Flows past flexible surfaces

Physiological flows in the cardio-vascular and pulmonary systems involve flows past soft and deformable solids. These flows are also becoming increasingly important in micro-fluidic applications, where soft lithography can be inexpensively used to fabricate nanoscale structures in soft materials such as polymer gels.
Mixing at the microscale occurs by a very different mechanism in comparison to fluid flows that we usually encounter. Large scale flows are usually turbulent, with large fluctuations in the velocity and chaotic streamlines, and mixing occurs due to eddies (packets of fluid in correlated motion). In contrast, the flow in microscale devices is usually laminar, with smooth streamlines, and mixing takes place due to molecular diffusion. This results in slow mixing and reduced rates of mass and heat transfer, in comparison to large scale turbulent flows.
One of the central ideas in fluid mechanics is the laminar-turbulent transition in pipe flows, which occurs when the Reynolds number Re = (ρ V D/μ) exceeds a transition value of Ret = 2100, where ρ and μ are the fluid density and viscosity, D is the pipe diameter and V is the average flow velocity. Our research over the years has shown that it is possible induce an instability in the flexible-walled channels and tubes at a Reynolds number lower than the transition Reynolds number for the flow in rigid channels and tubes. The transition Reynolds number is a function of a material parameter Σ which provides the ratio of the wall elasticity and fluid viscosity. Different instability mechanisms have been identified. Important among these are,

  1. At zero Reynolds number in the absence of inertia, there is an instability due to the coupling between the fluid and wall dynamics. The mechanism is the transfer of energy from the mean flow to the fluctuations due to the shear work done at the interface. The transition Reynolds number Ret is proportional to the parameter Σ for this case.

  2. In the high Reynolds number limit, there are two modes of instability. The inviscid instability is induced by a transport of energy from the mean flow to the fluctuations due to the Reynolds stresses in the bulk of the flow, and the transition Reynolds number scales as Ret α Σ 1/2. The wall mode instability is induced by the transfer of energy due to the shear work done in a boundary layer near the wall of thickness Re-1/3, and we find that Ret α Σ 3/4 for this instability.

  3. The low Reynolds number instability has been experimentally verified for the flow past a poly-acrylamide gel using a rheometer. Quantitative agreement between experiments and theory were obtained in this case.

  4. The high Reynolds number instability in the flow through a flexible tube has also been experimentally verified. Though we find that the scaling Ret α Σ is correctly predicted by theory, the numerical values of the experimental transition Reynolds number are much lower than the theoretical predictions.

This has important consequences for mixing in microchannels where the Reynolds number is small, since the slow mixing due to molecular diffusion in a laminar flow can be significantly enhanced by triggering an instability using flexible walls.
This study also has significant implications for the flow of fluids in physiological systems, such as the blood flow in arteries and veins. The modulus of the wall materials in arteries and veins typically varies between 105 -106 Pa.

Previous theoretical studies seemed to indicate that the transition Reynolds number cannot be lowered below the rigid-tube value of 2100 for materials with this shear modulus, indicating that wall flexibility is not likely to be a factor in the flow dynamics in physiological systems. Our present study shows that the transition is lowered below the rigid-tube value of 2100 even when the shear modulus is as high as 100 kPa, indicating that the transition due to wall flexibility could be having a significant effect on physiological flows.

Some recent results within the past 5 years in this area,

  1. The weakly non-linear analysis of the flow past a surface modeled as a neo-Hookean solid in the limit of zero Reynolds number has shown that an increase in the viscosity of the solid could de-stabilise the flow. This is in contrast to the usual expectation that the flow is stabilised when the dissipation is increased. We have carried out the analysis in both the Lagrangian and Eulerian reference frame, and has shown that the results are identical. This is an important validation of the solid elastic model which has been carried out for the first time.

  2. The weakly non-linear analysis for the high Reynolds number wallmode instability has provided an important result that the primary bifurcation in the high Reynolds number limit is a sub-critical bifurcation, and there are nearby stationary states. This has been carried out for both the linear elastic model and the neo-Hookean model for the solid surface.

  3. The weakly non-linear analysis of the flow of a visco-elastic fluid past a flexible surface has been carried out. Here, the focus has been on comparing different models, such as the FENE and Oldroyd models, and to examine how the stability characteristics of these models differ.

  4. The flow through a flexible microchannel has been experimentally studied, and we have shown the first evidence that the transition Reynolds number is lower than 2100 if the walls are made sufficiently soft. The transition Reynolds number is found to scale as Ret α Σ 3/4, as predicted theoretically for the wall-mode instability. However, the numerical value of the transition Reynolds number is more than one order of magnitude lower than that predicted theoretically. Further research is required to examine the causes for this difference.

Future work:
  1. Since the theoretical study so far has been restricted to linear and weakly non-linear stability analysis, a good understanding of the nature of the flow after transition is not available. We would like to carry out a complete numerical simulation, similar to the DNS simulation for turbulent flows, to determine the flow and transport characteristics after transition. This will be a challenge since it is necessary to incorporate a moving boundary in a DNS simulation.

  2. In microfluidics applications, one of our areas of focus will be the effect of mixing on nano-particle synthesis in microchannels.

  3. In biomedical applications, we would like to mimic the hardening of arteries by incorporating a hard (high elasticity modulus) section between two soft sections, and see how this affects the dynamics of the flow. In particular, we would like to see whether mechanical property contrast can induce instability in soft-walled channels.

  1. M. K. S. Verma and V. Kumaran, Transition in flexible-walled microchannels, J. Fluid Mech.submitted.

  2. P. P. Chokshi and V. Kumaran, Stability of the plane shear flow of dilute polymeric solutions, Phys. Fluids, 21, 014109, (2009).(PDF)

  3. P. P. Chokshi and V. Kumaran, Weakly nonlinear stability analysis of a flow past a neo-Hookean solid at arbitrary Reynolds numbers, Phys. Fluids, 20, 094109, (2008).(PDF)

  4. P. P. Chokshi and V. Kumaran, Weakly nonlinear analysis of viscous instability in flow past a neo-Hookean surface, Phys. Rev. E, 77, 056303, (2008).(PDF)

  5. P. P. Chokshi and V. Kumaran, Stability of the flow of a viscoelastic fluid past a deformable surface in the low Reynolds number limit, Phys. Fluids, 19, 014103, (2007).(PDF)

  6. P. P. Chokshi and V. Kumaran, Stability of the viscous flow of a polymeric fluid past a flexible surface, Phys. Fluids,19, 034102, (2007).(PDF)

  7. P. Chokshi and V. Kumaran, Stability and transition in the flow of polymer solutions, Sixth IUTAM Symposium on Laminar-Turbulent Transition, R. Govindarajan (ed), Springer, Dordrecht, The Netherlands, 2006.

Statistical mechanics of granular flows

Granular flow of particles of size such as sand or glass beads of size greater than about 100 microns in a air or a suspending gas. The inertia of the particle is sufficiently large that force that forces exerted on a particle due to the suspending fluid can be neglected in comparison to the force exerted by other particles.
Granular flows are often encountered in nature in the form of landslides, snow avalanches, etc. Many processes in chemical industries, such as vibrofluidised beds, chutes, hoppers, pneumatic conveyors, etc. also involve granular flows. Despite their many applications, we do not currently have acomplete fluid-dynamical description of a granular flow, similar to the Navier- Stokes equations for a simple fluid.
Granular flows are qualitatively different from normal fluids because they exhibit both solid-like and fluid-like properties. Sand can be heaped in a pile, but will flow if the inclination is greater than the angle of repose. This dual nature is very difficult to capture using fluid models. Often, a yield stress is postulated as the minimum stress required for the material to flow. Physically, a yield stress arises due to the friction between the static grains in a sand pile, and a yield stress model would correctly predict that the material will flow when the angle of the slope exceeds the angle of maximum stability. However, if we take a flowing layer and decrease the angle of inclination, the flow has to stop when the angle of inclination decreases below the angle or repose. This cessation of flow cannot be physically captured by the yieldstress theories, because there was not static friction between grains prior to flow cessation.
To answer the above and other questions regarding granular flows, we have been working with the hard-particle model for granular flows. In this model, the hard-particle potential is used, where the particles interact through instantaneous collisions. The collisions are inelastic and dissipate energy, and so it is necessary to have a steady supply of energy from external forces to maintain the flow. Our research has focused on two different types of flows where the energy supply is due to mean shear, the uniform shear flow in the absence of gravity and the flow down an inclined plane.
For the purpose of analysis, it is easiest to start with a very dilute granular flow, where the volume fraction of the particles is small. In this case, approaches similar to the kinetic theory of gases can be used to obtain a conservation equation for the velocity distribution function, and this can be solved approximately to predict the dynamical properties. In kinetic theory of gases, the collision between molecules are elastic (energy conserving), and the temperature is a thermodynamic variable. In contrast, in the flow if inelastic particles, the temperature (average energy per particle) is a dynamical variable determined by a balance between the rate of production of energy due to mean shear and the rate of dissipation due to inelastic collisions. Nevertheless, useful results can be obtained for very dilute granular flows using kinetic theory.
For dense flows, correlation effects become important, and we can no longer make the molecular chaos approximation, because the velocities ofcolliding particles are correlated. We have used two strategies to include the effect of correlations. The first is the Enskog approximation, where we modify the collision operator using the pair distribution function at equilibrium. The second is the use of simulations to determine the relative velocity distribution for very dense flows; this relative velocity distribution is used to predict stresses and dissipation rates.
Our results have shown that all the salient features of the flow down an inclined plane are predicted by the hard-particle model. Some of the important results are,

  1. The binary collision approximation is valid for the granular flow of materials such as sand and glass, with heights up to about 40 particle diameters, down an inclined plane. This was found to be true for all angles of inclination, except for the lowest angle at which there is initiation of flow.

  2. Though the binary collision approximation is valid, the molecular chaos approximation is not. There are significant correlation effects, due to which the pre-collisional two-particle distribution function is very different from the single-particle distribution function.

  3. When the effect of correlations is incorporated in a kinetic formulation, it is possible to predict the cessation of flow at a finite angle of inclination (angle of repose).

  4. For thick flowing layers, the rate of conduction of energy is small compared to the rates of production and dissipation. The rate of conduction of energy is significant only in conduction boundary layers of thickness δ = (h/(1-en)1/2) at the top and bottom, where d is the particle diameter and en is the coefficient of restitution.

  5. In the bulk, there is a balance between the rates of production and dissipation. A direct consequence of this is that the volume fraction is a constant in the leading approximation in (δ/h) where δ is the boundary layer thickness and h is the height of the flow. All components of the stress tensor are proportional to the square of the strain rate.

  6. An analysis of the boundary layer equations indicate that a boundary layer solution exists if and only if the volume fraction decreases withan increase in the angle of inclination. In the opposite case where the volume fraction increases with an increase in the angle of inclination, no steady flow is possible.

  7. The minimum height hstop, at which the flow stops, depends on the nature of dissipation at the base. For a dissipative base, as the thickness of the layer is decreased, there is a minimum height at which the rate of production of energy due to shear in the bulk is not sufficient to compensate for the rate of dissipation in the base. This results in the cessation of flow at h = hstop.

Future work
  1. The hydrodynamic description which we have obtained will be extended to more complicated flows, such as an inclined plane flow with side walls and a rotating drum flow. We will seek to develop theories similar to the boundary layer theory for this case.

  2. The relationship between flow and structure will be probed by looking at how ordering due to flow is frozen into a granular material after it has stopped. The object will be to determine whether the static configuration can give us any information about the flowing state that formed the granular heap.

  3. The analysis of correlations in the flows of elastic and inelastic hardparticle systems will be further analysed. The objective here is to see whether there are relationships similar to the fluctuation-dissipation relations, which do not require an equilibrium state as the reference state. If we are able to obtain such relationships without having to make the assumption of equal probability of microstates, then we could develop a statistical mechanical framework for non-equilibrium drivendissipative systems.

  1. K. A. Reddy, V. Kumaran and J. Talbot, Orientational ordering in sheared inelastic dumbbells, Phys. Rev. E,80, 031304, (2009).(PDF)

  2. K. A. Reddy and V. Kumaran, Structure and dynamics of a twodimensional sheared granular flow, Phys. Rev. E, 79, 061303, (2009).(PDF)

  3. V. Kumaran, Mesoscale description of an asymmetric lamellar phase, J. Chem. Phys., 130, 224905, (2009).(PDF)

  4. V. Kumaran, Dynamics of dense sheared granular flows. Part I: Structure and diffusion, in press, J. Fluid Mech.632, 109-144, (2009).(PDF)

  5. V. Kumaran, Dynamics of dense sheared granular flows. Part II: The relative velocity distribution, J. Fluid Mech., 632, 145-198, (2009).(PDF)

  6. V. Kumaran, Dynamics of a dilute sheared inelastic fluid. I. Hydrodynamic modes and velocity correlation functions, Phys. Rev. E, 79, 011301, 2009.(PDF)

  7. V. Kumaran, Dynamics of a dilute sheared inelastic fluid. II. The effect of correlation, Phys. Rev. E, 79, 011302, 2009.(PDF)

  8. A. V. Orpe, V. Kumaran, K. A. Reddy and A. Kudrolli, Fast decay of the velocity autocorrelation function in dense shear flow of inelastic hard spheres, Europhys. Lett., 84, 64003, (2008).(PDF)

  9. V. Kumaran, Dense granular flow down an inclined plane: from kinetic theory to granular dynamics, J. Fluid Mech., 599, 121-168, (2008).(PDF)

  10. K. A. Reddy and V. Kumaran, Applicability of constitutive relations from kinetic theory for dense granular flows, Phys. Rev. E, 76, 061305, (2007).(PDF)

  11. V. Kumaran, The constitutive relation for the granular flow of rough particles, and its application to the flow down an inclined plane. Constitutive relations, J. Fluid Mech., 561, 1-42, (2006).(PDF)

  12. V. Kumaran, Granular flow of rough particles in the high Knudsen number limit, J. Fluid Mech., 561, 43-72 (2006).(PDF)

  13. V. Kumaran, Velocity autocorrelations and viscosity renormalisation in sheared granular flows, Phys. Rev. Lett., 96, 258002, (2006).(PDF)

  14. V. Senthil Kumar and V. Kumaran, Voronoi neighbor statistics of homogeneously sheared inelastic hard disks and hard spheres, Phys. Rev. E, 73, 051305, (2006).(PDF)

  15. V. Senthil Kumar and V. Kumaran, Bond-orientational analysis of hard-disk and hard-sphere structures, J. Chem. Phys., 124, 204508, (2006).(PDF)

  16. V. Kumaran, Kinetic theory for the density plateau in the granular flow down an inclined plane, Europhys. Lett., 73, 1-7, (2006).(PDF)

  17. V. Kumaran, Kinetic model for sheared granular flows in the high Knudsen number limit, Phys. Rev. Lett., 95, 108001-108004, (2005).(PDF)

  18. V. Senthil Kumar and V. Kumaran, Voronoi Cell Volume Distribution and Configurational Entropy of Hard Spheres, J. Chem. Phys., 123, 114501-114513, (2005).(PDF)

  19. V. Senthil Kumar and V. Kumaran, Voronoi Neighbor Statistics of Hard Disks and Hard Spheres, J. Chem. Phys., 123, 074502-074511, (2005).(PDF)

  20. M. Bose, U. U. Kumar, P. R. Nott and V. Kumaran, The Brazil nut effect and excluded volume attraction in vibro-fluidised granular mixtures, Phys. Rev. E, Phys. Rev. E 72, 021305-021313, (2005).(PDF)

Turbulent gas-particle suspensions

Turbulent particle suspensions are encountered in various process industries, including fluidised beds, circulating beds, pneumatic transport, etc. The interactions between the particles and the gas can be of different types depending on the particle size and mass. Particles with diameter less than 1 micron are Brownian particles, and exhibit random Brownian motion in the suspending gas. When the diameter is in the range 1-10 microns, Brownian velocity fluctuations are small, but the particle inertia is small enough that the particles follow the fluid streamlines. When the particle diameter is greater than 100 microns, the particle inertia is large compared to the viscous forces exerted by the gas, and the gas can be neglected altogether.
In this project, we are interested in particles with diameters in the range 10-100 microns, the particle inertia is large. The ratio of particle inertia and fluid viscosity, referred to as the Stokes number, is large enough that the particles do not follow fluid streamlines. However, the Reynolds number (ratio of fluid inertia and viscosity) is small, so the dominant forces are the particle inertia and the fluid viscous drag. A complicating factor is that the fluid flow is usually turbulent, and so there are local fluid turbulent velocity fluctuations which affect the particles.
There is an interaction between the particles and the fluid is two-way in a turbulent particle suspension. The fluid velocity fluctuations induce fluctuations in the particles, and the particles in turn exert a force which modifies the nature of the fluid velocity fluctuations. It is known that the fluid velocity fluctuations cause a migration of the particles, called turbophoresis, but the exact relationship between the amplitude of the fluctuations and the particle migration is not understood. The particles could either enhance of dampen the fluid velocity fluctuations, but an exact understanding of how this modification takes place is not yet at hand.
The objective of this research is to use a combination of modeling, experiments and direct numerical simulations to obtain a better understanding of the interaction between the particle dynamics and the turbulent fluctuations in the fluid.
The simulation used are Direct Numerical Simulations, which resolve all turbulence scales completely. One-way coupling is used, where the effect of the fluid velocity on the particles is included, but not the reverse effect of particles on the fluid. Two different configurations have been used in the simulations, the plane Couette flow in the absence of gravity, and the gravity-driven flow in a rectangular channel.
We have formulated a Fluctuating-Force model, which is appropriate for the case where the relaxation time of the particles is much larger than the correlation time of the turbulent velocity fluctuations. The effect of the turbulent fluctuations on the particles is modeled as a Gaussian random force, which is delta function correlated in time, whose mean and correlation are related to the mean square of the fluid velocity fluctuations.
The simulation and model are compared with experiments for the flow of a particle-gas suspension in a rectangular channel. In the experiments, we resolve not only the mean fluid, but also the mean square of the fluid velocity fluctuations using PIV. Simultaneously, the complete velocity distribution function for the particles is determined by particle tracking velocimetry.
Our studies show that the fluctuating force model can quantitatively predict the particle distribution function when the particle loading is sufficiently small, even when the velocity distribution function is very different from a Gaussian distribution. The model breaks down at higher particle loading due to the formation of instabilities. Thus, the fluctuating force model can be used for quantitative predictions for flows with sufficiently low particle loading.

Important results of this analysis are
  1. Direct Numerical simulations of the turbulent gas-particle suspension, where all the fluid turbulent scales are resolved, and the particle positions and velocities are explicitly simulated. One-way coupling is used, where the effect of fluid turbulence on the particle phase is incorporated, but not the reverse effect of the particles on the fluid turbulence. This analysis provides the velocity distribution functions of the particles, the fluid velocity distributions as well as the distribution of the accelerations on the particles due to the turbulent velocity fluctuations.

  2. The fluctuating force simulations of the particle phase alone. In this simulation, the particles are treated as hard inelastic spheres. The effect of fluid is included as a Gaussian random noise, whose variances are determined from the distribution of velocities in the fluid simulation. Quantitative agreement is found between the model and the direct numerical simulations, even when the distribution function is very different from a Gaussian distribution, both for the Couette and the channel flow.

  3. Experimental study of the turbulent gas-particle suspension in a channel using Particle Image Velocimetry for calculating both the fluid and the particle phase velocities. There were two important effects, the polydispersity in the particle size distribution and the particle-wall coefficient of restitution, which need to be included to obtain quantitative comparison with experiments, at low particle loading. When the particle loading is high, there is a spontaneous instability which develops leading to channeling of the particles. The analysis of this instability is the subject of future study.

Future work
  1. The work done so far has used only one-way coupling, where the effect of the gas velocity fluctuations on the particle phase is included, but not the reverse effect of particles on the gas. In future, we plan to introduce two-way coupling into the simulations, to take into account the effect of the particles on the gas phase turbulence.

  2. Analytical models based on moment expansions will be developed for the particle phase. These models will involve closure approximations, which will be tested with simulations and experiments.

  3. The formalism will be extended to denser flows where the particle volume fraction is not homogeneous, and to more realistic situations such as fluidised and circulating beds.

  1. P. S. Goswami and V. Kumaran, Particle dynamics in a turbulent particlegas suspension at high Stokes number. Part 1. Velocity and acceleration distributions, J. Fluid Mech., 646, 59-90, (2010).(PDF)

  2. P. S. Goswami and V. Kumaran, Particle dynamics in a turbulent particlegas suspension at high Stokes number. Part 2. The fluctuating-force model, J. Fluid Mech., 646, 91-125, (2010).(PDF)

  3. P. S. Goswami and V. Kumaran, Channel flow of a turbulent gas-particle suspension, J. Fluid Mech., submitted.

  4. P. S. Goswami and V. Kumaran, Experimental studies on the channel flow of a turbulent gas-particle suspension, in preparation, J. Fluid Mech., in press.



Under development


Under development

Multiscale modeling of liquid crystalline phases

Many industrial applications involve the transport and processing of surfactant solutions. Depending on the relative concentrations of water, oil and surfactants, these self assemble into micelles, lamellar or hexagonal phases. In order to design process equipment, it is necessary to accurately predict the flow behaviour accurately.
Lamellar and hexagonal phases exhibit complex rheological behaviour because they are anisotropic fluids. A perfectly aligned lamellar phase, for example, exhibits fluid like behaviour when the normal to the lamellae is along the shear or vorticity direction, but has a solid like resistance to flow when the normal is along the flow direction. In addition, even though a perfect defect free stack of layers is the final equilibrium state, real samples are rarely defect free due to kinetic constraints.
For the above reason, usual non-Newtonian constitutive equations are not sufficient for these systems, and it is necessary to include additional fields (such as the unit normal to the layers) to accurately describe their rheology. Moreover, shear treatment alters the structure of the lamellar phase, and this in turn affects the rheology. It is essential to capture this structure-rheology coupling to be able to accurately model the system.
The most important issue, from an engineering point of view, concern the effect of changes in molecular chemical structure on the flow properties of the complex fluids. The relationship between molecular structure and macroscopic properties is complicated due to the hierarchy of length scales involved in the dynamics of these complex fluids. The lamellar spacing is typically small compared to macroscopic scales (the distance between layers in lyotropic liquid crystalline phases is usually a few hundred Angstroms), and so a macroscopic simulation which resolves details on the length scale of the lamellar spacing is unrealistic. It is necessary to formulate a different simulation techniques at different length and time scales, all the way from the molecular to the macroscopic scale.
While various simulations methodologies have been developed for molecular, mesoscopic and macroscopic systems, the challenge at the core of multiscale modeling is to link up the simulations at the different scales in a computationally efficient manner. This involves devising linking methodologies for obtaining parameters in the larger scale simulations from those in the smaller scale simulation, and daisy-chaining these all the way from the molecular to the macroscopic scale.
In our research, we have evolved a framework for relating parameters in mesoscale simulation (involving tens of layers) based on a coarse-grained concentration field, to the results obtained from molecular simulations for lamellar liquid-crystals.

  1. At the molecular level, we have simulated stack of bilayers with different chemical composition and at different temperatures, and show how the temperature and chemical composition affect the structure and dynamical properties of the bilayers.
  2. A mesoscale simulation procedure based on a free energy functional has been devised using the lattice Boltzmann simulation technique.
  3. For nearly aligned layers, we have devised a framework for determining the parameters in the free energy functional for the mesoscale simulation from molecular simulations. The coarse-graining procedure correctly reproduces the equilibrium properties such as the layer spacing and concentration modulation, layer bending and compression moduli, as well as the dynamical relaxation rates of the hydrodynamic modes in the system.
  4. The effect of shear on an initially disordered lamellar phase have been studied using the lattice-Boltzmann technique. We have devised parameters to quantify disorder and identify defects during alignment, and shown that the dynamics strongly depends on the system size. While small systems align to a perfectly ordered state, large systems reach a disordered steady state where there is a balance between the annealing of defects due to shear and the creation of defects due to different instability mechanisms. Two different mechanisms of defect creation have been identified in our simulations.
  5. Experiments are currently being set up to make contact between the mesoscale modeling approach and real systems.

Future work
  1. One important issue at the molecular scale is the water permeation rate through the bilayers. This is important for obtaining the diffusion coefficient in the concentration-based mesoscale. It is also important for studying water transport through biological membranes. We are devising new techniques for obtaining the diffusion rates using a non-equilibrium simulation, in contrast to present techniques which are based on the equilibrium partition of water in the membrane.
  2. Further work will be carried out on defect motion and the formation and destruction of defects, and their effect on rheology. One focus is the instability mechanisms which give rise to the formation of defects.
  3. The mesoscale simulations will be extended to larger systems. In experiments, we plan to analyse smaller systems than those currently

  1. V. Kumaran and D. S. S. Raman, Shear alignment of an initially disordered lamellar phase, Phys. Rev. E, submitted.

  2. V. Kumaran, Mesoscale description of an asymmetric lamellar phase, J. Chem. Phys., 130, 224905, (2009).(PDF)

  3. A. Debnath, K. G. Ayappa, V. Kumaran and P. Maity, The Influence of Bilayer Composition on the Gel to Liquid Crystalline Transition J. Phys. Chem. B, 113, 10660-10668, (2009).(PDF)

  4. V. Kumaran, Y. K. V. V. N. Krishna Babu and J. Sivaramakrishna, Multiscale modeling of lamellar mesophases, in press, J. Chem. Phys., 130, 114907, (2009).(PDF)

Engineering nanoscale architectures for fuel cells

Fuel cells are emerging as one of the most important energy conversion sources, due to the expected decrease in availability of conventional nonrenewable fuels, as well as due to environmental consideration. Of these, hydrogen fuel cells are the most popular currently, though they have their advantages and disadvantages. The heart of the fuel cell are the catalyst layers at the cathode and anode, and the proton exchange membrane. The oxidation of hydrogen at the anode results in the formation of electrons which pass though the external circuit, and protons which pass through the proton exchange membrane to combine with oxygen at the cathode to form water. Currently, fuel cells can operate at a maximum efficiency of about 0.5-1 amperes per square centimeter of area of the proton exchange membrane, and the potential difference between the cathode and anode side decreases as the current is increased. Though the losses are due to resistances and current leakage at small currents, transport losses become dominant at high currents.

Our objective is to design novel catalyst layers using nanoparticle synthesis and self-assembly, which will provide catalyst layers that minimise transport losses. This will involve engineering nanoscale architectures which can serve as catalyst sites, and which transport electrons across the external circuit and protons through the proton exchange membrane. While reducing transport losses and increasing the current per unit area is the primary objective, a second objective is to decrease the amount of catalyst used, since catalyst cost is a major component of the cost of the fuel cell assembly.

Dynamics of rarefied gas flows

High-speed rarefied gas flows are characterised by high Mach number (velocity is greater than the speed of sound) and moderate or high Knudsen number (mean free path comparable or larger than system size). Continuum Navier-Stokes equations, which are applicable to incompressible gas flows, encounter difficulties at high Mach number due to the formation of shock waves. They cannot be applied at high Knudsen number because the continuum approximation (mean free path much smaller than system size) breaks down. In these cases, it is necessary to use a more fundamental description, which is the Boltzmann equation for the velocity distribution function for the molecules.

In this area, the issues we are interested in is how do the phenomena such as flow instabilites and turbulence, which are continuum phenomena (obtained by solving the continuum Navier-Stokes equations) manifest in a discrete molecular system. An interesting issue is, in the molecular description of a turbulent flow, how would one distinguish between the molecular fluctuating velocities and the turbulent velocity fluctuations. We are setting up both continuum (Discrete Numerical) simulations of the continuum Navier-Stokes equations, as well as simulations of the Boltzmann equation using the Direct Simulation Monte Carlo (DSMC) technique. The latter is challenging because we have to carry out sufficiently large system sizes to reproduce macroscopic phenomena in a molecular simulation. A comparison of these would provide us insights into the molecular origins of continuum dynamical phenomena such as flow instabilities and turbulence. We are currently interested doing test studies on simple configurations such as the flow in a two-dimensional channel and the driven cavity flow.