 --> 00:03:35.849
the large scale would be a pipe in a small
scale it is a circular micro channel or a
00:03:35.849 --> 00:03:48.750
micro tube. So, how you are driving the flow
is you are having a pressure here p 1 here
00:03:48.750 --> 00:03:58.099
you are having a pressure p 2 which is less
than p 1 and by virtue of this pressure difference
00:03:58.099 --> 00:04:05.420
the fluid is flowing . Of course, you have
to understand that sometimes this pressure
00:04:05.420 --> 00:04:14.370
includes the fluid pressure plus the effective
pressure due to the height, which is the gravity
00:04:14.370 --> 00:04:22.230
effect like effective pressure due to height
is h rho g so that might add to this.
00:04:22.230 --> 00:04:34.100
But in case of a horizontal channel that effect
is nullified so what drives the flow is essentially
00:04:34.100 --> 00:04:41.110
not just p, but p plus rho g h where h is
the height g is a acceleration due to gravity
00:04:41.110 --> 00:04:57.860
and rho is the density . Under these situations
let us take
00:04:57.860 --> 00:05:17.040
a small fluid element with radius r ok, radius
of the pipe or the channel is capital R . So,
00:05:17.040 --> 00:05:31.790
now let us identify various forces, so the
first force that we can identify is the shear
00:05:31.790 --> 00:05:41.100
force why is this shear force coming you have
various layers of fluid and one layer of fluid
00:05:41.100 --> 00:05:49.190
is trying to slide over the other at the wall.
Because of the fact that wall molecules are
00:05:49.190 --> 00:05:55.700
immobile they are trying to hold the fluid
molecules therefore the velocity is 0.
00:05:55.700 --> 00:06:03.330
But as you go away from the wall the velocity
becomes more because the effect of the wall
00:06:03.330 --> 00:06:09.180
is not directly filled, but it propagates
through the fluid by virtue of the fluid property
00:06:09.180 --> 00:06:16.150
called as viscosity. So, viscosity make sure
that although this is not directly in contact
00:06:16.150 --> 00:06:24.080
with the wall there is a shear here which
is transmitted from the wall to this and that
00:06:24.080 --> 00:06:30.810
transmission of shear across various layers
is by virtue of the fluid property viscosity
00:06:30.810 --> 00:06:44.170
. So, now if you call this as tau which is
the shear stress then and let us say that
00:06:44.170 --> 00:06:56.640
this is dz then this force is tau into the
surface area of this imaginary cylinder.
00:06:56.640 --> 00:07:13.840
So, 2 pi r into dz ok then there will be a
force due to pressure gradient, here the force
00:07:13.840 --> 00:07:27.430
is p into pi r square here it is p plus dp
into pi r square . Now the question is are
00:07:27.430 --> 00:07:35.730
all those forces balanced there is no necessity
that these forces will be balanced, but under
00:07:35.730 --> 00:07:43.110
the condition that these forces are balanced
and these forces are balanced in most circumstances
00:07:43.110 --> 00:07:48.350
in micro channel flows, I do not have enough
time to get into the reason why all these
00:07:48.350 --> 00:07:55.670
forces will be balanced.
But when all these forces will be balanced
00:07:55.670 --> 00:07:59.840
the situation resembles to something which
is called as a fully developed flow. So, to
00:07:59.840 --> 00:08:06.170
give you a qualitative understanding of what
is a fully developed flow I will try to go
00:08:06.170 --> 00:08:14.070
through this slide.
So, you see here that the fluid enters the
00:08:14.070 --> 00:08:20.380
pipe with a velocity profile such that there
is a layer close to the solid boundary where
00:08:20.380 --> 00:08:25.470
the viscous effects are important, but as
you go away from the solid boundary the viscous
00:08:25.470 --> 00:08:33.940
effects become less and less. So, this
layer within which the viscous effects are
00:08:33.940 --> 00:08:38.950
important and outside which the viscous effects
are not important this layer is called as
00:08:38.950 --> 00:08:44.930
the boundary layer.
So, the dotted line here is basically the
00:08:44.930 --> 00:08:52.520
edge of the boundary layer, so when the boundary
layers from the all the walls they merge then
00:08:52.520 --> 00:08:57.900
after that you will have a velocity profile
which is called as fully developed velocity
00:08:57.900 --> 00:09:05.850
profile . So, this fully developed velocity
profile is the consideration that we are assuming
00:09:05.850 --> 00:09:11.260
here, when the flow is fully developed the
velocity profile does not change further as
00:09:11.260 --> 00:09:18.740
you move along this direction.
So, if you see here in the slide if you
00:09:18.740 --> 00:09:26.180
if you see in the slide I request them to
show the slide please low please show the
00:09:26.180 --> 00:09:36.340
slide yes. So, if you see this velocity
profile this velocity profile will not change
00:09:36.340 --> 00:09:43.610
further with the axial position and that means
that all these forces are balanced. Because
00:09:43.610 --> 00:09:47.200
if the velocity profile changes with the axial
direction there will be an acceleration and
00:09:47.200 --> 00:09:54.190
acceleration means there is an unbalanced
force. So, here there is no unbalanced force
00:09:54.190 --> 00:10:06.260
that means you can say that p into pi r square
minus p plus dp into pi r square minus tau
00:10:06.260 --> 00:10:17.980
into 2 pi r dz that is equal to 0 .
So, if you simplify this you will get tau
00:10:17.980 --> 00:10:33.330
is equal to minus r by 2 dp dz ok. So, then
by Newtons law of viscosity if this fluid
00:10:33.330 --> 00:10:43.690
is Newtonian, now this is where you can make
sure that you apply this equation to different
00:10:43.690 --> 00:10:51.340
types of fluids. So, if it is a Newtonian
fluid that is the Newtonian fluid is a fluid
00:10:51.340 --> 00:11:01.680
which will obey the Newtons law of viscosity,
then this tau will be minus mu du dr why minus
00:11:01.680 --> 00:11:08.730
mu du dr see if you have a solid boundary
, then for a flow unidirectional flow tau
00:11:08.730 --> 00:11:16.020
will be mu du dy this is Newtons law of viscosity
that all of you have learnt through some of
00:11:16.020 --> 00:11:22.830
your basic courses in physics .
Now, here so this is the wall the r direction
00:11:22.830 --> 00:11:31.010
is towards the wall, so mu du dy will be minus
mu du dr because r and y are in opposite direction.
00:11:31.010 --> 00:11:37.420
So, for a Newtonian fluid which will be minus
mu du dr, if it is not a Newtonian fluid let
00:11:37.420 --> 00:11:45.750
us say it is a fluid layer fluid like blood.
So, then what we will do instead of this whatever
00:11:45.750 --> 00:11:52.780
is the constitutive behavior of that fluid
that we need to substitute instead of this
00:11:52.780 --> 00:12:00.230
expression, so this is where we will model
the bio fluid in a particular way. So, here
00:12:00.230 --> 00:12:04.870
the fluid is modeled as a Newtonian fluid
as an example, but if it is modeled as a bio
00:12:04.870 --> 00:12:10.480
fluid modeled as a non Newtonian fluid
then the corresponding expression has to come
00:12:10.480 --> 00:12:17.010
out here. So, now so this u is nothing but
the velocity in the z direction.
00:12:17.010 --> 00:12:35.230
So, we will call it is as a V z z is the axial
direction of the tube . So, dVz dr r by 2
00:12:35.230 --> 00:12:52.720
mu dp dz . So, if you integrate this once
more Vz is equal to r square by 4 mu dp dz
00:12:52.720 --> 00:13:07.170
plus a constant of a integration C1. So, how
do you get C1 you get C1 by noting that at
00:13:07.170 --> 00:13:17.100
small r is equal to capital r which is the
solid boundary you have Vz equal to 0 , this
00:13:17.100 --> 00:13:28.550
is called no slip boundary condition. We will
see briefly what is slip in in case you have
00:13:28.550 --> 00:13:38.110
slip instead of no slip .
So, you will have zero is equal to r square
00:13:38.110 --> 00:14:28.600
by 4 mu dp dz plus C1. So, C1 is sometimes
it is we will keep this equation in mind because,
00:14:28.600 --> 00:14:39.130
we will be using this for certain purpose
But you can also express it in terms of
00:14:39.130 --> 00:14:46.000
the average velocity why average velocity
is important because, in experiments you can
00:14:46.000 --> 00:14:53.110
measure flow rate the total rate of flow at
a given section in the pipe and if you divide
00:14:53.110 --> 00:14:56.990
the flow rate by the cross sectional area
you will get the average velocity.
00:14:56.990 --> 00:15:04.110
So, average velocity is an experimentally
obtainable parameter and that is why instead
00:15:04.110 --> 00:15:12.390
of this you can express the same in terms
of the average velocity average velocity is
00:15:12.390 --> 00:15:43.959
the flow rate divided by the area of cross
section ok. So, this becomes so this r square
00:15:43.959 --> 00:16:01.270
into rdr is. So, r cube so this becomes
rdr that is r square by 2, do this becomes
00:16:01.270 --> 00:16:14.820
r 4 by 2 minus this is r cube dr that is r
4 by 4 .
00:16:14.820 --> 00:16:40.480
So, let us work it out here so V average , so
this becomes r 4 by 2 minus r 4 by 4 this
00:16:40.480 --> 00:17:09.400
is r 4 by 4. So, r 4 by 4 into 2 pi so that
becomes minus 1 by 4 mu dp dz into so 5 get
00:17:09.400 --> 00:17:23.079
is cancel this becomes r square. So, by considering
equation star and equation double star you
00:17:23.079 --> 00:17:38.700
can write
00:17:38.700 --> 00:17:48.880
this flow is classically known as Hagen Poiseuille
flow and although it appears to be a very
00:17:48.880 --> 00:17:57.269
fundamental aspect of fluid mechanics, this
was actually derived and developed by a person
00:17:57.269 --> 00:18:01.360
called as Poiseuille who by profession was
a physician.
00:18:01.360 --> 00:18:09.389
So, he was a medical doctor and his interest
was actually to see how blood flows through
00:18:09.389 --> 00:18:17.360
the capillaries in human bodies and this
is one of the very simplified old models that
00:18:17.360 --> 00:18:25.720
tried to mimic that physical picture . So,
this is the velocity profile and it shows
00:18:25.720 --> 00:18:30.590
that the velocity profile is parabolic, which
is the the velocity profile that I showed
00:18:30.590 --> 00:18:39.139
in the slide. So, the velocity profile
is something like this a parabolic velocity
00:18:39.139 --> 00:18:47.489
profile.
Now, the big question is see as a bio microfluidics
00:18:47.489 --> 00:18:53.660
engineer, you may be interested in the velocity
profile of course are the fundamental information,
00:18:53.660 --> 00:19:00.179
but you may also be interested you know how
much power will I require to drive the flow.
00:19:00.179 --> 00:19:06.440
Because that is where your pumping cost effort
and all those things will be related. So,
00:19:06.440 --> 00:19:15.059
the primary things are how much pumping power
I will require to achieve a given flow rate
00:19:15.059 --> 00:19:25.049
that is the you know output of my device.
So, that in hydraulics is often measured by
00:19:25.049 --> 00:19:31.999
a quantity . So, we will look into this equation
and build it up from here .
00:19:31.999 --> 00:19:49.780
So, V average is minus 1 by 4 mu minus 1 by
8 mu actually 1 by 4 and a half is there dp
00:19:49.780 --> 00:20:07.369
dz into r square. Now this dpdz you can write
because pressure versus z is linear; why pressure
00:20:07.369 --> 00:20:15.440
versus z is linear you can see from this equation
I mean that equation is erased from
00:20:15.440 --> 00:20:21.320
this board, but if you look the look at the
first equation tau is equal to minus r by
00:20:21.320 --> 00:20:29.149
2 dp dz I am writing this again . So, tau
is a function of r only .
00:20:29.149 --> 00:20:36.369
So, tau by r is a function of r only. So,
in this equation the left hand side if you
00:20:36.369 --> 00:20:44.239
bring r here. So, you may bring r here tau
by r is a function of r only dp dz is a function
00:20:44.239 --> 00:20:51.159
of z only a function of r is equal to a function
of z only if it is a constant so; that means,
00:20:51.159 --> 00:20:59.399
dp dz is a constant. So, p versus z is linear.
So, you can write dp dz as minus delta p over
00:20:59.399 --> 00:21:16.139
L; where L is the length of the tube. So,
then this delta p you can write the pressure
00:21:16.139 --> 00:21:23.370
drop, you can write in terms of a length unit
which we call as head loss hf.
00:21:23.370 --> 00:21:30.350
So, why head loss head loss is essentially
an energy loss to overcome viscous effects
00:21:30.350 --> 00:21:36.789
in the flow. So, physically why do you require
a pumping power? You require a pumping power
00:21:36.789 --> 00:21:42.149
because there is viscosity in the fluid and
viscosity in the fluid resists the relative
00:21:42.149 --> 00:21:47.509
motion between the fluid layers. So, you have
to maintain to maintain the fluid motion you
00:21:47.509 --> 00:21:55.679
have to give certain energy to overcome the
viscous resistance and that energy per unit
00:21:55.679 --> 00:22:01.399
weight is called as head h f for f f subscript
for friction.
00:22:01.399 --> 00:22:11.659
So, minus hf rho g by l . So, you will get
V is equal to these 2 minus signs get cancelled
00:22:11.659 --> 00:22:40.700
out. So, hf rho g by 8 mu R square ,
00:22:40.700 --> 00:22:49.809
so V average you can write as a Q by pi R
square where Q is the flow rate in the unit
00:22:49.809 --> 00:22:56.740
of Q is meter cube per second so Q by pi R
square is the average velocity, so this is
00:22:56.740 --> 00:23:25.720
hf rho g by 8 mu r square . So, hf is 8 mu
Q there is there was a L right there was a
00:23:25.720 --> 00:23:37.559
L 8 mu QL by rho g pi R to the power 4 .
Sometimes engineers prefer to use diameter
00:23:37.559 --> 00:23:53.919
instead of radius so R is d by 2. So, it becomes
hf is equal to 128 mu Q L by rho g phi d 2
00:23:53.919 --> 00:24:11.850
the power 4 . This is classically known as
the Hagen Poiseuille equation , the corresponding
00:24:11.850 --> 00:24:28.109
flow is p let me write it properly
00:24:28.109 --> 00:24:34.799
the corresponding flow is Hagen Poiseuille
flow and this equation is Hagen Poiseuille
00:24:34.799 --> 00:24:42.539
equation. So, what do we get from here, so
if we want to maintain a particular flow rate
00:24:42.539 --> 00:24:48.989
in a pipe then the head loss why head loss
is important because, to overcome this loss
00:24:48.989 --> 00:24:53.460
you have to give pumping power as a input,
so more the loss more will be the pumping
00:24:53.460 --> 00:24:59.010
power.
So, the head loss is proportional to fourth
00:24:59.010 --> 00:25:04.179
power of the hydraulic diameter or the diameter
of the pipe in this case. Hydraulic diameter
00:25:04.179 --> 00:25:10.359
is an effective diameter, but for a pipe it
is the diameter itself . So, what does it
00:25:10.359 --> 00:25:18.159
indicate it indicates that it indicates a
very important scaling law for microfluidics
00:25:18.159 --> 00:25:30.559
applications, that if you reduce your pipe
diameter from 1 meter to one micron ok, so
00:25:30.559 --> 00:25:34.629
1 meter to one micron is 10 to the power 6
times the reduction.
00:25:34.629 --> 00:25:43.809
So, 10 to the power 6 to the power 4 that
is 10 to the power 24 times you will have
00:25:43.809 --> 00:25:52.350
the increase in the head loss. So, to maintain
the same flow tremendously large pressure
00:25:52.350 --> 00:26:01.259
you have to pumping power you have to
give. So, it is not normally advised that
00:26:01.259 --> 00:26:06.100
you use microfluidic devices for achieving
large flow rates.
00:26:06.100 --> 00:26:12.769
So, typically you use microfluidic devices
only when small flow rate, but in precise
00:26:12.769 --> 00:26:21.389
volume is is needed to be delivered and that
is the hallmark of microfluidic applications
00:26:21.389 --> 00:26:29.129
as compared to other applications. I will
talk little bit about another aspect
00:26:29.129 --> 00:26:36.429
which is called as the slip at the wall , in
microfluidics instead of the no slip boundary
00:26:36.429 --> 00:26:46.679
condition sometimes there happens a slip at
the wall . So, I will explain it through
00:26:46.679 --> 00:26:55.350
through a small slide.
So, the explanation is something like this
00:26:55.350 --> 00:27:02.820
so if you look into the velocity profile at
the wall, there are some cases when the velocity
00:27:02.820 --> 00:27:10.929
profile is does not show 0 velocity at the
wall. So, to quantify the velocity at the
00:27:10.929 --> 00:27:17.850
wall what is done is the tangent to the velocity
profile which is the dotted line here is extrapolated
00:27:17.850 --> 00:27:26.639
and it shows 0 not at the wall, but at the,
but at a distance of ls from the wall, this
00:27:26.639 --> 00:27:35.159
ls is called as slip length. So, let me draw
it with a figure to understand to make you
00:27:35.159 --> 00:27:39.590
understand better .
So, you have a velocity profile like this,
00:27:39.590 --> 00:27:44.379
velocity profile means here you are plotting
velocity here you are plotting the distance
00:27:44.379 --> 00:27:58.340
from the wall. So, you draw a tangent this
tangent meets here at ls , this is the velocity
00:27:58.340 --> 00:28:07.090
of fluid at the wall and let us say this angle
is theta. So, if this angle is theta you will
00:28:07.090 --> 00:28:21.450
get cot theta because tan theta is dy du so
cot theta is this one.
00:28:21.450 --> 00:28:34.820
So, cot theta from this right hand right
angle triangle is u wall by ls . So, you can
00:28:34.820 --> 00:28:47.139
write u wall is equal to ls del u del y at
the wall . So, this ls is called as Navier
00:28:47.139 --> 00:28:55.389
slip length because, in Navier in 1823 he
was a very famous mathematician in the domain
00:28:55.389 --> 00:29:02.320
of fluid mechanics and mathematics applied
mathematics and he first postulated this
00:29:02.320 --> 00:29:07.360
boundary condition.
So, if ls is 0 then velocity of the fluid
00:29:07.360 --> 00:29:13.440
at the wall is 0 that is the no special no
slip boundary condition. So, now the question
00:29:13.440 --> 00:29:18.759
is why will the fluid slip at the wall we
we are arguing that there could be a slip
00:29:18.759 --> 00:29:23.739
it is quantified by this slip length and this
can be obtained either through experiments
00:29:23.739 --> 00:29:29.830
or through molecular simulations, but the
question is why it will slip.
00:29:29.830 --> 00:29:38.119
So, why it will slip is described in
this very simple model, where you will see
00:29:38.119 --> 00:29:49.700
that at the wall there can be a a small layer
a thin layer of nano bubbles or a thin layer
00:29:49.700 --> 00:29:56.179
of rarefied gas. So, when the liquid is flowing
on the top of this wall the liquid is not
00:29:56.179 --> 00:30:03.059
feeling the effect of roughness of the wall
directly, the nano bubble layer which is shown
00:30:03.059 --> 00:30:11.330
up to this dotted line this will act like
a cushion and the liquid will slide or glide
00:30:11.330 --> 00:30:16.440
over this cushion that will make it as if
it is slipping over the solid boundary.
00:30:16.440 --> 00:30:24.779
So, that is one of the very important considerations
and there has been lot of research work actually
00:30:24.779 --> 00:30:31.169
in this domain to understand hydrodynamics
over slipping surfaces. So, it is important
00:30:31.169 --> 00:30:41.970
because if you try to understand how you can
control the slipping of fluid over a very
00:30:41.970 --> 00:30:47.379
rough surface, rough and hydrophobic surface
can promote slip in a confinement research
00:30:47.379 --> 00:30:52.279
has shown this.
Then it may be possible that overcoming the
00:30:52.279 --> 00:30:58.539
huge resistance that you can otherwise get
in a pressure driven flow, you can pump fluid
00:30:58.539 --> 00:31:06.340
at an unprecedented rate and this kind of
large level of pumping by utilizing slip has
00:31:06.340 --> 00:31:14.039
been a a hallmark of the fluid flow in
the nano channels, where in carbon nano tubes
00:31:14.039 --> 00:31:22.210
or fluid flow over graphene type of materials
have shown that you can have a high level
00:31:22.210 --> 00:31:25.129
of slip and if you can have a high level of
slip.
00:31:25.129 --> 00:31:31.139
So, in the nano scale it is because of the
behavior of the material fluid interaction
00:31:31.139 --> 00:31:37.109
in the nano scale, in the micro scale it could
be that you can use roughness as a blessing
00:31:37.109 --> 00:31:44.529
in disguise. The roughness of the wall
might trigger the formation of small gas pockets
00:31:44.529 --> 00:31:50.639
and liquid can flow on the top of that without
creating much of a frictional hindrance.
00:31:50.639 --> 00:31:58.219
So, we will summarize the discussion or
conclude the discussion in this lecture by
00:31:58.219 --> 00:32:03.779
pointing out advantages and disadvantages
of pressure driven flow. So, for that I will
00:32:03.779 --> 00:32:11.139
refer to the slide, the advantage of pressure
driven flow is that it is the simplest flow
00:32:11.139 --> 00:32:17.440
actuation right you we just need a need
a syringe pump to drive the flow.
00:32:17.440 --> 00:32:23.229
It is very easy to integrate with microfluidic
chips anybody who has started working in a
00:32:23.229 --> 00:32:28.679
microfluidics lab we will be knowing how to
operate a syringe pump and it can have a good
00:32:28.679 --> 00:32:36.889
control over the flow parameters. But this
has disadvantages also for example, the primary
00:32:36.889 --> 00:32:43.950
disadvantage is high frictional loss especially
in a microfluidic conditions were you know
00:32:43.950 --> 00:32:48.539
the head loss being inversely proportional
to the fourth power of the diameter, if the
00:32:48.539 --> 00:32:52.289
diameter becomes very small the head loss
becomes very large.
00:32:52.289 --> 00:33:00.249
It is not easily reconfigurable since you
essentially depend on a displacement of a
00:33:00.249 --> 00:33:05.359
plunger. So, it is a positive displacement
type of device even small blockages in the
00:33:05.359 --> 00:33:11.070
pathways can lead to severe damage in the
system. So, mechanical friction wear tear
00:33:11.070 --> 00:33:18.519
damage these are some of the bottlenecks of
implementing this. Despite that being one
00:33:18.519 --> 00:33:24.909
of the very traditional methods the pressure
driven flow is commonly considered to be one
00:33:24.909 --> 00:33:30.740
of the very prominent methods of flow actuation
in a micro scale.
00:33:30.740 --> 00:33:37.919
But in micro scale the advantage also remains,
what is the advantage that instead of creating
00:33:37.919 --> 00:33:43.129
a positive displacement pressure gradient
you can use surface tension to generate the
00:33:43.129 --> 00:33:48.249
equivalent pressure gradient, because surface
tension is a beautiful force in a small scales.
00:33:48.249 --> 00:33:53.950
So, in our next lecture we will see what is
surface tension and how surface tension can
00:33:53.950 --> 00:34:00.499
be used to manipulate a flow, which is fundamentally
pressure driven but the pressure gradient
00:34:00.499 --> 00:34:03.009
is created by surface tension.
Thank you very much .