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Good morning.
We are going to start our part of the course micro scale transport process with an introduction
in micro process engineering which is an inter disciplinary approach.
And towards the middle of this lecture,we would see how different branches of science
has enriched micro process engineering and which is quickly becoming an effective tool
for physicists, chemists and the engineering issues involved are immense.So, we would like
to how the micro process engineering which is a science of enhance transport process
in small devices.
Basically, what we are looking at is that, whenwe scale down to micrometer dimensions;
this not only changes the length and volume of a device but, init influences the basic
physics invariant physics of the process and thereby affecting the rates of the unit operations
which are prevalent in such devices.
Just to give you an overview of the different processes; the time scales involved and the
length scale, mostly in this slide we will concentrate on the characteristic lengths
of some of the processes and equipment commonly used in chemical engineering andcompare them
with the equipments used in micro systems technology.
If we look at the top one; thelet us say, when we talk about computers over here this
is of the length scale of about a metre whereas, the computer chip is of the order of few millimetres
to centimetres.The electronic structures in those chips areless than a micron.If we think
of a chemical engineeringequipment such as the starred vessel; then the stares vessel
consists of reactors and tubes.Whereas, on the other hand if we compare that with micro
structured process equipment they are in the range of few microns to about thousand microns
or so. When we think about let ussay anadsorbent or let us say catalyst consisting of consisting
ofpores mesopores and micropores obviously the time scalelength scale are quite different
from that of a computer or even from an electronic chip.If you think of a basic process, a diffusion
process, a diffusive process by which a material goes from one point to another through molecular
means; the diffusion coefficient of gases are relatively large whereas, the diffusion
lengthof liquids are of the order of may be 100s of microns.
So, we go from 1 millimetre of diffusion length which is characteristic of a gas to about
thousand or to about 100 microns for that of liquids.When we compare the wave lengths
like we can start with microwave where the wave length is few millimetres and we can
go all the way up to x-ray where it isit could be even smaller than a nanometre.Some of the
common examples which we see inour everyday life; rain drops about 1 millimetre of length
scale whereas, thecigarette smoke can be as small.The particles present could be as small
as less than a micron which is one of the cause of why it is so harmful.
We can also think of these sizes of the mammals.Compare that with that of a protein so from few metres
we come to few nanometres and also we can think aboutthe small in organic molecules
which are the building blocks of all of us.So, less than nanometre length to about a metre
length.Now, when we think of the different processes the equipments the processes and
so on what we see here is that the length scales involved are enormously different between
a computer and an electronic structure or between you and the small in our organic molecule
which is the building block of our our bodies. So the physics could be vastly different between
what is happening on this side of the figure to the processesis which become important,
the forces which become important on on the other side on the nanometre and micron length
scales and theyou would see that some of the forces which are important in this region
will become almost negligible in this in this in the in the smaller scale in the micro scale
and some of the forces which are which are not which are present but, not important would
probably govern the entire process.An example of this could be let us say the gravity force
is extremely important in the macro scale whereas, the gravity force or the body force
loses its importance when we go towards the towards the micro scale.A surface tension
which may not be important in terms of a starred vessel that reaction taking place in a macro
reactor but, when you think a flow through a micro channel, the surface tension force
will start to become a verystart to play a very important role.
So, these are some of the basic inherent differences which can happen whichwhich will govern different
forces, different processes and multimode physics which are involved when you go from
a macro scale to a micro scale.
When we we would like to give in this course an overview of the effects and the phenomena
for example, in a micro channel which can have characteristic dimensions from 10 to
about thousand micron and one of the basic reasons why the processes taking place in
a micro channel are so fast or how the miniaturisation of the channel size canplay an important part
in the intensification of the process, in the better yield of products on in the process
or for example, to maintain the constancy in temperature in an exothermic reaction is
due to the fact that most of the processes usually in chemical engineering take place
within a very thin layer closed to let ussay a solid liquid interface or a solid gas interface.
Let us say think about thereaction which is taking place on catalytic surface.What would
happen is from the bulk.Let us say it is a it is a gassolid reaction solid is the catalyst
and we have two reactants coming atwith the gas phase with the inlet gas phase they will
diffuse, reach the solid surface on the presence of the catalyst, the reaction will take place
a product will form and the product has to diffuse back to the main stream to be carried
with the bulk flow. Now, this reaction and subsequent back diffusion
all this will take place in a very thin layer closed to the surface which is known asboundary
layer in this case mass transfer boundary layer.We also have hydrodynamic boundary layer
and thermal boundary layers.These boundary layers are generally millimetres inthe length
scale would be involved would be aboutfew millimetres and most of the transport phenomena
takes place in this thinregion closed to the solid surface.
So, if you think about the transport process the rest of the fluid outside the boundary
layer they do not take part into the reaction or into let us say the frictional force or
intointo thermal thermalinto thermal transport at all.So, if we code somehow reduce the length
scale of the devices down to the size of the boundary layer then the overall efficiency
of the process has to increase. This is the reason why the micro structured devices or
micro devices will have a high value of a, will definitely work in terms of a its its
transfer length is going to be very small in the scale of the boundary layer and the
higher transport rates which one encountersin these type of devices is a is a direct resultthat
the sizes are going to be comparable with that of the boundary layer and you would see
the examples ofreactions taking place into micro reactors.For example, if they will be
characterised by rapid mixing.If you have a temperature sensitive reaction then you
would be able to maintain the temperature to a preset level in a much better way if
you have such a small system because your system is of the dimensions of a boundary
layer.So, it would be easier for you to control let us say the temperature to control let
us say for example, precipitation of nano particles in a system or to have reactions
take place in such a way, thatthe undesirable side reactions can be can be eliminated or
if noteliminated completely, they can be reduced and the yield of the product will be increased.We
will will seemore examples of that in the future.
So if we have to think about micro process engineering let us first start with the macro
scale engineering processes which is process engineering.Now, process engineering can be
divided into mainly three parts; one is the simulation or the unit operations which are
the building blocks of any engineering, any macro scale engineering process.There is an
renewed thrust on green and sustainable chemistry which is also affecting, which is also going
togoing to affect the process engineering outlook of today’s engineers. But, the basic
aim is tohave some sort of a process intensification.The process intensification would increase the
efficiency of the process on one hand also yield increase the yield of the product and
so on. Now we would like to integrate the process
engineering with micro systems engineering.If we think of the processintensification part,
we would like to see how micro systems engineering can play a part in the in in the intensification
of the process.So, if you let us think about the micro systems engineering micro systems
engineering consists of three parts; one is fabrication and what kind of materials are
going to be used for micro systems engineering?If you think of fabrications the newer and newer
methods of making smaller and smaller devicesbecoming available everyday and materials available
to us willkeeps on increasing and we can have exotic materials for a very specific purpose.In
all these fabrication techniques, newer fabrication techniques newer materials enable us to integratedifferent
devices.For example, sensors, actuators having specific functions.
Now, combine these together the fabrication part and the sensor part together; we have
come across a new area of engineering which is known as which is known as micro fluidics
micro fluidics is nothing but, the transport of fluids through micro devices with associated
physics which could be vastly different from the physics that we encounter in macro devices.So,
in order to in order to attain process intensification we look towards micro fluidics which is based
on the available micro systems engineering technique, fabrication techniques that are
available to us. So the combination of process with the with
the aim of process intensification micro fluidics can be applied and the branch which has generated
out of these two is commonly known as micro process engineering.Now, one has to also identifythat
micro process engineering gets inputs from different branches of science. I have given
the example of chemistry over here with let ussay the catalysts.So, newer and newer catalysts
are becoming available witheveryday and how do we incorporate the knowledge of chemistry
and physics into micro fluidics with an aim to intensify the process; that is becoming
a challenge and we are going to meet that challenge and this has given rise to newer
technologies and specifically that is going to be the thrust of the subject which I am
going to cover in this part of the course. So, we would see how micro fluidics is going
to helpintensification of the process, increase the efficiency of the process, enhance the
selectivity of a reaction, can maintain temperature equallyat all points in a micro device, can
work towards a better selectivity for a desired product and many other interesting applications.So,
my building block for this course would be our knowledge in micro fluidics and based
on the knowledge in micro fluidics and its application in different areas; we would see
how a new branch of engineering has been created and which would probably provide us with better
methods to make a specific chemical in the future.
Now, if I give just you a brief history of the genesis of micro mechanical devices; they
have started coming into the literaturein the nineties, late eighties and early nineties
which enables fluidic systems, different fluidic systems to be developed.So, we now have micro
systems which are presentin data processing, in many optical fluid mechanical and chemical
having many fluid mechanical, chemical functions and they they perform a variety of task in
case from sensing analysing controlling the chemical controlling the chemical functionsystems
and producing goods and growing application fields in therapeutics and in diagnostics.
Many of us have heard about the word lab on a chip.So, if you think of if you know what
is lab on a chip;it is it has bought revolution in the diagnostics field.Now, we all have
given blood for 1 reason or another to have certain tests performedby the doctors.Now,
it require certain quantity of blood usually in the order of a few cc and a host of reagents
and in this process could be very chemical intensive, time intensive and you will have
a large number of different tests to be performed for somefor a specific patient.
If we could have on the other hand, a small quantity of blood which will flow through
parallel micro channels and the parallel, each of these parallel micro channels will
have certain reagents which are parked in it and as the blood flows through that specific
micro channel that reagent is going to react with the blood and gives a specific signal
which can be interpreted to let us say, it can be calibrated with the concentration of
blood glucose or concentration of blood urea present in the system.So, using a tiny volume
of the blood and using a fraction of chemicals involved in the process; one would be able
to1 would be able to perform an array of different tests on a single chip.
So, this has generated interests and there are manylab on a chip devices which are presently
in use and are coming up and will very soon be available commercially and some of them
are already available in which you can do specific tests with a small quantity of blood
and a small quantity of reagents compared tobefore.So, this will revolutionise the diagnostics
as we know today. Now when we think aboutwhy it is so important,the
so useful thatwe again come back to I think what I have covered before that a micro structured
process equipment are.So much superior to other devices to macro devices because of
two distinct reasons; one is that the high surface to volume ratiowhich you would obtain
in a micro device and secondly this is probably the keywords of this course.Tiny volumes dominate
everything in a micro device.So, not only you are working with very small volumes; millilitres
less than millilitres, 1 100th of a millilitre and at the same time since the sizes are so
small the radius of the droplet is so small that your surface to volume ratio is going
to be very large.Some of the forces which were important before will be unimportant
for micro scale devices and some some forces can become very useful and can control the
flow of a fluid because the surface area is surface area is very large compared to that
of a volume.
So, if we try toorganise our thought so far as that we are just going to be difference
between the fluid mechanics at micro and micro scale and in the macro domain and we are going
to concentrate on four specific points to highlight the differences in between the two.
The first is going to be the non-continuum of effects.We know thatvery common boundary
condition that we are very much familiar within fluid mechanics is a no slip boundary condition.We
know thatin most of the engineering the macro engineering process is the no slip condition
would be valid.That means the relative velocity between theliquids molecules and solid molecules
at the liquid vapour interface would be 0 liquid or gas molecules.
Now, this no slip condition may not be valid if we scale down to millimetre or micron level.So,
there will be situations in which there can be slipvelocity non-zero slip velocity present
at the interface.This would be even more pronounced when we think of low pressure gases.So,for
example, a gas in which is at very low pressure such that theinter molecular spacing or the
molecular mean free path becomes comparable to the device size, it is very well possible
that the continuum limit may not be valid for such a case and we are going to have actually
a slip at the at the fluid solid interface. So the non-continuum effects one has to be
very careful about while analysing the physics of flow inside a micro scale device.The same
applies viscosity what would be the viscous fluid viscosity how would it vary based on
how close to the surface we are.Based on how many particles how many particles are present
in such a system. So, the non-continuum effects the different flow regimes which are going
to be characterised by different types of non-continuum effects would be very important
in understanding flow in a micro channel.And there would be surface dominated effects.The
surface forces which were probably not very important in a macro scale will start to become
important in micro scale.The electrostatic forces, the viscouseffects are going to give
rise to situations in which we may have flows, which are going to be, due to entirely due
to electrostatic forces.The viscous forces near a charged surface could be different
and this difference in viscosity due to the charges present on the sides of a solid channel
will give rise to interesting effects which we will covertowards the later part of the
course. They are known as viscoelastic effects.So you would seewhat they are.
Most of the flows which take place in a micro channel are going to be smaller Reynold’s
number flows or low Reynold’s number flows because it is difficult due to the higher
values of pressure drop associated with flow in a micro channel to a very high velocity
flow inside such small channels.So, the flow is going to be at low Reynold’s number flow
and the approximations that one can make for low Reynold’s number flows will be equally
applicable, mostly applicable for low Reynold’s number for micro channel flows.So one has
to think about how the low Reynold’s number effects are going to create some sort of difference
between the fluid mechanics that we know atat macro scale and at micro scale.And finally,
this is going to be important as I have described before the scales aregoing to be vastly differentfrom
a metre or a centimetre scale that we are, that we are comfortable with.That we know
of at the macro scale we are probably going to the to the scale ofnanometre or micro metre
level. Soso the devices could be a few micrometre
and in some cases we can devices which would be asthe length scale could be in nanometres
as well and then we have multi physics effects.The different forces which are acting or acting
inside such a system would give rise to phenomena that can be only explained by a a treatment
which is going to be paradigm shift from the treatment that we have encountered so far.So,
this multi scale and multi physics effects are also going to make certain differences
between the fluid mechanics atmicro scale and at themacro domain.
So we we can say that the micro devices they are tend tobehave differently from the objects
that we are generally encountered with in daily life and as I mentioned before.The gravity
starts to become relatively unimportant surface effect starts to dominate the behaviour of
fluid in such small system and the forces, the friction electrostatic viscous surface
tension forces due to the surrounding air or liquid they are going to become more and
more important as the device size become smaller and smaller.
In this I would like to bring to your attention to an very interesting preposition or law
which is there, which is existing for a very long time it is known as the square cube law.And
over the years it has found use in different branches of science and engineeringand biology.So,
what is square cube law?So, it simply says that when an object undergoes a proportional
increase in size or a decrease in size; the new volume is proportional to the cube of
the multiplier and its new surface area is proportional to the square of the multiplier.All
of us know that.That the volumewhich is going to increase with l cube and the surface area
is going to scalewill be different as l square. So if we think about the surface by volume
it is going to be l square by l cube would be somewhat related to it will scale as 1
by l.So,let us think about aan interesting example from biology.Now, what you can see
is that when an suppose you scale up an animal, an antyou scale it up three times.So, its
volume is going to be scale, volume is going to increase,it is mass is going to increaseconsiderably.Since,it
is going to beproportional to l cube whereas, its muscles the cross section of the muscles
are going to increase only by l square. So it is weight is going to increased by l
cube whereas, its its the strength muscle strength is going to increase somewhat to
some extent it will scale with the squarethe scaling factor would be the square of thesquare
of that factor.So, its mass would increase by the cube of that scaling factor as a result
that ant which has beenwhich you have arbitrarily increased its size by its length scale by
three times, its mass is going to be 9 times but, its strength of the muscles, are not
going to be increase in the strength of the muscles and not going proportional to l cube.As
a result it is going to have cardiovascular and respiratory functions which would be severely
affected. So,that is you canwe can have some commonidea
common or commonality with the weight of a person.So, if the weight of a person increases
thenhe he or she will iswill most likely going to have cardiovascular and respiratory problems
and alsoalso muscle problems and they will they are basically due to the reason of the
square cube law.
Now, if we if wetry to express it more scientifically what we see is that any property which is
a function of the area of interaction; it decreases more slowly than properties that
depend on the volume. Sowe, if we think of mass then it is going
to scale as l cube but, let us say we are talking about surface tension which is a function
of the area it is going to vary with l square.So, the propertywhich let us say is surface tension
and the ratio of that with the mass of the system is going to scale as 1 by l, where
l is the characteristic dimension of the micro device and this this has very interesting
applications or the the result of this could be very interesting when you think about micro
devices.A typical order of magnitude of this ratio ofp 1 which could be surface tension
and p 2 which is something which depends on the volume, which could be mass.So, p 1 by
2 is going to scale as 1 by l and for a micro device, if you think of this as a micron size
micro device then this ratio is going to have a a ratio of 10 to the powerof 6 metre square
per metre cube.Now, if you think of it this way, you would see that when you skip on reducing
the size of a device slowly the surface tensionwill start to predominate over something, over
a force which denotes on the mass.It could be the inertia.So, surface tension effects
are dominant at these scales when the size of the device is in in the order of microns
and there are micro pumps and micro valves which have been fabricated taking advantage
of the principle where the surface tension is going to cause or going to make the fluid
flow from one point another and the inertial effects are rather unimportant.So, we can
device off surface tension driven pumps to make liquid flow or to deliver a packet of
fluid from one point another.
So you would see an example of that in in in subsequent slides.When you think of the
applications thisinitial application 1 can think of is in computed components which is
the Winchester’s type harddiskdisk drive mechanism where the read write head floats
roughly about fifteen a micron over the spinning disk.So, the separation between the 2 two
solids; one the head and the other is the disk is about 50nanometer and no matter whatever
be the speed of the spinning disk; the flow is essentially going to be a very low Reynolds
number flow.It is also itsmach number is also going to be small you we have a typical situation
in which the mach number is about 0.3 could be 0.3 and the Reynolds number even though
that thisdisk spinning at a very high speed could be as small as 0.6.
Now, when you think of the think of such a situation low a Reynolds number, low mach
number flow even though the velocity is involved a very large since the length scale involve
is only 50 to 100nanometers.Theseare prime candidates for large Knudsen number flows
and the Knudsen number is defined as lambda which is a mean free path by l divided by
l which is the length scale.So, here we have the length scale as about 10 to the power
over the order of 10 to the power 9 meters in at some conditions thisinter molecular,
the molecular mean free path could be of the order of 10 to the power minus eight.
So you have a situation in which this Knudsen number could be as large as 10 or even beyond.If
that is the keys for values of Knudsen number which ofof the order of 10, you are going
to definitely not going to work in the continuum limit.You will be definitely working in a
in a in a situation in which many of the assumptions of continuum limit will not be valid anymore.
To give youanother example ofhow theseparticles, some nono particles or micro particles can
be effectively utilized their motion manipulated from outside so that they can give rise to
the working of a pump.It has comeinrelatively recent paper in science, I think I believe
it is in 2002 where itit was shown that micro particles of the size 20 nanometres about
3 micron can be used to fabricate micro devices, micro pumpswhich can be used in turn for the
control of microfluidic devices.So, we have a microfluidic devices in which the flow rate
could be microliter, smaller than microliter in many cases it could be nanoliters.So, how
do you device a pump which would create a flow such a small flow.So one of the novel
and innovative examples of use of ofofof these micro particles is one can fabricate a self
assembled structures using paramagnetic particles by liquids in micro channel and their ability
to form such a large particle, large structures and you can control their their motion from
outside would give rise to colloidal micro pumps and colloidal micro valves.I will give
you an example over here.
So if you concentrate on the right hand side of the picture; you would see that there thereare
there are thereare particles which are going to form a string a string like structure and
you you can create the motion of this particle.Let us say this particle in such a way that it
is going to,it is going to as if there is sin wave which is going through these particles.As
a result of which the liquid is going to be pushed.The liquid is going to be pushed from
one side to the other in the direction and small packets of fluid canflow due to the
motion.Due to the controlled motion of these particles of these large relatively large
particles in this case latex microspheres through a nano tube and you can have a flow
as slow as 0.25 nanometer per hour. So the motions of this particles can be as
small as 2 to 4 micron per second but, interestingly this would give rise to a flow which isonly
nanoliter per hour order.So, if we have a very, if we have a small, if we have a reaction
which is taking place and you have to supply reactantsin a very small device at a very
small flow rate you cannot have normal pumps peristaltic pumps or such suchor such pumps.Then
1 has to device and this is an example of how to design a pump based on the motion of
latex microspheres.
AhThis is a graph which tells us about on the x axis the values of Knudsen number and
correspond to each of the values of these Knudsen number where we are in terms of the
types of motion that is taking place in a device.So, usually Knudsen number less than
0.001; we are going to have 0.01 we are going to have continuum flow.So, from here down
for a value of knudsen number of 0.011 can assume it continuum flow.You are going to
have no slip condition valid in such a in such a zone and your no slip, your properties
are going to be invariant with position so if you maintain other conditions the same
the property will not change in such a system but, the moment you go beyond point 1 up to
beyondpoint 0 and up to point 1 then the properties will still remain same but, you have to assume
slip flow at the solid fluid interface.So,that is known as the slip flow regime.If you go
beyond that for even high values of slip flow for Knudsen number greater than 10 the motion
of the motion of the species present can be interpreted as free molecular flow and in
between .1 and 10 you have a transition where the flow changes from slip flow. But, still
property is same to free molecular flow where the properties are also going to vary with
position and time and in somewhere in between you have transition flow.
So when we think of micro channelsthis 1 the micro channels over here are generally at
the border line between continuum flow andslip flow.So, the analysis of micro flow, micro
channel flow that you would see the boundary conditions in many cases will involve a slip
boundary condition.So, one has to be careful to find outthe based on the value of knudsen
Knudsen number whether we can assumea continuum mechanism that is in place or we have to go
to slip or transition flow as well. So some of the devices which you see here
are placed areare placed along along these two lines where slowly we go from this which
iswhich iscontinuum flow up to the point where the flow is not continuum and whenever we
have, we are working with let us say about point 1 micron and smaller that isnano technology
and on the other side we have mems and in this course we are mostly going to concentrate
on this side.What happens to a micro system, the transport phenomena that is taking placein
a micro system and these are some of the devices which we arewhich we are going to concentrate
on, which we are going to concentrate their physics of flow inside such devices, how to
fabricate such devices, the design issues, the engineering issues which are involved
in such devices that is what we would like to analyze in depth in this course.
Soto summarizewhatever we have covered so far; the relevant issues which are going to
be important in this course are what is the characteristic length and time scale involved
in the process that we are going to that we are designing?What is a transport phenomenawhich
is taking place in such microstructures?Is the phenomena phenomenon taking place in the
continuum range or we have to think of a slip flow or a transition flow?The engineering
aspects involved beenthis micro process how to what are how to make how to fabricate such
micro devices?We would also like to know what is the momentum and heat transfer how is the,what
is the mechanism of momentum and heat transfer in such devices.Are they coupled?Are the heat
transfer and fluid flow for example, heat transfer and fluid flow are they coupled together?Do
we require any unified solution or is it possible to obtain the velocity profile from the fluid
mechanics part of the problem and then use that velocity profile to obtain the temperature
profile in such a system?Or are the processes coupled in such a way that independent solutions
of fluid mechanics is not possible, you have to solve both together which would make the
process even more difficult?So you would see that as well.And finally, we are also going
to look at the micro fabrication technologies which are available today which is a still
evolving at a veryrapid rate and how the use of this fabrication technology results in
intensification of any process.That is going to be the goal.
So, we in through all these studies our main goal is how to intensify the process, how
to increase the rate of formation of a specific materialin a much more controlled way, in
a process and that is what we are going to look at in this course.
So we come back to again what as I said the most important line of this course that their
transfer lengths are short, areas are small but, high surface to volume ratios and tiny
volumes are going to dominate everything. Now we would like to put a slightly mathematicaltreatment
to this and see what what exactly do we mean by that.If your channels are small then you
are going to have shortertransport lengths which would definitely be beneficial for heat
and mass transfer.So, if your shorterif your length scales involved are very small, transfer
lengths are very small then they are going to lead to high transfer rates.And the diffusive
mass and heat transport and momentum transport could be could be very large and this is a
famous equationwhich relates the property of the material that we are handling, the
length scale which is given by x and the time scale which is given by t.
So,let us think of the diffusion coefficient of gases or liquids.They are of the order
of 10 to the power minus 6 to about 10 to the power minus 10 where as x the length scale
involved in micro fluidic devices; they are of the order of 1 into 10 to the power minus
6 microns meters.So, about 1 micron.So, what you see then is the result gives you a very
small value of time scale.So, the transport length could be a could becould betransport
length by diffusive mixing is for gases is 10 to the power minus 6, liquids its 10 to
the power minus 10 and this would this would give rise to a very small value of the time,
the frequency the time scale of of the transformation frequency and which is connected with the
property of of the system. So, the diffusion coefficient the transport
length theirway,they govern what would be the time scale of the process and we can see
that the time scale of the process is going to be very very small.So, the transformation
frequency of such a process is going to be small which ismade clear in the next figure.
Now, over here we have the length n k l o in on on thex axis we have the time.So, it
is basically a characteristic length and time scales for mixing in small devices.
Now when we think ofa macro device a macro device has a length scale which is typically
in the range of centimetres. In in this fluid packets with with which you can represent
the thethe process in a conventional equipment their sizes are for from 100 micron to about
1 millimetres and a corresponding, if you look at the corresponding diffusion time over
here.So, we are we for micro devices we are we are working in this length as far as as
far as the length scale is concerned and this would give rise to this as of time scale for
gases and for liquids this is roughly of the order of 1 into 10 to the power minus few
1 millisecond. So we are probably working at 10 to 100 millisecond
to aboutI amsorry 10 into 1 into 10 to the power minus 5 seconds for gases where as 1
mille second for the case of liquids when we think about the micro mixers.For conventional
equipments the same things are roughly over here.So, this is the time scale of a micro
mixer where as this is the time scale of a macro mixer or a conventional equipment.
Now, that is what I have written over here if we think of micro structure devices; their
typical length scales from 100 micron to 1 millimetre and the fluid structures are having
lengths of approximately one micron.So, your mixing times are shorter than 100 micro second
in gases and approximately 1 mille second in liquids.So, you can seewhat is the difference
between this for gases and this is for liquids.So, you get roughly about a thousand times change
in the in in in the mixing times between a macro scale device and a micro scale device.So,
this shows why working the main reason for the enhance selectivity yield is of maintaining
constant temperature in a micro reactor compared to a macro reactor.
So, summary we can say that the shorter the length, the shorter is a characteristic time
for the transport process and the transformation frequency is going to be higher.Andjust to
give you an idea that what we are talking about in terms of diffusion length, is roughly
about 7 millimetre in gases and approximately seventy micronin liquids.That isthat is the
diffusion length length covered by a diffusing molecule in a second.
When we try tolook at the conduction lengthfrom the basic balance equation; we know thatfor
momentum the conduction length is given by root over 2 nu t where nu is the kinematic
viscosity and t is the time scale.For heatheat transfer the length scale involved isroot
over 2 alpha t where alpha is thethermal diffusivity.So, the characteristic time is proportional.This
is important to the square of the length variation and to the transport coefficient.So, the smaller
if weif we if you can keep on making a device size smaller and smaller if the characteristic
time is going to be reduced by square of that. So,its one can see that how the time requiredto
complete a process decreases drastically once the sizes of such devices are made smaller.
So, information about this typical length scale and time scale for first chemical reactions
are necessary in order to compare the processes and the mass transfer in micro mixers they
act on a length scale which could be a few microns and they take place the the time required
would be a few milliseconds or less.So if we have three or four reactions; 1 principle
reaction and the other side reactions are taking place in a in a device 1 can control
the process in such a way that the slower reactions the side reactions would be made
even slower and using the less smaller values of the frequency of transformation of such
reactions. The main reaction can be made faster.Thereby the product form, the yield of the product
form would be a much higher and in such a way the overall yield of the desired product
can be increased many times in a micro device.So,that is the direction in which we arewe are going
in the design of micro reactors.
Another important thing one has to keep in mind is what is the scale of the fluid residence
time inside such a deviceandwithin what we know is at within small devices the fluids
are going to rest only for a very short time inside the reactor. So, if you have a slow
reaction a micro device may not be the ideal option available for you because the residence
being small the reaction may not be complete at the exit of the micro device.
So, you have to probably, generally speaking it is a faster reactions who are prime candidates
forprime candidates for a for a micro device.So, a slower reaction you probably have to use
a conventional method.The faster reactions require very shortlength of the micro devices.Similarly,
if you have an exothermic reaction; exothermic reaction would be the right candidate for
a micro device because you can control the temperature of the reactant and the products
very well in a micro device since the length scale involved are close to that of the boundary
layer thickness. So for temperature homogenization, a micro
reactor would be ideal.So, fast exothermic reactions are preferred over slow reactions
in a micro reactorfor better control and for better conversion of of the reactants to the
products.
Andwhen we think about the, this is just to look at theenhanced transport that is taking
place, enhanced values of the transport coefficient which are which are available in a micro device.All
of us know that the Nusselt number, the constant Nusselt number for a constant wall temperature
case when a fluid flows through a pipe when a flow becomes thermally fully developed;
the Nusselt number becomes constant and is equal to 3.65. And we also know that the Nusselt
number is nothing but, h d by k h being the convective heat transfer coefficient, d the
length scale in this case the diameter of the tube and k the thermal conductivityof
the fluid.So, if we are using smaller diameterchannels for suchsuch reactions then, the value of
d is going to be so small, the value of h is going to increase.So, as a result of which
you can see that the value of d h as it reduces the value of h will automatically increase
since h d b by k is a constant.So, this tells us that small channel diameter, the heat transfer
coefficient h increases andthis is one example of why we should have a high value of transfer
coefficient in a small channel flow. Additionally we are going to havenot straight
channels but, channels which are probably bending in this form.So, if we have flow in
such a micro channel then over here there is going to lot of lateral mixing, vortex
formation and these lateral mixingsand vortex formation will additionally increase the value
of h beyond that that is predicted by this equation. So, this is also something which
one should look at while designing a micro channel for a heat transfer for any experiment.
So wecome back to, so but, everything comes at a price whenever we increase the value
of a transport coefficient by making it flow through a small channel we also increasethe
pressure loss in a system.So, the pressure loss in a micro fluidic system is going to
be many times more than that of a macro scale flow.So, how do we provide this excessive
pressure drop in micro channel flows?So you want to see that in a micro channel, the flow
is mostly laminar.The pressure drop per unit length is quiet high and this is one of the1
of the limitations of a micro scale effectiveeffluelization of micro scale devices for fluid transport.So,
the high values of h or any other transport coefficient can be offset by the requirement
of high pressure drop. So in many cases the, we would go for micro
channel flows for some specific applications.
And we will give I will you examples of that later on.Now very quickly I will go through
something whichyou are familiar with that is temperature of the temperature of the fluid
flowing through a tube is going to vary exponentially and where x is the length scale of the device.
I mean l is the length scale of the device and x is the channelis ais a distance at which
its flows. So if we have flow of liquid through this then this is your x andl h could be the
diameter of the channel.
So, the temperature isgoing to exponentially change with the distance traversed and when
we connect this characteristic length with the velocity and so on then this t x, the
temperature change in temperature can be related to an exponential change with time andwe could
see that the characteristic time which ishere in the denominator is it can be connected
with rho, the density, c p thec pthe heat capacity thermal conductivity but, most importantly
with the square of the size of the device. So this simply tells us that with decrease
in channel diameter the fluid temperature exponentially approaches the wall temperature.So
one can have the temperature of the fluid approaching that of the,that of the wall very
fast if its flow in a micro channel.So, this is anotherexample how the homogenization of
temperature can be obtained in a micro channel compared to a macro channel.
So we need to look at the requirementrequirement of efficient heat transfer where high exothermic
reactions andthis slide is essentially a summary of what we have covered so far.We know that
high surface to volume ratio is responsible for fast heat transfer in micro channels and
additionally we have very high surface to volume ratio which would be very important
beneficial for surface reactions such as catalyzecatalysisheterogeneous catalysisemulsification or other transport
limited processes.
And this again is tells us something about the timenecessary for the time scale involved
in unsteady state heat transfer processes. So, a smaller length scale the characteristic
reduction relaxation time also becomes shorterand we will have aa faster reaction taking place.The
system is going to reach steady state at a much, at a value which issmaller than that
of a macro system. Thank you.