 start with a new topic lab on a CD. So the motivation behind studying this chapter is to talk about a microfluidic platform which is low cost and which can be used for many potential applications using medical diagnostics. So how does it look? Let me just try to show you that essentially how the product looks like. So this is a typical example where you have a disc. Now this disc has several channels. I mean the camera will not be able to capture all the channels but this disc has several channels. Cross-radial channels and there are various holes which are like reservoirs. So through these holes you can inject samples of blood or other chemicals and there can be reactions taking place on this. So just like a big pathological lab you can have all the activities like say for example mixing, reaction, valving all these types of activities you can do on this disc. Now how will you actuate the fluid flow? You will actuate the fluid flow by rotating this disc and that rotation will create some forces due to rotation. By virtue of these forces the fluid will start moving and there will be some aiding forces, there will be some opposing forces and as an interplay of all these forces the final motion of the fluid will be decided. So we will try to understand the fundamental science that goes behind this particular technology and then I will try to demonstrate the fabrication process maybe through a small video that how these devices are fabricated and then we will talk about some research issues. I mean it is not that we will be resolving all the research issues but I will just discuss that what are the important research issues that have been going on. And many of these discussions for many of these related discussions I acknowledge the support of Professor Mark Madhu of the University of California at Irvine who has been our collaborator in this particular program and with his strong and active support we have been able to establish the CD fabrication facility in our own lab. So with this little bit of note we will start with different micro flows a comparative study. So pressure driven flow we will compare 4 types of actuation not that these are only types of actuation pressure driven acoustic, electrokinetic and centrifugal. Pressure driven acoustic, electrokinetic and centrifugal out of this you will see that electrokinetic is a little bit different from the others because in electrokinetic transport we will see later on the transport is strongly dependent on the chemistry of the sample that is pH concentration all these. Now on the other hand the other mechanisms are not so much dependent on the chemistry or electrochemistry scaling of these forces like pressure driven flow the head loss scales with inversely as 4th power of the characteristic length scale for a given flow rate. For acoustic it is L square instead of L to the power 4 electrokinetic also L square centrifugal quite intuitively it is also L to the power 4 because it essentially generates a pressure gradient by the driving rotational force. So it is another way of perceiving a pressure driven flow but we have to keep in mind that when we are talking about the rotational forces the rotationally actuated microfluidic platform the channel may be of small size but the rotational force may be strong enough so that inertial effects may be important. So we may not always trivially neglect inertial effects just as we commonly do in low Reynolds number hydrodynamics flow rate in pressure driven flow these are very typical. So one can get from nano litre per second to even litre per second but you know I mean there I mean if you want to get flow rates as high as litre per second you have to have very I mean powerful driving actuation. Acoustics typically of the order of 10 microlitre per second and these are just orders of magnitude rough idea. See as practical engineers say I always wanted to when I try to design this course I always try to make a balance between what is engineering practice and what is fundamental science. So if you make a balance between these two then it becomes better and becomes easier for you to implement these ideas into practice. So electro kinetic flows typically 0.001 to 1 microlitre per second centrifugal actuation see the range of flow rate from less than 1 nano litre per second to greater than 100 microlitre per second this wide range of flows can be covered and you can understand very easily why. Because I mean you can vary the rotational speed in a wide range and if you vary the rotational speed in a wide range you can vary the flow rate. The materials used for pressure driven flow common materials are PDEMS poly dimethyl siloxin that is PDEMS plastic for acoustic the material used acoustic actuation the material used is commonly piezoelectric material electro kinetic plastic glass PDEMS centrifugal also commonly plastics and PDEMS associated problems pressure driven flow dispersion like I mean I have discussed this earlier little bit that if you have a parabolic velocity profile then it might be possible that if you want to achieve a reaction at the wall of a micro channel then because of the big difference between the centre line velocity and the wall velocity what will happen is that the fluid will try to carry the sample along the centre line and the wall may be depleted or the wall may be deprived just in a very simple term the wall may be deprived of the sample which will react with the reactants present on the wall. Acoustic streaming is little bit an expensive process electro kinetic flows we will see that like joule heating is a very significant problem in electro kinetic flows we will see later on. In centrifugal also see we are studying lab on a CD but that does not mean that like I mean there is always a tendency that whenever we are studying something we always tend to talk about the positive points but there are shortcomings associated for example if you want to have a very high throughput what we will do you will try to rotate that CD at a very high speed and if you are rotating the CD at a very high speed then there can be vibrations in the setup and these are purely mechanical vibrations and these vibrations can disturb the transport processes significantly. So as I told you that you have a motor on which you mount the CD on which you have microchannels engraved you can control the fluid flow by rotational speed and design of microchannels see you by looking into the CD that I have shown you it is it will not appear to be of made of a material which resembles with the CD that you use for external data storage in computer it is it is just the shape but if you can somehow combine the optics that you commonly use for the CD platform with the fluidics that you have in a rotational platform then you can use this for detections of several things in a very smart optical environment. So it is possible that you can take the CD based micro fluidics I mean to a new level where you can combine optics with the rotational micro fluidics. So rotationally actuated micro fluidics so I will start with a very simple example then I will derive the governing equation for the rotational platform but I will start with a very simple example. Let us say that just look at this picture so there is a rotational disc there is a rotating disc and there is a fluid and you can see that this fluid meniscus is such that the surface tension force in which direction it acts? Can you tell is it radially inwards or outwards? It is radially inwards just draw the tangent to the interface you see the tangent to the interface is inwards. So the surface tension force so this is like a typical hydrophobic type of meniscus where the surface tension force is inwards and when the disc starts spinning there is a centrifugal force which is acting on it and that force is radially outwards. So there are 2 forces which are I mean there might be other forces we will come into the picture but these are 2 major forces one is a surface tension force. Surface tension force might also be radially outwards and if it is radially outwards then the there is no control that means then the fluid will spontaneously flow on the disc radially outwards there is no need to have actually such a platform because then surface tension will spontaneously drive the flow but you can use it as a control mechanism when the surface tension is opposing the radially outward force. The radially outward force will increase beyond the critical angular speed and it will increase sharply because it will scale with omega square or square of the rotational speed. So beyond the critical rotational speed what will happen the centrifugal force will overcome the surface tension force and at that speed the fluid will start moving. Why are we not bringing the viscous force in that analysis? The reason is simple that the fluid has not yet started moving we are thinking about the forces acting on it and when the fluid has not yet started moving viscous force has no role to play. Viscous force will start playing his role when the fluid has started moving. So we can understand from here that you can use this as a smart bulb the rotational speed can be used as a parameter to control the onset of flow. So you only if you rotate the CD beyond the critical speed then the flow will start and that critical frequency if the speed is omega angular speed then omega is equal to 2 pi f that f is called as frequency and the critical frequency at which the disc starts spinning that is called as burst frequency. So we will try to see we will try to establish that how we can derive an expression for the burst frequency. So the final result is given in the slide but we will try to derive that by a very simple type of analysis. We will try to make more involved analysis as we progress in this particular lecture. So let us say that you have a micro channel whatever channel I mean it is it may not be micro channel you have a channel which is rotating. So there is a big platform and this is say one of the radial channels. So because of the rotation so assume that there is a small fluid element of length dr and width of the or area of the cross section of the channel is A. If it is a of rectangular shape then it is the width into height but let us forget about the shape. Let us say that the cross sectional area of the channel is cross sectional this is A. Now when the disc is spinning there are several forces but we will first discuss about the interplay of the centrifugal force and the surface tension force and then I will discuss that what are the other forces and I will show you technologies where we have utilized the other forces to achieve some task. So in this kind of a situation the let the pressure here be p and the pressure here be p plus p is a function of r only say. So p plus dp basically p plus dp dr into dr okay. So the force is p into a here p plus dp into a. So how do you estimate that what should be this pressure gradient when this disc is spinning? See it is not necessary that you bring the surface tension force in the picture because you have taken a small element where it is expected that on the both sides it will be neutralized. So when you are talking about the pressure distribution what force you should bring in centrifugal force. So it depends on how you are looking into the problem. See let us consider it from the fundamental mechanics point of view okay. So when you are referring to a fundamental mechanics point of view you can consider 2 types of reference frames. One reference frame which is inertial, one reference frame which is non-inertial. So if you are there watching the entire proceedings from an inertial reference frame you will see no force, no question of centrifugal force. What you will simply see? You will simply see that there is an acceleration which is radially inverse which is called as centripetal acceleration. However if you are yourself sitting on the disc which because of its rotation is a non-inertial reference frame you will experience a force which is a pseudo force and that pseudo force is called as centrifugal force. So I mean centrifugal force is one of the examples of such a pseudo force. So if we are so what is the difference between the between the these choices when you are considering the inertia force you can write the equations of static equilibrium by referring to the inertial force as a force. However if you are considering the inertial reference frame then the resultant force will be mass into acceleration. So in other words if you are writing resultant force equal to mass into acceleration that must be from a inertial reference frame and there no question of inertial force. However if you are writing resultant force equal to 0 it is as good as writing resultant force plus minus m into acceleration equal to 0 that minus m into acceleration is the inertial force and here the acceleration is because of the centripetal depends on how do you interpret it if it is it is a centripetal acceleration if you are talking in terms of acceleration. If you are talking in terms of inertial pseudo force by being located on the rotational reference frame then that is manifested in the form of centrifugal force. So let us choose that second path. Yes, yes pressure is in in what is right pressure is in what is right of course. So let us write the inertial force which is so they say this is the radially outward direction. So just to indicate that is inertial force I am drawing an arrow with i across it to mean that is not actually an applied force. It is a pseudo force that is experienced because the observer is is located on a non-inertial reference frame okay. So this is what m omega square r right. So m is rho a dr into omega square r right. So all these forces must be balanced that means p into a minus p plus dp into a minus rho a omega square r dr is equal to 0. So you have this is plus right plus right this plus rho a omega square r dr equal to 0. So that means you have dp dr is equal to rho omega square r. So dp is equal to rho omega square r dr. Let us say that you are interested about a length of a capillary of finite dimension delta r not a infinitesimally small dr but some finite dimension delta r. So let us say that this is 1 this is 2. So from 1 to 2 this is 1 to 2. So delta p is equal to p 2 minus p is equal to rho omega square r 2 square minus r 1 square by 2. So rho omega square into r 2 minus r 1 is delta r into r 2 plus r 1 by 2 that is r average. So by rotational force what you are doing? You are actually inducing a pressure gradient. Now if this pressure gradient is sufficient to overcome the pressure gradient due to surface tension then and if the surface tension was opposing the radially outward flow then the fluid will start moving radially outwards. So what is the pressure difference due to surface tension? Sigma cos theta into what is the total force? Sigma cos theta into perimeter right. So in this particular chapter in the slides also I have kept c as the perimeter. But the reason is many times we commonly confuse between the symbols of pressure and perimeter. So this is perimeter but we have used c as the symbol. So this is the force divided by area. So the fluid will start flowing when you have rho omega square delta r into r bar is greater than or equal to sigma cos theta into c by f. Omega is 2 pi f. So omega square is 4 pi square f square. So f is greater than or equal to sigma cos theta c by pi square rho r bar delta r. 4 is also there. 4 then a to the power half. So by this simple formula you can calculate that what is the expected speed at which the fluid will start moving? What is the expected rotational frequency of the disc? This is a very basic design parameter right. You must know that what is the speed at which you should rotate the disc so that the fluid will start moving. Otherwise you cannot do any fluidics with it. If you want to do a fluidics with it, you must first make sure that the fluid moves. And this is the very simple design consideration that can tell you that what is the... So you can see that when the fluid is designed to move radially outward you can see that what is the... So you can see that when the fluid is designed to move radially outwards depending on at what speed you start moving it. And why you want to have micro channels on the CD? You want to have micro channels on the CD because you are trying to utilize an interplay between the pressure differential due to the centrifugal force and the surface tension force. And surface tension is important only over small scales. So that is why you want to have micro channels on a CD. Otherwise you could have ideally had large size channels on the CD. That would have made the fabrication may be easier but that will have the effect of surface tension less and less fail. So what you can do here is that you can make the CD acting like a smart centrifuge. So it is possible that depending on the rotational speed you can start a particular flow on a CD. So let us go to the slide. So that is what we had summarized and the expression for the bars frequency. So you can see here that in the final expression 4 area by perimeter is written as the hydraulic diameter DH. So just an alternative way of expressing the same parameter. Possible applications, biochips I have started with that example that you can use this CD as a platform for medical diagnostics. Nano and micro scale water power systems, diagnostic devices, other optically powered nanomachines in aqueous environments. I mean like actually the CD is such a technology like it is actually I would say from my experience that is like a giant under sleep. So if you make use of the CD as a technological platform I mean there is no limit to which it can be exploited for microfluidics applications. And many of the applications in microfluidics where you can have the CD, I mean the challenge that it gives is that one is a technological challenge and but the other is also scientific pleasure, scientific challenge that the science of fluid flow over such a rotational platform where micro scale forces in addition to inertial force effects may be important. It is a very rare combination that you get. Now question is why do you use CD as a microfluidic platform? First it is biocompatible, biocompatible means you can use it for biological purposes. It is an effective substitute for standard consumables which you use in biological laboratory like slides, micro wells, centrifuge tubes. These are very common consumables that you will find in biotechnological or biomedical applications or even in pathology, pathological diagnostics applications. It is having versatility in handling a wide variety of sample types. So lots of different types of samples can be handled. Non-mechanical valving, ability to get the flow of liquids just by controlling the rotational speed you can use the rotational speed as a valve. So you do not require a mechanical valve to control the flow. Simple rotational motor requirement, the motor that you commonly use for rotating this disc, I mean it can be a simple servo motor. So you can have a very simple motor by which you can rotate it. Economized fabrication method, I will say that this is one of the big, big advantages that I mean after we complete this chapter, we will study the chapter on micro fabrication that how micro channels are fabricated. And we will see that there are many micro fabrication processes which are very sophisticated, but they require expensive environment, expensively maintained environment. On the other hand, this lab on a CD is for making micro channels on a CD, you can use very simple apparatus, low cost apparatus in a very, in a sort of unquote unquote uncontrolled environment. An environment where the level of dust particles is not that strongly controlled. So for that purpose, you can use simple mechanical manufacturing processes. Possibility of performing simultaneous and identical fluidic operations. So this point is like if you have a CD, on a CD you have many channels. So identical but simultaneous operations, on each channel you can do one thing. For example, if you think of a CD with 100 channels, then if you take one blood sample, one small drop of blood, in each of these channels you can make one test. So technically by using one drop of blood, simultaneously with a single rotation of the disc, you can make 100 pathological tests. So that is a very unique advantage of this. So for making the fluid flow through different channels, you do not have to use different actuation. A single actuation will be able to transmit flow in all channels. Features of centrifugal actuation. See the actuation is centrifugal, but once the fluid flow gets actuated, other forces in a rotational platform come into the picture. And I will show what are the other forces which come into the picture. Flow rates ranging from less than 10 nanoliter per second to greater than 100 microliter per second. Pumping is relatively insensitive to physicochemical properties, which I have mentioned that it does not depend on pH ionic strength or chemical composition. In electro-kinetic flows, there are many advantages. But this is one point, I mean this may be actually used as an advantage, but it sometimes very tricky because it is sensitively dependent on the pH of the solution in electro-kinetic flows. But in centrifugal fluidics, you do not require that. Different solvents, surfactants, biological fluids like blood, milk, urine have been pump successfully. Already these have been technologically established. Miniaturization and multiplexing easily implementable. So that means you can make microchannels on the CD quite easily and you can do multiple reactions, you can study multiple reactions on the same CD platform, which is called multiplexing. A whole range of fluidic functions including valving, decanting, calibration, mixing, metering, samples, splitting, separation I mean what and what not can be implemented on the same platform. So it is just like another form of lab on a chip. Instead of the chip, you have the CD and analytical measurements may be electrochemical, fluorescent or absorption based and informatics embedded on the same disk could provide test specific information. So as I told you that just like optics, you can embed informatics on the CD because CD is a natural like data storage type of platform. So if you can use the CD material that you use commonly for external data storage, then you can combine the informatics of the CD with the fluid flow on a rotational platform. So there are tremendous possibilities in these regards. Unfortunately, the picture here is not coming properly, but I will better use this figure, I mean which is showing that how to establish the equations of motion, equations of motion on a CD. So how to write for example Navier-Stokes equation with respect to a platform that is rotating. We have derived Navier-Stokes equation with respect to a platform which is inertial platform. So far that is what we have done. If you recall that the Navier-Stokes equation that we derived in our one of the Aldi lectures or a few of the Aldi lectures, there we did not consider any acceleration of the reference frame. But how do we modify the equation to take care of the acceleration of the reference frame? That is the first thing that we will be doing. So to do that you refer to this sketch, I will reproduce this again in the board. So you have a reference frame capital X, Y, Z, this is inertial. And you have a reference frame small x, y, z which is non-inertial which is accelerating. So there is a vector, this red color vector r is the position vector in small x, y, z. And with respect to capital X, y, z it is capital R and the position vector which demarcates the or which specifies the origin of the small x, y, z coordinate system with respect to the origin of the capital X, y, z coordinate system is r naught. So now even if r is fixed, even if small r is fixed in small x, y, z but small x, y, z is rotating then there will be an acceleration. Why there will be an acceleration? Because you will see that this vector r is continuously changing its direction even if it is fixed. So what we will do is we will try with a generic formulation. We will consider a fixed vector in a moving reference frame. We will consider a fixed vector in a moving or rotational reference frame and we will try to find out the derivative of a fixed vector in a moving reference frame. So we will start with that. Derivative of a fixed vector in a moving reference frame, fixed quote unquote. That means fixed if you see from the moving reference frame. So if you see it on the moving reference frame, you see it as fixed. But if you look from a rotating reference frame, when we say moving reference frame it may be rotating, translating. But if you think of rotation then if there is a vector let us start with a sketch that you have a vector a fixed on the small x, y, z which is a rotating reference frame say. But because of the rotation after some time the a will come here. This is a at t, this is a at t plus delta t. So you can see that although the vector is fixed on small x, y, z but if you see from outside you will see that the orientation of the vector has changed as it is rotating. So over a small time delta t the change in the vector is delta a. Let us say this angle subtended is delta theta. We are thinking of purely rotation. Then if there is translation there is a translational component added. But we are thinking of purely a rotation. So when we say moving basically we are talking about a rotating reference frame. So movement can be moving can be an arbitrary motion. But I mean here this example is specific to rotation. So what is dA dt as you see from capital x, y, z. You know I mean when I am writing in the board with a pen it is I mean sometimes my handwriting may be confusing. So I will tell what is small x, y, z and what is capital x, y, z because it is difficult to distinguish between small and capital when we write in the board. So please be alert about this. So dA dt capital x, y, z is equal to limit as delta t tends to 0 a at t plus delta t minus a at t divided by delta t. So limit as delta t tends to 0 delta a by delta t. Delta a is the green colored vector. You can see that a plus delta a is equal to nu a. So what is this delta a? Delta a is the magnitude of a times delta theta because this delta theta is small. So this is as good as a small arc of a circle with radius of magnitude of a. So you can write this as limit as delta t tends to 0 a delta theta this is the magnitude and what is the direction? Direction is see it is it is the direction which is tangent to a. So let us call it epsilon theta unit tangent vector which is which is tangent to a divided by delta t. So this is a limit delta t tends to 0 delta theta by delta t. What is that? Omega that is the rotational speed epsilon theta. You can write the angular velocity omega as omega into epsilon z. So this is the arc coordinate arc direction. This is theta direction and perpendicular to the plane of the board is z direction. So omega epsilon z epsilon z is unit vector along z. What is a? A epsilon r. What is omega cross a? Omega a epsilon z cross epsilon r. What is that? This is epsilon theta right just like k cross i j. So this is omega cross a. Very important result that if you have a fixed vector in a rotating reference frame then it is dA dt with respect to a inertial reference frame is omega cross a where omega is the angular velocity with respect to the inertial reference frame angular velocity of the small x, y, z or non-inertial reference frame with respect to the capital x, y, z or the inertial reference frame. Now if it so happens if it so happens that a is not fixed that is a is moving in small x, y, z. Why such consideration is important? Think of fluid. If you consider a particle in the fluid that particle is continuously moving in the CD rotation CD reference frame. So you do not you are not actually dealing with a fixed vector but you are dealing with a ready with some vector which may be a position vector that is continuously changing in even with respect to the rotational reference frame. So to generalize it you have dA dt capital x, y, z you have to add one term dA dt small x, y, z plus omega cross a. This takes care of the first term takes care of the derivative with respect to the moving reference frame. So this is derivative of a vector any arbitrary vector a with respect to a fixed or inertial reference frame expressed in terms of that with respect to a moving reference frame. This is known as Chezel's theorem. Let us get back to our scenario of finding the acceleration on the disc. So let us draw the schematics you have capital x, capital y, capital z then small x, small y, small z. Let us say this is r0 consider a point on small x, y, z which is r and the resultant of this is capital R. So we can write capital R is equal to r0 plus small r. What is the acceleration with respect to small x, y, z capital x, y, z? First we start with velocity. What is velocity with respect to small x, y, capital x, y, z? dr dt. This is dr0 dt with respect to small x, y, z sorry capital x, y, z plus dr dt capital x, y, z. Now in the experiments with CD you are observing everything with respect to the rotational reference frame. So this term you have to transform in terms of dr dt with respect to small x, y, z. To do that you can use the Chezel's theorem. Replace capital A with small r. So if you replace capital A with small r then this is dr dt with respect to small x, y, z plus omega cross r. Look at this. We have just used this formula. Replace A with small r. Now to get acceleration what we need to do? We need to differentiate it again with respect to time. So A x, y, z this is the acceleration capital x, y, z is equal to so this term differentiated this entire thing with respect to small x, y derivative with respect to small x, y, z plus omega cross this entire thing. So plus, so this is now like capital A. So d dt of this is small x, y, z plus omega cross. So A capital x, y, z is equal to this capital x, y, z plus what is d dt of dr dt small x, y, z this is acceleration with respect to small x, y, z right. The second derivative of the position vector with respect to small x, y, z that is acceleration with respect to small x, y, z plus d dt of omega cross r what is that? omega dot cross r omega dot is the angular acceleration plus omega cross r dot all with respect to small x, y, z plus omega cross dr dt small x, y, z this is again omega cross r dot small x, y, z plus omega cross omega cross r dot small x, y, z plus omega cross omega cross r. So let us clean it up and write at the top of the board. So A capital x, y, z is equal to d 2 r not dt 2 capital x, y, z plus A small x, y, z plus let us first write omega cross omega cross r because it is the well understood centripetal acceleration term. So omega cross omega cross r then let us write what is r dot small x, y, z that is a velocity with respect to small x, y, z. So you have omega cross v small x, y, z another omega cross v small x, y, z. So 2 omega cross v small x, y, z plus omega dot cross r. So this is the centripetal component of acceleration this is called as the Corioli component of acceleration that means you can see that if there is a translational velocity with respect to a rotational reference frame then there is a component of acceleration and this component of acceleration is not just there in such a small scale system it is there even in a large scale geophysical system because of this ocean currents in the northern hemisphere will move in a certain direction and it will move in the southern hemisphere in another direction. So this is the Corioli component of acceleration. So remember its origin is translation relative to a rotational reference frame and then this is called as Euler component of acceleration angular acceleration, Euler component of acceleration because of angular acceleration force sorry because of angular acceleration of the rotating reference frame. So if the rotating reference frame is rotating with a constant angular velocity this term does not come into the picture. We will discuss more about these terms in the next lecture. Thank you very much.