 Welcome you all to the course of microfluidics. Today we will be starting with some introductory concepts related to microfluidics and before entering into the topic we will be discussing about certain motivations I mean which give us the necessary impetus to study microfluidics. So but first of all we have to understand what is microfluidics and why is it important and what are its possible applications and we will go forward with that. Now microfluidics is not a technical term as such I mean it is not a scientific term I mean it is sort of an interface between various subjects and its interpretation depends on the manner in which you look into it. Like for example like I mean microfluidics I mean it may have the name micro but in terms of its scope it is like an elephant it has a gigantic scope by itself. Now if you want to say somebody wants to say what an elephant is. Now somebody who knows the tail of an elephant will say that the elephant is like a thread. So obviously it depends on how you look into it. So microfluidics being a multifaceted subject its interpretation depends on how we look into it. Now although this is an interdisciplinary course this course is being offered as a part of our mechanical engineering curriculum. So we look into it from a particular perspective and accordingly describe microfluidics like this that microfluidics is all about studying flows with characteristic length scales of the orders of microns. So what is the characteristic length scale? Characteristic length scale is a length scale over which characteristic changes take place. So when we say that the characteristic length scales are of the order of microns what we essentially mean is that the characteristic changes that take place these changes take place over length scales of the orders of microns. Now when we say microns there is no great sanctity about it it could also be nanometers. Now there is a closely related subject which is called as nanofluidics a part of which we will also cover as a part of this particular course and when we go down to the length scale of nanometers it is not necessary that all the physics which is occurring over micrometer scales becomes invalid. Over nanometer scales also typically beyond the critical length scale the physics which is occurring at the over micrometer scales is still valid but as you go down to length scales over which continuum considerations do not work continuum hypothesis do not does not work and you have to treat the discreteness of the individual system that means you have to consider the discreteness of the molecular arrangement you have to consider the molecular entities and all those things then the paradigm shifts a little bit and I mean many of the continuum considerations which we will be considering as a major part of this particular course will not be valid and then you have to go for molecular understanding and molecular simulation. So a part of this course we will dedicate towards that so understanding nanofluidics and how to effectively address nanofluidics through molecular simulations but we have to understand that nanofluidics does not necessarily demand molecular simulations I mean it is not always necessary sometimes by stretching a little bit of imagination towards the I mean modifying the continuum description one can address many nanofluidics problems. So whatever I am giving as like the description of microfluidics is a way in which as a fluid dynamics I look into microfluidics so obviously I will show you that microfluidics is an interdisciplinary subject and it is not possible for an individual to know all the facets of microfluidics from all the angles and from all fundamental considerations but we will briefly talk about all the facets. So when we say characteristic dimensions of the orders of microns I mean as engineers we should have a feel of I mean how I mean how thick or how thin these are. So typical dimensions of the orders of microns are like dimensions of human hair like so that is the typical thing that you talk about. So if you have a transparent substrate on which you have a micro channel it will look like a scratch if you look by naked eye. So microfluidics devices so and their dimensions so if you look at this view graph you will see that I mean there are wide ranges of dimensions of microfluidic devices. So I mean as I said that there may not be sort of hard and fast distinction between microfluidics and nanofluidics and I mean you can think of microfluidic devices even of the order of angstroms. I mean it is not that engineering has made it possible to make those devices very effectively but we have to understand that the whole advent of the subject microfluidics had come into the picture because of the advancement in micro and nano manufacturing micro and nano fabrication processes because many of the underlying scientific issues have been studied and have been reasonably well understood for a long time but engineers could not translate those understandings in the forms of devices until and unless there has been a significant advancement in fabrication micro fabrication and nano fabrication. So keeping that in spirit fabrication over small scales will also be a part of this course. So we will sort of I mean try to see how fabrication influences fluidics and how fluidics influences fabrication. These considerations we will come across. Now so we can start with dimensions of the orders of angstroms to nanometers and micrometers and then we can have I mean sort of large length scales where the micro scale physics may not be that important but we have a sort of an intermediate length scale where some effects of micro scale are apparent although not very significant. Like for example in engineering typically we talk about micro channels, nano channels there is a terminology called as mini channel. Mini channel is sort of like it is not micrometer dimension but it is not also macroscopic channel so it has its characteristic feature somewhat in between the microscopic and the macroscopic channel. So these are all terminologies I am just trying to make you familiar with the terminologies but keep in mind that these are not scientific terminologies. These are terminologies which have been coined by people to describe certain technologies. So like if you are thinking of like I mean how these dimensions relate to real applications like when you talk of angstroms to nanometers you think of molecular dimensions of the orders of angstroms and then nanometers to micrometers you have smoke particles, viruses and I mean over this regime you have nano devices and the common buzzword nanotechnology is used for technological applications over these length scales of nanometers to microns. So little bit of larger length scales I mean you think of like other substances which closely relate to microfluidic devices like for example bacteria and you can think of substances or devices which are closely associated over this length scales like micro needles, micro reactors, micro filters, micro analysis systems. So these are many terminologies which are used for microfluidic devices. Now microfluidic devices are commonly associated with certain names. For example many microfluidic systems are integrated in the form of a chip. So it is like a credit card type of device on which you can have all operations of a laboratory like mixing, metering, bulving, pumping all these fluidic operations which you normally do in a process industry, processing industry it may be chemical processing, biological processing all these are miniaturized in the form of a small chip and these types of devices are called as lab on a chip or laboratory on a chip. So the lab on a chip and many of this lab on a chip devices are used for certain chemical analysis or biotechnical, biotechnological or biomedical analysis and then these have alternative names as micro total analysis systems and I mean these names are so popular that like for example there is a journal called as lab on a chip or you have like a conference named micro task. So there are I mean these names have become quite popular to the community. So and just to give you an idea of the volume flow rates that these devices can handle. So like typically they will be in the range of femtoliter, picoliter to nanoliter to microliter and not very commonly beyond microliter because beyond microliter you enter into millimeter dimensions of length scales. So typically whenever we are talking about microfluidic devices we are essentially talking of devices which can handle small volume flow rates or which are designed to handle small volume flow rates. Now when we say microfluidics of course all of you have a fair idea that these days micro and nanotechnology these are very fascinating areas of research. I mean these are very popular areas of research not just in any specific country but globally. The question is that why we should go for microfluidic devices? I mean what are the advantages that these devices are going to give us? Is it totally because of fashion or there are scientific or technological interests in the background? So here are some reasons why we go for miniaturization. So this is not true just for microfluidics but for any devices where we are intended to miniaturize the product. So the first point is one can minimize materials and sample consumption. So why you can minimize the material consumption is because the device itself is small. Now sample consumption I will give you an example. Let us say that you want to perform a blood test. So medical diagnostics is one of the applications which we will discuss briefly now and much more elaborately as we proceed in the course. Now if you want to test a blood sample if you have one drop of blood then the amount of chemical reagents that are necessary to test the sample will also be of small amount. On the other hand if you have a large amount of blood as a sample then you require large volume of chemicals. So we can see that in a miniaturized system you may require a small volume of the reagents to achieve the necessary task. Not only that because of miniaturization one can run the device with low power. So one can reduce the power budget. Many of these devices operate first or operate because of favorable scaling over micro and nano scales. So we will discuss about this that different forces scale favorably as you reduce your dimensions. For example if you reduce your dimensions you will see that surface forces become more important. So surface forces can help the transmission of fluid which are otherwise active but not so important over large scale systems. So one can use that favorable scaling. Increase selectivity and sensitivity with non-linear effects, exploitation of favorable scaling laws which I have already explained and exploitation of new effects. So some effects which are not when I say new what I mean is that which are not very intuitive which are not very intuitive over large scales some of those effects may become important. So keeping that in purview we say that miniaturization is not always a fashion many times it is essential not only that miniaturization achieves certain thing which is very practical it makes the device small it makes the device portable. See you think of the old day computers gigantic and you think of the modern day computing gadgets I mean which have become slimmer and thinner. So you can carry them and you can work while you are travelling. So I mean it is not always just the scientific need but the demand from our fast changing lifestyle that has also given rise to the advent of miniaturization based technology. Question is what are its applications or why is it important? We will go for applications but first why is it important? Microfluidics is required when the application demands handling of very small volumes. As we saw in the previous slide that the volume flow rates that are handled in a microfluidic device these volume flow rates are small because the volume flow rates are small you cannot use these devices for applications where large volumes are required. So you essentially use microfluidics for those applications which require the use of small volumes like inkjet printing. In fact inkjet printing or inkjet printers are sort of the first generation microfluidic products used in the industry. It was in early 1980s that inkjet printers were introduced in the market and in those days the subject was not known as microfluidics I mean it evolved as a subject by itself but I mean that was one of the technological revolutions so far as microfluidics is concerned. You can use small volumes for precise drug delivery. For example if you want to administer very small volumes volume flow rate of drug very precisely to certain disease cells then you can use microfluidics. Most are performance advantages in many cases we want to use microfluidic devices because they are less expensive and they have some advantages of performance by exploiting the science. So microfluidics is sort of a is located at a nice interface between science and technology. So on one hand the objective of studying microfluidics from an engineering point of view is to make new devices for certain applications but these new devices have to be designed based on some fundamental scientific principles which come from the basic principles of physics chemistry and so on. So it is at a nice interface improved reproducibility accuracy and reliability is what we expect that we have in microfluidic devices although there are questions I mean or issues to be addressed if you want to ensure this. Now there are certain terminologies called as self assembly and self repair and which are closely linked with many of the microfluidic systems although those are more associated with the nanotechnology than with the little bit larger scale systems. And many of the microfluidic devices like for example if you think of a microfluidic device for blood extraction so many of the microfluidic devices they are not just functioning nicely because of the small scale effects but they may also have minimal invasive pain. So these are some of the features that we look for in microfluidic devices. Now see I am teaching this microfluidics course to you but I must confess that I am not a big expert in microfluidics because microfluidics is interdisciplinary. So it requires the agglomeration of so many disciplines that is it is impossible for one individual to be an expert in the entire gamut of microfluidics. So for example let me talk about what are the sort of specializations that are needed to address a microfluidics problem and once you understand this you will appreciate that any study of microfluidics is basically a team effort and how does it go on. So microfabrication like to study microfluidics you require to fabricate micro channels or if you go down to even smaller scales fabricate nano channels. So these are jobs of fabrication or manufacturing specialists chemistry over small scales surface chemistry can dictate the flow in a very interesting way we will later on address those issues and see that how does surface chemistry alter fluid dynamics. So but for the time being just take as it is that chemistry of the surface can dictate the flow in a very interesting way so one requires chemistry biology is not that one has to be a core biologist to work with the interface between biology and microfluidics but most of the or many of the challenging applications in microfluidics are actually from the area of biology. So that is why many times like I have seen this experience I have gathered this experience that I mean when somebody some person some professional working in microfluidics is asked that well what is your like specific area of application in microfluidics. He says I work in two areas one is bio applications another is non bio applications that means it shows that bio applications is sort of a big thrust area of activity by itself. So it is so important that a big application area of microfluidics has emerged which we call as bio microfluidics and that also we will cover as a part of this particular course. So and again the importance of the subject is such that there is a journal called bio microfluidics. So like bio microfluidics is a very activity of research mechanics like I mean there are hardly engineering systems which we can think of without thinking of basic mechanics and microfluidics is of no exception. So mechanics is important and in particular we will talk about mechanics over micro and nanoscales. So sometimes the classical laws of mechanics a little bit sort of they have to be explained in the light of small scales not that they become totally invalid but they have to be explained in the context of small scales and that is where mechanics becomes so attractive in small scales. Control systems so when we say control systems what we essentially mean is that like just like any engineering system if you have a micro if you have a microfluidic system which executes certain tasks I mean many of the microfluidic systems are electromechanical systems and the closely related area which I mean which can be thought of as a more generic area is micro electromechanical systems or MEMS. So sometimes we associate microfluidics very closely with MEMS and in fact for many of the MEMS applications microfluidics appears to be a building block. So in many of these systems you have to design a very nice control system for the system to operate efficiently and control systems become critical. Microscale physics and thermal fluidic transport that is where we will mainly focus on in this particular course. So by micro scale physics what we mean is that like the classical mechanics of fluids that we study commonly I mean many times I mean it is not that all those equations that you have learnt in your basic fluid mechanics will be invalid but those equations sometimes do not take into consideration certain features which are not important at large scales. But as you scale down your system those features are important and those features have to be taken care of. Numerical modeling is a very important area or a very important aspect of microfluidics now when we say numerical modeling we have to keep in mind that it is still a numerical modeling of fluid flow problems. So broadly in the purview of CFD but not always traditional CFD because the traditional CFD you can use when the continuum considerations are valid. So that traditional CFD considerations are used for many microfluidic applications with certain modifications maybe in the boundary conditions and sometimes in the description of the effective properties of the fluid and so on. On the other hand when continuum considerations are not valid then one has to go for molecular simulations. So molecular simulations I mean either explicit execution of the dynamics over molecular scales that means directly capturing the dynamics of individual molecules which is called as molecular dynamics or some statistically averaged considerations over simulated molecules and like these are called as Monte Carlo simulations for example. So on one side you have molecular level simulations on another side you have continuum simulations but there are some simulation paradigms which sort of act as a bridge between these two like which are neither fully of continuum nature or they are apparently of continuum nature but they incorporate certain molecular considerations not by explicitly capturing the molecules but implicitly and on the other hand you have the explicit capturing of molecules. The in between paradigm is called as mesoscopic simulation it is neither the continuum scale nor the molecular scale something in between which is called as mesoscopic simulation and one of the very well known mesoscopic simulation techniques is the lattice Boltzmann method. So there are issues of numerical modeling and in microfluidics there are research groups working solely dedicated towards numerical modeling material science. Now I mean can you think of an engineering system without due consideration of materials it is impossible because like in a microfluidic device the surface effects have a strong role to play and the surface effects are in many cases dictated by the material property of the surface. So you can engineer the surface properties by designing the materials. So and that you can choose a particular material for some functionality you can create the gradient of the functionality for example you can make a surface with a weightability gradient instead of a constant weightability you can make a weightability gradient surface and that weightability gradient surface can use very low energy to achieve certain fluidic operations. So it is possible to like achieve magical fits by playing with the surface and when we try to achieve that the material plays a very important and deciding role. System integration and packaging so system integration and packaging when we say what we essentially mean is that like essentially if you want to make a usable microfluidic product it like if you want to translate it from the laboratory scale to a usable scale may be a commercial scale. So you have to package the product in a proper way and this packaging has also scientific issues by this packaging I do not mean a business oriented outlook towards packaging that is a part of that but one needs to take care of many scientific issues as well for the packaging and system integration. Validation and experimentation so just like the numerical modeling is important it is so but by simulations whatever design parameters we get now whether those design parameters are good for operating a particular device how do you know so for that you have to validate and do experiments. So validation and experiment reliability engineering so I have not listed many more disciplines but just to make you feel understand make you feel that microfluidics is not just a subject of say maybe mechanical engineering, chemical engineering, biology, chemistry like that or physics so it is a subject where all aspects of science and engineering they merge together to work on certain applications so it is very it is it is not possible for an individual to be experts in all these. So now what should be the outlook see I can share my personal outlook with you that how I perceive microfluidics research see it is very important that you may not know all aspects of microfluidics in depth but you should try to develop a working knowledge to interface with experts of those but you should yourself be a domain expert in at least one of the areas that means at least in one of these facets you should be the last word. So it should not be an approach that by being a microfluidics engineer we intend to be jack of all trades but master of none that should not be the spirit so we should be at least master of one particular aspect of microfluidics and for other aspects we should have a working knowledge to interface with the experts that is our teamwork in microfluidics develops. Now what are the applications of microfluidics so we have already discussed that what are the aspects that need to be taken care of for microfluidics applications so using if all those features are there in a device then there are very special applications that we talk about mixing and reactive system analysis so why mixing is important in micro scale so let me just give you a perspective so you know that when you think of classical fluid mechanics when you think of mixing the first concept that comes to your mind is turbulent flows because turbulent flows because of enhanced diffusive transport have good mixing. Now in microfluidics typically because of the small length scale the Reynolds number is small and at low Reynolds number turbulence effects cannot be realized so you have to design that device by clever means to achieve mixing without necessarily having turbulence so that is a big challenge by itself and but why is mixing important you may always ask that why should we have enhanced mixing now to have rapid reaction if you have say two reactants these reactants must first mix before they react and so if you want to achieve rapid reaction you need to achieve rapid mixing as well so to enhance the rapidity of a process of a chemical process maybe it is important that you have also rapid mixing so mixing is a big problem in microfluidics fundamental understanding of biophysical processes fundamental understanding of biophysical processes like for example I will talk about this in details but just to create a perspective that in human body there are cells and cells are there in blood vessels of various dimensions so blood vessels like there is a hierarchy of blood vessels and this hierarchical length scale variation is very interesting you have large arteries which are which are macroscopic scale features large veins small arteries small veins then arterioles venules and micro capillaries micro capillaries in human body are micro channels so now it is it is a I mean there are many outstanding questions I will talk about one outstanding question that when a cancer cell is traveling through the this circulatory system right it there is a stage of cancer where a cancer cell from its origin moves to a distant location within the human body by the blood stream and creates a new cancerous growth at a new location this process is known as metastasis and it is a very critical stage in cancer progression and during that stage the cancer cell has to also pass through micro capillaries and because of the extremely stressful condition it is very difficult for a normal cell to survive under those conditions but a cancer cell can survive we will try to address this question later on and see that how microfluidics can solve this problem but you can understand that bio physics of cancer progression or hemodynamics the dynamics of blood in small capillaries in a human body so all these things are related to fundamental understanding of bio physical processes and these are critical now why we say these are critical because these are not straightforward extensions of the traditional understanding of fluid mechanics let me talk about a very simple apparently or elusively simple problem like flow of blood through arteries and veins or even flow of blood through micro capillaries now when you think of its analogy with a large scale engineering system it is like its closest analogy is flow of water through pipes which we study normally in fluid mechanics in the undergraduate fluid mechanics course now if I ask you that what is the difference between that and flow of blood through a blood vessel like you will have certain ready answers what are those answers like for example like you may say that blood is a much more complex fluid than water I mean blood may have non-Newtonian characteristics over certain regime and it may hold newtonian characteristics over some other regime and the effective or apparent viscosity of blood varies in a very complicated way with the blood chemistry like blood composition and so on so blood is not a very simple fluid having appreciated that it is not that the blood the rheological aspects of blood remain a mystery it is not like that rheological aspects of blood have been reasonably well studied and extensively understood by people so one can borrow that understanding for studying the flow of blood through blood vessels there are in fact other more subtle complications the second point about this flow of blood through blood vessels is that the blood vessels are flexible unlike the standard rigid pipes these are flexible but mathematicians may argue ok it is fine let it be flexible let us assume the radius of the blood vessel r equal to r0 plus r1 cos omega t plus r2 sin omega t whatever some nice Fourier series may be but you know in reality the blood vessel the local diameter of the blood vessel varies in a very complicated way with the local blood pressure and it is not universal that is the difference between the mechanical world and the biological world in the mechanical world when we say that this is the material it will behave in this way the same material will behave in that way provided the other conditions are the same but human beings the system is very complex like you will have a certain like variation of your blood pressure based on certain emotional conditions which are not sort of mimicked in the same way by some of your other friend so you do not have a universal rule of how the diameter of the blood vessel varies with local blood pressure it is so much individualistic that it is very difficult to bring in bring it in the context of a fundamental mathematical model so you see that an apparently simple problem in the living systems gives rise to such a complex understanding which is yet an unsolved problem so fundamental understanding of biophysical processes manipulation and analysis of biological macromolecules like DNA RNA I mean these are important and I will show you that later on we will discuss that how these are related to biotechnological applications that is handling of DNA RNA handling of cells handling of proteins and all these biomedical diagnostics biomedical diagnostics is a big area and biomedical diagnostics I mean I will discuss about this in more details that what are the demands of biomedical diagnostics which are more apt more aptly addressed by microfluidics than the traditional technique that why microfluidics is so important for biomedical diagnostics drug delivery blood extraction I mean these are all related to medical applications so biomedical diagnostics drug delivery blood extraction all together there is a whole bunch of applications of microfluidics in medical sciences and because it is mainly an engineering interface with medical sciences these days it is given a terminology called as healthcare engineering so microfluidics is a sort of an essential element of healthcare engineering now non biological applications there are several applications like the inget printing I have already discussed with you that why inget printing is important and I mean important as a microfluidic device because it is traditionally like one of the very early microfluidic devices that was introduced electronic schooling so electronic schooling is again another area see where if you want to have a miniaturized chip which because of heating it is trying to fail in terms of it thermal design then it has to be cooled now that cooling has to be done by a system which system which is matching in terms of miniaturization with the small device itself. So if you have a small device, you cannot have the area large fan to cool a small device. I mean you may have of course but that will kill the purpose of miniaturization. So you require microfluidic systems to cool electronic devices and systems and electronic cooling or like a more scientific terminology that is associated with this field is called as thermal management of electronic devices and devices and systems. Now we have learnt about the microfluidics, I mean its fundamental inception and I mean what are the disciplines involved in studying microfluidics, some basic motivation in studying microfluidics and of course some applications. Now we will sort of get into it further by noting the fundamental flow physics, how are microfluidics different from or microfluidic devices different from macro flows. This is important because all of you have a particular perception about fluid mechanics because of your exposure to the classical subject of fluid mechanics. Now if all those issues can directly be used in microfluidics, there would perhaps not be a separate need of introducing another subject. So one has to prepare this little bit of scientific motivation that in terms of flow physics how things are different. As the length scale becomes smaller surface effects tend to dominate, why? The reason is that as you reduce the length scale the surface area by volume ratio increases. Let me give you an example, I mean not typically related to microfluidic device but let us say that you have a sphere of radius r. So if you have a sphere of radius r then what is its volume 4 by 3 pi r cube and what is its surface area 4 pi r square. So area by volume is proportional to r square by r cube that is 1 by r. So as you reduce r as you reduce r the area by volume ratio increases. So this is a typical example of course there are hardly microfluidic devices which are spherical so I do not want to mean that you borrow the understanding exactly on the phase value but just to give you the concept if you take r as a length scale if you make the length scale smaller and smaller then area by volume ratio of the geometrical feature increases. So when the area by volume ratio increases what essentially happens is that whatever forces are important over surface that forces become more prominent. So that means inertia forces may turn out to be negligible in comparison to electrostatic, electrodynamic, viscous or capillary effects. That does not mean that inertia forces are important for all microfluidic problems. Please do not keep this prejudice in mind. There are many microfluidic devices which operate with important inertial effects and that particular aspect of microfluidics is known as inertial microfluidics. So because it covers certain special problems other than those special problems the more common problems are associated with negligible inertial effects as compared to other effects. Next point. Layering of fluid atoms parallel to the atomic layers adhering the solid boundary may give rise to strong density, local density fluctuations. So when we say density we do not mean density as a continuum property. It is the local number density of molecules. The local number density of molecules near the wall there is a structure that the molecules assume. Now these structures occur over length scales which are small but if the device length scale itself is comparable with that length scale then the near wall variations in density or the near wall density distribution may have a strong role to play. So in some case there may be less density of liquid in the near wall region and then that kind of situation is typically encountered for hydrophobic surfaces that is surfaces which have phobia for water for example that is what I mean is a literal meaning of hydrophobic. So on the other hand you can have surfaces where there is a strong local distribution of liquid. So these density distribution differences may alter the local fluid dynamics. So they might essentially invoke certain like sort of non-intuitive boundary conditions like slip boundary conditions instead of no slip. Now the slip may also occur. We will discuss about this in details but just to summarize I mean just to give you some initial thoughts. It may occur when liquid molecules are sheared very vigorously. So that means so liquid molecules let us say they are attached to a solid boundary. Now with a very high shear rate it is possible to dislodge them from the attraction of the solid boundary. So how is that shear rate possible? That shear rate is so high that normally that will not occur but in devices approaching molecular length scales it may be possible because the shear rate is what? So think of a quate flow. You have flow between 2 parallel plates. The shear rate like out of the 2 parallel plates one plate is moving at a velocity relative to the other. If that relative velocity is u like let me draw a schematic to explain this. So you have 2 parallel plates. Let us say this plate is moving with a velocity u relative to the bottom plate and the gap is h. So the shear rate is related to u by h. So at a very high shear rate the liquid molecules may be dislodged. So high shear rate will require a very small value of h. So for normally engineer channels that may not that kind of high shear rate may not take place but in channels which approach molecular dimensions that may take place and then you can have a literal dislodging of molecules liquid molecules from the solid boundary. This kind of slip behavior is more common for gases because of relatively weak molecular compactness. For liquids it is very difficult to dislodge the liquid from its surroundings because of strong level of attraction but because liquid is a relatively dense system. For gases the intermolecular attraction is relatively weak. So it is possible it is more easily possible to dislodge the gases and slip in gas flows is not a very uncommon thing over my nanoscales. We will discuss more about this just I am trying to give you some preview of I mean what are the interesting scientific features. Different diffusion characteristics near the wall in comparison to that of the bulk may give rise to anomalous diffusion. So normally when we solve a problem we use problem of mass transfer we use a diffusion coefficient. Now that diffusion coefficient many times we use a common value for both the bulk and the near wall regime. But the near wall behavior may be different from that of the bulk in a small scale system where surface effects are very important. So one has to think of a different aspect of diffusion as we go from the surface to the bulk. Surface characteristics of the device strongly influence the flow behavior. This is quite intuitive and it follows from the argument that in a microfluidic device the area by volume ratio is large. Therefore surface effects are important. So surface characteristics like surface charge, surface weightability these strongly influence the flow behavior. So that is where like for example if surface charge is important then you have to consider the electrical aspects. So the physics of the charge dynamics or the charge distribution close to the wall will affect the fluid flow. So these types of problems are called as multi physics problems. So where the physics of fluid flow is not just plain and simple fluid dynamics but it is related to electrostatics, electrodynamics and so on. So in many of the microfluidics problems you essentially have to address multi-scale, multi-physics and also physics over multiple scales. That is a length scale which is very close to the wall and the system length scale which dictates the bulk behavior. So multiple length scales or multiple physical scales and multiple physical features. So these are called as multi-scale multi-physics problems and many of the microfluidics problems are like that. Many of the fluid may be very significant for flow manipulation and control. So the constitutive behavior of the fluid that is the stress versus strain rate relationship may be very significant and the manner in which the fluid behaves close to the wall may be different from that in the bulk as I already mentioned and the rheological aspects may interface with that and by that you can manipulate the flow in a very interesting way. Surface roughness being comparable to the system length scale is likely to play a very critical role. This is something which is very important even for laminar flows. The classical fluid mechanics says that for fully developed laminar flow the product of friction factor and Reynolds number is a constant which is independent of the surface roughness just is dependent on the geometry of the cross section of the channel. So this is the classical fluid mechanics understanding. Now these understandings assume that the surface roughness length scales are not comparable to the system length scales but in microfluidics in many of the micro channels and nano fluidic channels you may have the surface roughness elements comparable to the characteristic system length scales and then these may influence the flow non-trivial. We will discuss about that and all these aspects taken into account mean that micro floats are often characterized by multi physics and multi scale features which I have already discussed. So we have discussed some aspects of microfluidics and I mean how these are different from macro scale flows and what could be the possible applications, what are the challenges and so on and the way in which we will proceed further is like this that like we have to think of that what microfluidics can do by stretching our imaginations before getting into the mathematical description of the subject. So I mean we will of course I mean after one or two more lectures move on to the mathematical description of microfluidics which we will build up from classical fluid mechanics. I am not assuming that all of you have sufficient background of classical fluid mechanics because I understand that many of you come from diverse backgrounds and it is an interdisciplinary course. So I am not presuming that everybody has undergone a standard course of undergraduate fluid mechanics. So we will start with some basic considerations that lead towards the foundation of fluid mechanics and then more specialized towards microfluidics. But before that we will talk about by stretching our imaginations that what marvels we can do with microfluidics. So in the next lecture we will be talking about some interesting research findings related to microfluidics mostly from my own research group but also from the research activities of others as reported in the research literature world wide. This is just to give you a feel that if you learn the basics of microfluidics what are the cutting edge problems that you might be in a position to solve. Anyway let us stop here today. Thank you very much.