 In the previous couple of lectures we discussed about some applications of microfluidics in the biological and the medical sector. Now microfluidics and nanofluidics their applications are not only restricted to the bio area but also many other areas as we have mentioned in our earlier discussions and one of the important areas of application happens to be energy the energy sector. So today we will discuss on energy conversion using nanofluidics which is a very important and emerging topic of research and it is considered to be the technology of the future by many researchers. So the outline of today's discussion we will discuss about the motivation the physical principles the scaling down from microfluidics to nanofluidics paradigm how it helps the coupled nature of slip towards maximizing the energy conversion efficiency what we can do and some open issues. Now as a general note we can say that human civilization has witnessed of newer energy sources harvested to obtain greater power density as we have progressed in civilization. Now as we have seen that the advancement in technology has demanded that we would require energy conversion capabilities with a greater power density. For example if you appreciate that we had at one time certain electrical or electronic gadgets which have now become miniaturized to such an extent without sacrificing their power rating that the power density is significantly increased as we have gone for handheld devices miniaturized devices and so on. At the same time we have to keep in mind that the energy sector is still dominated by the classical sources of energy. So for example the fossil fuels the nuclear, solar, hydro or wind the fossil fuels are of course having several advantages that is there easily available and one require low infrastructure cost but these are non-renewable and there is some carbon footprint. The nuclear sector has an advantage of high power density and easy grid integration but of course there are controversial issues related to radiation hazards, installation issues and so on. The solar energy which is like one of the very prime sources of energy being considered for modern day applications has great advantages of renewability, decentralized generation and so on and of course sun is a natural source of all energy but I mean sometimes it becomes unpredictable and not only that one of the big concerns is high power watt cost. For wind these are renewable and predictable so I mean in that sense this obvious some of the previous disadvantages but these require large installations and there are geographical limitations you cannot utilize the sources of energy at all geographical locations. So energy conversion process or the energy sector is always in demand of energy conversion devices or energy conversion systems with certain capabilities like it may be ideal if the device is perpetual or quasi-perpetual not perpetual in machine in terms of a thermodynamics notion but it should have a self-sustaining type of mechanical system if it operates mechanically 0 or low emission it is one of the very big, big areas of concern the emission characteristics should be favorable. High power density we have already discussed that why high power density is important in modern days easy installation and transport minimum human interference predictability low cost so this is the kind of a wish list. Now whether the wish list will be satisfied or not or all the items in the wish list can be simultaneously catered or not that is something which depends on the particular technology not only the technology also the techno economic environmental combination. Now downsizing so if we reduce the size of the device then what happens and how does it affect the energy conversion micro nano systems provide low cost lightweight mode for energy conversion such systems tend to explore an entirely new paradigm where certain macro scale features cease to be important and interesting small scale factors start becoming important. We have gone through a whole course of micro fluidics and partly nano fluidics by which we have appreciated that what are the important small scale factors. The increasing surface area to volume ratio enhances interfacial effects and can be used to propel fluids without external fields for example you can propel a fluid by surface tension gradient without using any external field. So that can make a system highly energy efficient under extremely small confinements the constituent fluids may interact in a non trivial way completely altering the flow physics like some of the issues are related to high level of slip in nano fluidic channels. So high level of slip is something which is of great importance and high level of slip can give rise to augmented transport of the species in the say charge species in a fluid sample because if the fluid sample moves faster because of slip then the charge species along with the fluid sample will also move faster. So slip is an important phenomenon there are other interactions like interfacial interactions may be solvation interactions and so on. These interactions come into the picture and Van der Waals interaction and so many other interactions and therefore the physics of nano scale devices as we have earlier seen that the physics of nano scale devices is something which is significantly which may be significantly different from the physics of even micro scale devices and this physics can be exploited to a benefit for energy conversion. Now we will focus our attention to a system which utilizes the hydraulic form of energy as an input. So initially we make a discussion that we apply a pressure gradient to drive the fluid flow and we see that how from hydraulic to electrical energy conversion may be possible. But we should keep in mind that the applied pressure gradient driven flow in a nano fluidic system may be energy intensive by itself because huge frictional losses need to be overcome but as we said that this is something which is notional instead of an applied pressure gradient you could use a surface tension gradient designed in the system to drive the flow and then the system can be highly energy efficient. So in this kind of a system we essentially rely on the mechanism of streaming potential which we have discussed in the context of electro kinetics and I will revisit that. So what kind of advantages that we expect here is less material consumption, localized generation, zero emission, lightweight, minimal losses, customized production and of course you can get high energy density or high power density. Now to revisit the streaming potential, the concept of streaming potential we try to first discuss about the electrical double layer phenomenon. So let us say that you have a surface which is in contact with an aqueous solution, salt water solution then because of electro chemical interactions at the interface the surface can assume a net charge. In this example shown in the figure the surface assumes a negative charge because the entire system is electrically neutral so the fluid, the bulk fluid preferentially is positively charged although there is both positive and negative charge but positive surpasses the negative charge so that you know the net system is electrically balanced. Now this net charge density distribution within the fluid means that you have a potential distribution close to the solid boundary. This potential distribution falls from a surface potential value to zero value in the first stream condition and at the interface between the immobile and the mobile layer of ions which is called as a shear plane the potential is known as zeta potential and the characteristic length scale over which the potential reduces to zeta by e is a characteristic length scale of the electrical double layer and that is known as the Debye length. So with this little bit of recapitulation let us discuss about the fundamentals of electro kinetic energy conversion. Let us listen to this very carefully because this is the very fundamental consideration based on which we will discuss about the energy conversion. So consider a pressure driven flow from say left to right so you can see a pressure driven flow. Now the surplus ions within the system let us say surplus positive ions they will be migrated towards the downstream direction with this flow. Once the ions are preferentially migrated you when I say migrated you have to keep in mind that there are also negative ions in the flow which we are not showing in this diagram for clarity but there are also negative ions but positive ions are there more as compared to negative ions. So there will be a preferential positive polarity developed in the downstream end as compared to the upstream end. So because of this preferential polarity what will happen? There will be a potential developed under dynamic condition across the system. This is known as streaming potential and this streaming potential what it will do? It will try to create a back flow which will oppose the driving pressure driven flow. That means to some person who is not aware of the streaming potential it will appear that the fluid is getting as if more viscous. The fluid is getting resistance against the flow because you are having a flow which opposes the pressure driven flow. So that is a kind of an artifact but the positive point is that because you have developed an electrical potential out of the pressure driven flow if you now connect this system with an external resistor then a current will pass through the external resistor because of the potential developed and some power will be generated. So this is the basic principle of hydraulic to energy conversion in a microfluidic or nanofluidic system. Now why we are interested so much about the nanofluidic system? Other than the compactness interfacial phenomena become more intricate in nanofluidic channels. So it may be possible for example to drive the flow very easily by creating patterns of or patches of weightability so that you can create a surface tension gradient driven flow instead of a pressure driven flow by using say nano patterning for example but we will not discuss that today. What we will discuss is something which is a little bit more obvious that in nano channels we expect the slip phenomena and the slip boundary condition at the interface between the fluid and the solid to be one of the key factors and this key factor is not by any means intuitive. So how the non-intuitive slip phenomena and the coupling of slip phenomena with other physical phenomena become important at the nano scale and how they decide the energy conversion efficiency that will be the focus of today's discussion. Now as you see here we will revisit the simple analytical model for calculating the streaming potential because to calculate the energy conversion efficiency we need to calculate the streaming potential. So let us say that you have a rectangular channel and with z plus z plus as the valence of positive ions and z minus as the valence of the negative ions and u plus and u minus are the velocities of the positive and negative ions. So the total ionic current expression is given this actually I have derived in full details earlier in the lecture on streaming potential. So I will not spend much time on this today but I would just give you a pointer to this that if you want more details on the derivations of this please refer to my lectures earlier lectures on streaming potential. Now to summarize the velocities of ions is a combination of the advection velocity plus the velocity relative to the fluid flow because of electromigration that is the because the ions are charged and we are assuming for this case that you have a z is to z symmetric electrolyte for simplicity. So you have an electromigration of ions relative to the fluid. So that means the net velocity is some of the advection velocity and the electromigration velocity. Now you can simplify this equation by assuming that the friction coefficients of the ions are the same which of course is not the physical reality and we will not put that restriction when we go for the nanofluidic domain because the friction coefficient is a strong function of the ionic size and the ionic size can play a dominating factor in the nanofluidic domain. However, just to establish the basic principle that in the absence of any applied electric field what is this E by which the ions are moving here this E is the streaming potential that is spontaneously induced across the channel. So you can set E equal to ES and set the ionic current equal to 0. Why we can set the ionic current equal to 0 is because you have a system where you have applied no net electric field. So therefore there should not be any net ionic current. So the advection current should be balanced by the conduction current which is basically the current of ions due to electromigration. So that the net ionic current is 0. So if you saw this equation you can see you can get an expression for E which in our case is the streaming potential. Now this simple model that we have presented has some limitations. First the model does not account for the interfacial slip at the boundaries. Interfacial slip may considerably alter the advective transport of ions. Water being a polar molecule has its own charge distribution and a resulting field which organizes the adjacent water molecules. The analysis which has been presented so far bypasses such structure of water molecules in the flow. But this structure can be very, very important in the nano domain when the device size is comparable to molecular length scales. The finite size and hydration of ions alters the value of ionic friction coefficient and hence the electromigrative transport term deviates from the one predicted using the analytical model and very often the analytical model is based on the classical Stokes law. But the finite size and hydration of ions may alter and the confinement effect hindered diffusion. So many other aspects can alter this to a significant extent. Now in the nano fluidic regime the reduction of length scales to nanometer regimes opens up new arenas of maneuverability. So in nano fluidic channels we want to combine some aspects of micro scale flows like their compact abilities and maneuverability of free molecular flows. So one can have alternative pumping methods and one can selectively address molecules in the nano fluidic system to augment the transport and hence the energy conversion efficiency. So today I will discuss about some results from molecular dynamics calculations which will help us to assess the energy conversion efficiency of a nano fluidic system using exploiting the principles of streaming potential. Now just to recapitulate again we have discussed about the molecular dynamics platform. So essentially we use a computational tool to describe how positions, velocities and orientations of molecules evolve over time. The simulation is based on essentially Newton's second law. So we start with the Newton's second law. The force field is calculated from the negative of the gradient of the potential field and then we integrate this to get the velocities and the positions. Now when we get the interaction potential, the interaction potential how is it sensitive to physical parameters? Now the interaction potential if you recall like the standard components in the interaction potential will be the attractive and the repulsive potential commonly destroyed by the Lennard-Jones parameters. In addition to that you have columbic interactions in a system where charges are present and I have discussed that how these interactions can be taken into account in a molecular dynamics simulation. Now how do you relate these interactions with the physical parameters? Now if you have a substrate with a particular weightability gradient that drives the flow then the weightability parameter can be reflected or the weightability issue can be reflected in the Lennard-Jones parameters. So by altering the numerical values of the Lennard-Jones parameters you can basically implement the features of weightability of a substrate and you may also include the effect of roughness. Now as I mentioned that at the end we need this molecular dynamics calculations because we need to calculate the slip length. We need to calculate the slip length and there is no other way by which we can estimate slip other than looking into the interfacial phenomena and when we look into when we proven to the interfacial phenomena we have to basically go for molecular simulations over the length scales that we are considering. So what we do to get the slip length? So this picture will give you a clear idea. The velocity profile in the bulk, how do you get the velocity profile we have discussed that you basically make a statistical averaging of the molecular velocity based information and you fit that so that you get a velocity profile in the bulk. You then extrapolate it so that it leads to a 0 velocity condition at a hypothetical distance away from the wall and this hypothetical distance is the slip length. So to implement this the simulation domain is split into large number of beams and the velocity of the particle is in each beam is averaged over time. The resulting data gives the velocity distribution in the channel which is shown by the blue line. The particles of the molecules are the red circles clustering around the blue line. Now question is the big question which we will be addressing throughout the remaining part of this presentation is what are the parameters that affect the slip length? One obvious parameter that affects the slip length is the weightability although there should not be any prejudice of making a one to one correlation between the weightability and the slip length. There are other more complicated issues that may come up. So weightability modulation is a mixed blessing towards fluid propulsion in a nano channel. Why? Hydrophilicity causes capillarity and can aid transport with adverse pressure gradient. So that is one of the advantages of hydrophilicity. However hydrophobicity encourages slip although this should not be generalised it depends on other conditions and can lead to get greater throughput. So a combination of both of these advantages ideally can lead to increase slip with capillary action at the expense of surface energy of a partially weightable substrate. Not only that it depends on what is the composition of the solution. See typically in many of these systems we are using salted solutions and our molecular dynamic studies have revealed that dissolution of salt in pure water can lead to increase slip lengths in hydrophilic substrates. Now what is the general role of concentration of the salt solution? Greater the concentration of the salt solution, it implies a large number of charge carriers and hence more current is generated in the external circuit. However greater concentration implies lower debilength or the characteristic electrical double layer thickness and lack of electrical double layer overlap reduces the current. Now it all depends on what kind of boundary condition also we are looking for. So far as electrokinetics goes. So for example we can think of a constant surface charge density boundary condition which is somewhat more realistic than a constant zeta potential boundary condition for nanofluidic channels. With constant surface charge density the number of charge carriers does not increase in the channel. However decreasing the debilength reduces the current. So you can see that you have the streaming conductance for the constant surface charge density varying with the concentration of the solution. This is based on this based on a report earlier published in the physical review letters. With constant zeta potential the surface charge and hence the charge carrier concentration increases and with the increasing salt concentration this increase results in increased current. So you can see the characteristic curve for the constant zeta potential. In reality the boundary condition is close to I mean conceptually close to constant surface charge density boundary condition. But it is more aptly described by the chemical equilibrium condition at the wall which relates the zeta potential and the surface charge density. And you can see that for that also you can have a decreasing strain in the streaming conductance with increasing salt concentration. However the studies that we have presented in the previous slide they do not consider the sizes of the ions. Now we have to also consider the ionic size because over the length scales of few nanometers that we are considering the ionic size and the size of the system may become comparable. So what we have seen in terms of the density fluctuation of water near a wettable wall and near a non-wettable wall. So this is an example of a wall with a contact angle of 10 degree. So here addition of salt reduces the fluctuations and the height of the first density peak. On the other hand for a non-wettable wall with a contact angle of 120 degree you can see that addition of salt increases the fluctuations and density peak near the wall. So inclusion of salt will affect the density peak close to the wall in a different manner depending on the intrinsic wettability of the substrate. Now for different salt types we can calculate the slip length and just for a typical example of a contact angle of 10 degree the slip length for different types of salt and salt concentrations those are shown in the 2 figures which are displayed in this view graph. So this is slip length for some chloride salts and this is slip length for in general other alkali halide like the fluoride bromide iodide salts in addition to the chloride salts. Now where does the thermodynamics and chemistry play a role? Ions composing the salt can be kaotropic which is called as structure breaking or cosmotropic or structure making and slip length would depend on these properties. This is grossly overlooked. See this is where I want to focus a lot of attention chemistry is dictating fluid dynamics. How it is dictating fluid dynamics is it is give the chemistry or the thermodynamics thermodynamic interactions at the wall that is giving rise to a particular slip length and using this slip length we can make calculations for the advection current the electro migration current and so on. So what we can see that this particular slip length will decide what will be the transport of ions and the distribution of water molecules and that will dictate the energy conversion to a significant extent. So over this length scales it is obvious that chemistry is dictating the flow physics and the flow physics in turn is dictating the energy conversion characteristics. Now regarding this kaotropic and cosmotropic effect we can mention that ions are hydrated according to the entropy difference of water between the bulk and the vicinity of the ion. A kaotrop is a structure breaking ion that preferentially tries to reside near the interface and a cosmotrop is a structure making ion that has an affinity for the bulk. So now how these ions behave differently in contact with the hydrophilic and hydrophobic substrate. A kaotropic ion approaching the wall displaces the highly ordered arrangement of water molecules reducing the contact density and hence increasing the slip length. A cosmotropic ion on the other hand remains in the bulk and creates coordination shell around them leading to modification of the hydrogen bond structure and closer approach of water molecules to the wall this is for hydrophilic substrate. For hydrophobic substrate a kaotropic ion approaching the surface modifies the surface potential facilitating more closer approach of water molecules and thus greater contact density and less slip length and the inverse is for cosmotropic ions. So the moral of the story is the behavior of kaotropic and cosmotropic ions are somewhat different depending on whether they are in vicinity of a hydrophobic surface or a hydrophilic surface. However these effects discussed do not explicitly consider the ionic size. In addition if you take the size effect in consideration large ions like CS and I instead of their highly kaotropic nature cannot approach the interface due to their size. A slight decrease in slip length is observed with salt of these ions in hydrophilic channels as compared to the expected value because of the size effect. Whereas a slight increase in slip length is observed with salts of these ions in hydrophobic channels as compared to the expected value because of this size effect. Now how do we relate this density distribution and slip with the electrokinetic transport? Now as we have recalled that narrow confinements induce fluid fluctuations. We have plotted the density profile close to the wall and you can see that there are oscillations in the density profile. Now these fluid fluctuations can dislodge the ions. So what we can say is that see the electrical double layer structure, classically we considered a structure such that there is a layer of ion adhering to the solid boundary which is immobile that is called as the stern layer which is shown by the red colour here. However with this density fluctuations the stern layer may become mobile and immobility of the stern layer can become a myth. So ions dislodged from the stern layer would mean more ions in the flow. So if you have slip at the interface the slip phenomena will dislodge the ions in the stern layer and it will induce more ions in the flow and hence more current and hence more power. So now you can have basically a non-linear amplification of the zeta potential as a function of the bare zeta potential or the effective zeta potential as a function of the bare zeta potential depending on the slip length and from our group we reported extensive molecular dynamics lattice Boltzmann and some analytical studies based on this conjecture and this paper was report this work was reported in PRL. So I summarise the final result here but give the reference so that if you are interested you can read this paper and see that how this formula is derived. Now we can clearly see that the effective zeta potential which indicates the effective charge condition of the substrate depends on the slip length and this slip length therefore can non-trivially alter the energy conversion characteristics depending on what are the other factors on which it depends. Now traditionally in the literature slip length is considered to be a function of the surface weightability but it is not explicitly related to the surface charge of course there have been few exceptions in the literature which have pointed out that this is indeed not the case. So the slip it is something which is very non-intuitive that is surface charging is a electrical phenomenon slip is somewhat related to hydrodynamics. Now the coupling between the electrical phenomenon and the hydrodynamics is expected to come from the standard governing equations of electrokinetics like coupling of the Navier-Stokes equation with the Poisson equation and the Knott-Splank equation. Now where from the coupling between surface charge and slip length comes because then the coupling becomes more intense there is an intricate relationship between the boundary condition of hydrodynamics and the boundary condition of electromechanics. So it is a stronger electromechanical coupling that we expect than that we get than what we expect. So look at this graph very carefully we have plotted the slip length as a function of surface charge. Now we have divided this graph into 3 regimes the zone 1, zone 2 and zone 3. So you can see the I mean notionally so this is not a hard and fast border line but notionally some vertical dotted lines are plotted to demarcate these zones. The zone 1 which is blown up blown up here it is a low surface charge density regime with constant slip length that means the slip length is not a strong function of the surface charge in this regime. This regime is dominated by hydrodynamics rather than electrostatics. The ions and the surrounding water clusters respond rapidly to the bulk shear and with effect of electrostatic attraction of the wall is not felt. There is an intermediate surface charge density regime with rapidly decreasing slip length so that you can clearly see here. So if you increase the surface charge here the slip length is decreasing. This zone witnesses combined effect of electrostatics and hydrodynamics. So why the slip length is decreasing? So what happens as you increase the surface charge ions and the water in the hydration shell so basically ions will form hydration shell. So if you increase the surface charge there will be stronger hydration effect close to the wall and this results in increased pinning of water molecules at the wall. So what will happen is that because ions will form hydration shells and with the or water will form hydration shells with the ionic species and ions are present abundantly close to the wall that means water molecules are pinned to the wall. So they cannot freely move because of formation of the hydration shells. So that leads to the rapid decrease in the slip length. There is a third regime which is a high surface charge density regime with gradually decreasing slip length. This regime is characterized by electrostatics completely overpowering hydrodynamics. Since the wall is already covered with ions and pinned water molecules further increase in surface charge does not introduce any appreciable change. Now you can make a further fine tuning of this by several other technological innovations. For example you can use active nanoparticles heated nanoparticles and this view graph shows the slip length as a function of contact angle. So for different increase in temperature of the active nanoparticles. So you can see that in zone 1 slip increases with decrease of weightability and there is no effect of nanoparticles. The blue colored line is basically for pure water without any nanoparticle heating effect. So you do not have any heated nanoparticles when this blue line is plotted. So you can see that in the regime of contact angle of 50 to 100 degree pure water has actually the maximum slip length and water with nanoparticle shows increasing slip trend but towards the end of the weightable region only. But in early part of zone 1 actually with heated nanoparticles you are getting less slip. But if you come to this regime at contact angle of 100 to 150 degree you can see slip length increase tremendously with the increase of nanoparticle temperature and minimum slip is there for pure water. However slip with nanoparticle again decreases if you increase the contact angle beyond that. So this regime of about 100 to 150 degree can be utilized for augmenting the slip with the aid of heated nanoparticles. Now the effect of temperature that we have discussed in this particular system is not very trivial because you can have cations and anions which will have different thermo diffusive migration strength. So there is a thermo electric field that is generated not only that because of the temperature dependence of properties electrical properties of the system there is an electro thermal effect this we have already discussed. So the thermo electric field and the electro thermal field they may aid or oppose each other and therefore it may be possible that it either augments the streaming potential or it reduces the streaming potential. So it depends on the regimes and the kind of temperature gradient that we are applying. So we have seen that how the surface chemistry, surface charge, ionic size, nanoparticles all these affect the slip length. Now how can we exploit this slip phenomenon depending on these parameters to augment the energy conversion efficiency. So if you calculate the current and the flow rate in a nano fluidic or a microfluidic system so you can see roughly the schematic scenario. So you have a potential developed across the channel you connect it with an external resistor. So let us say that RCH is the intrinsic channel resistance and ZCH is the intrinsic fluid impedance. So I is a linear combination of delta P the pressure drop and delta V the voltage drop which is induced due to streaming potential and Q the flow rate again is a linear combination of delta P and delta V. So you can see here that interestingly the coefficient of delta P in the expression for I is same as the coefficient of delta V in the expression for Q and this follows from a very classical relationship in mechanics known as Onsega reciprocity principle. So if you are interested please read literature on Onsega reciprocity principle which gives the idea behind this kind of symmetrical relationship. Now what current flows with the external resistor definitely not the I not the streaming current but it depends on the resistance of the external load. So what we can say that we can have an indicator of course we have to keep in mind that when we calculate this efficiency parameter as delta V square by RL. So this depends on this RL whatever is the external load you are applying but in principle you can get a battery which is called as a nano fluidic battery where a current will flow through the external resistor which is delta V square by RL where RL is the load resistance and the efficiency of this is the input power. Input power is the flow rate times the pressure drop Q into delta P. So this is the cost that you are paying. So you can reduce the cost by eliminating the pressure gradient driven flow and implementing a surface tension gradient driven flow which can be a natural consequence but that requires maybe more complicated nano fabrication. So fabrication cost will go up. So there will be a trade off when this comes into industrial practice. So you so this is the input power Q into delta P and delta V square by RL is the output electrical power. So the efficiency is the output by input and we will see that how this efficiency varies in a lab scale experimental scenario. So how good the system can be? Without slip typical energy conversion efficiency obtained from experiments have been in the tune of around 5% with slip I mean one can get something greater than 15% further modifications can make it around maybe greater than 30%. So what modifications are necessary? How high we can go? Smaller surface, smaller nano channels will help, higher surface charges will help and what are the limitations of theoretical prediction? These are some of the issues that we have to keep in mind and when we make the prediction where comes the complication? The complication is that slip length cannot be independently posed. Slip length depends on several factors like the surface charge for example would redistribute the ions in the channel. Water as a polar molecule would also have its distribution affected by the surface charge. The density variation of water molecules determines the flow profile. The velocity profile again determines the stern and diffuse layer and redefines the ionic distribution. The ionic distribution would alter the distribution of water and all these so the coupled nature of surface charge and slip become important and that will decide what could can be the nanofluidic energy conversion efficiency. So two important factors that we have identified in the nanofluidic domain one is the slip length another is the ionic density. So increase in surface charge has counteracting effects. Increase in surface charge leads to pinning of molecules near the interface and hence reduction in slip length. So this is a reduction in slip length. However increase in surface charge means more ion dissociation which leads to increase in number of charge carrier and more ions in the system implies more current. So the net effect is that with the slip length now you can have with the higher slip length you can have dislodging of the water and the ion clusters near the wall and that can lead to more current flow. So if you have more ions in the system that will imply more current that will come from ionic density if you have more slip then interfacial slip will dislodge the water and the ion clusters near the wall and leads to more current flow. So this win-win combination between slip and ionic density can actually give rise to a tremendously unprecedentedly augmented efficiency energy conversion efficiency of a nanofluidic system. So if you look into now the variations of the energy conversion efficiency as a function of surface charge for different contact angles this somehow follows the trend of the slip length as a function of surface charge for different contact angles. Here the contact angles studied in this figure are about 100 in one case 110 degree and the blue coloured plot is for 110 degree and the red coloured plot is for 120 degree contact angle. So why we have used that particular regime is because that particular regime appears to be a good regime for exploiting the benefit of slip. So the however we see that the you know the efficiency first increases with the increase in surface charge then it comes to a peak and you see this trend is very similar to what we get in the slip length because with the intermediate surface charge if you recall the previous plot the slip length started decreasing rapidly that is because of formation of the hydration shells with the water molecules for the ionic species. So that what this plot essentially means is that see in technology or science there is always an intuition and the intuition is let us increase the surface charge and the energy conversion efficiency will increase. However we have found out that actually one should not indiscriminately increase the surface charge in an effort to get and increase the energy conversion efficiency. In fact the energy conversion efficiency is at its peak with an intermediate surface charge not that you will have a trivial increase in energy conversion efficiency with an increase of surface charge. So low surface charge leads to less number of free ions in the bulk and hence lower number of charge carriers. On the other hand very high surface charge density pins the adjacent interfacial water leading to lower ionic mobilities and hence lower current in spite of higher number of free charge carriers. So in between there is a peak in the energy conversion efficiency. Now that means that we can other than the factors with the ionic size and all these things which are more subtle there are couple of obvious factors with which we can play with to augment the energy conversion efficiency. And what are these obvious factors? One is the wettability of the substrate and the other is the surface charge. So you can see here that if you get a combination if you get a combined plot of the energy conversion efficiency as a function of the contact angle and the surface charge you can obtain maximum energy conversion efficiencies for intermediate surface charges and typically in the higher regime of the contact angle. So higher contact angle values can be used to obtain higher efficiencies and greater control over the contact angle can be implemented in technological scenario to obtain or to enable optimum design performance. So we have discussed something about how to augment energy conversion efficiencies of nanofluidic systems but there are still several open questions, the road ahead. Now some of these questions have been addressed in the paradigm of micro fluidics but we are still having these as open questions. Can a time periodic driving field augment the current density and hence the efficiency? Can ion specific effects can be used to harness more power? How to device special fluids which can maximize slip without compromising the ion density? How can natural weightability gradients as well as rheology of complex fluids be utilized to a benefit for augmenting the energy conversion efficiency and finally the most important thing which can bring these kinds of efforts from the laboratory scale to the practical industrial scale is that how to manufacture devices of commercial use with high energy conversion efficiency that is the golden question to answer. Now we have come to the end of this course on micro fluidics. I hope I mean I have tried my best to share my own understanding, my own very little understanding about micro fluidics and nanofluidics with all of you and I hope that it could be of some use and it will trigger more interest in your mind. Now I would like to conclude the series of my lectures on micro fluidics and partly nanofluidics with the acknowledgement of my colleagues, colleagues, faculty colleagues and student colleagues I mean who have contributed significantly to my understanding of micro fluidics and nanofluidics which I shared with you through these particular lectures. So first I will acknowledge my faculty colleagues. Professor T.K. Maithi is my colleague from the department of biotechnology of my own institute and Professor Sunanda Das Gupta is my colleague from the department of chemical engineering from my own institute. So Professor Maithi is an expert in the area of biological applications of in several biotechnological scenarios and of course in this particular presentation I mean whatever aspects of bio micro fluidics I have presented those have been highly enriched with the discussions with Professor Maithi. Professor Das Gupta is an expert in interfacial phenomenon and typically he is an authority in the area of micro heat pipes and like the discussions on micro heat pipes that we have had through in this particular course have been based on stimulating interactions with him. Then Professor Mark Madhu like the lectures on lab on a CD could not have been possible without his contributions. He has helped our research group tremendously to develop the facilities and the expertise on the CD based micro fluidic platforms. Professor Zungli Zhang from the University of Southampton UK we had UK India collaborative research projects and a couple of projects with his research group and this projects have helped my students to learn many things which we have utilized for our understanding in bio micro fluidics and when we say bio micro fluidics typically that is related to several applications including cancer biology. Then Professor Suchia has been our collaborator for the micro needle project that was supported by the Indo-Japan collaborative program and without his input I could not, could never work in the micro needle project in which we have successfully contributed. Professor Juan Santiago I think I had very very stimulating discussions when I have been there in the Stanford University as a visiting professor I mean I interacted with him in many ways and his tremendous high level of knowledge in electrokinetics has helped me to understand various mechanisms of electrokinetic transport to a significant extent. When we say students you know there is an interface like some students are currently there in our research group but some students have now graduated and they are established researchers either industrial researchers or faculty members. I should acknowledge Dr. Siddhartha Das whose contribution in the series of lecture comes through mainly the DNA hybridization project in which he worked. Dr. Tamal Das mostly the entire bio micro fluidic paradigm that I have discussed in this particular series of lectures is because of my learning of bio micro fluidics from him. He is a student specialized in biotechnology and I am of course not a professor specialized in biological applications. I am primarily a mechanical engineer so I have learnt a lot from him. Dr. Devapriya Chakravarty has contributed in the lab on a CD based research in our group and he is the, he was the student who actually developed the facilities by himself and Dr. Jeevanjati Chakravarty has contributed significantly towards the enrichment of electrokinetic research in our group. Last but not the least the present students. I would like to acknowledge Pranab, Ranabin, Chirudhip, Aditho, Uddipto, Kiran and Shantimoa for their tremendous contribution in developing these particular lectures which I have presented in this particular course. It might appear to you that this is just an individual effort but it is not an individual effort it is a collective effort from our group and I think that I must acknowledge that I have learnt a lot from all these students so that I have tried my best to present these lectures in front of you. So, thank you very much for your patient hearing of my lectures and all the best for your future endeavors. Thank you very much.