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Complex fluids, such as polymeric or amphiphilic systems, are governed by processes interacting within a broad range of time and length scales, from the nanometre to microns and beyond. Standard simulation techniques are not suited to bridge this gap because they are built to independently describe each complexity level, from the nanoscale via molecular dynamics (MD), to the mesoscale and beyond, via dissipative particle dynamics (DPD) or continuum fluid dynamics (CFD).
In many cases, the complex region of the system is located near a surface or interface (e.g. membrane) which may exchange mass, momentum, and/or energy with the surrounding fluid. In this talk we present a new multiscale technique that can link the several complexity levels within these scenarios. The proposed hybrid scheme connects a domain described at atomistic level with a region treated via continuum fluid dynamics. The complex interfacial region is solved via MD and connected to a CFD description of the bulk flow that enables the exchange of hydrodynamic information from and to the MD region. This hybrid description can greatly reduce the computational time, without losing any relevant atomistic information. Our coupling protocol is based on the balance of fluxes of conserved quantities across the particle/continuum interface and it works for unsteady flows involving mass, momentum, and energy transfers.
The particle-continuum hybrid scheme is also extremely useful to study complex boundary conditions in micro-fluidics (such as rough surfaces in microchannels), adhesion, wetting, or even crystal growth from fluid phase, where energy and mass exchanges are dominant processes. Most of the applications involve time-dependent flows and to illustrate the applicability of the method we shall present simulations of oscillatory shear flow in microchannels. In this example, the bottom region of the channel is described at atomistic level, while the rest of channel, including the moving boundary condition (top wall), is described via CFD.
Concerning applications, we have used the hybrid method to study the dynamics of a single tethered polymer under shear flow. The results agree extremely well with those obtained via full MD simulations and with the available experimental data on tethered DNA chains stretched under shear flow, published by Doyle et al. [Phys. Rev. Lett. 84, 4769 (2000)]. Some comments on this relevant problem and future applications shall be also mentioned.
For further information we refer to: R. Delgado-Buscalioni and P. V. Coveney, Phys. Rev. E 67, 046704 (2003) R. Delgado-Buscalioni and P. V. Coveney. J. Chem. Phys. 119, 978 (2003) R. Delgado-Buscalioni and P. V. Coveney, Hybrid particle-continuum fluid dynamics, Phil. Trans. R. Soc. Lond. (in press), http://xxx.arxiv.cornell.edu/abs/physics/0401093. S. Barsky, R. Delgado-Buscalioni, and P.V. Coveney, Comparison of molecular dynamics to hybrid molecular dynamics-computational fluid dynamics for a single tethered polymer in solution (submitted to J. Chem. Phys), http://arXiv.org/abs/cond-mat/0401392.
We report results obtained with Aaron Wynveen of hybrid gas dynamics-hydrodynamics simulations that show that experimentally produced vapor pulses have structure arising from shock waves formed in the vapor. The shock waves form due to the presence of a gradient in the small ambient background of helium vapor in the experimental chamber and are extremely sensitive to the pulse power. The methods by which conservation laws are satisfied across the gas dynamics-particle dynamics boundary will be described and further potential applications of the method will be mentioned.
I shall show how Galilean-invariance can be restored in the Stochastic Rotation Dynamics Model (Multi-Particle Collision Model) by a random shift of the computational grid before the collision step. Green-Kubo relations will be derived for this modified model by means of a projector-operator technique.
I will discuss how the random shift makes it possible to resum the terms in the Green-Kubo relations. This enormously simplifies the evaluation of these infinite sums and leads to exact formulae for all transport coefficients. Numerical evaluations of the density correlations are presented in order to obtain the heat conductivity and the bulk viscosity in the microcanonical ensemble.
Finally, corrections to the viscosity due to correlations among particles prior to collisions are analyzed numerically and theoretically.
I will introduce the real-coded lattice gas (Malevanets-Kapral) model of colloidal systems. Colloids are systems containing at least two components, one dispersed in the other. The dispersed components are generally small particles, droplets, or vesicles. Polluted water, milk, cosmetics, and blood are cited as examples of colloids.
Since the effective solute-solute interaction is modified by the fluid flows, the nature of the colloidal system would be changed when an external flow field is applied to the fluid. The straightforward calculation of dynamics on solutes and the solvent is required to capture complex flows of colloidal systems.
We have developed two models of colloidal systems using the Malevanets-Kapral model. One is a model of a colloidal system consisting of rigid obstacles and fluid. We have derived the probability distribution function (PDF) for the post-velocity of fluid particles collided against obstacles. In the simulation, the post-velocity of those particles is decided randomly from the PDF, and the net difference of momenta between pre- and post-collision of those particles is regarded as the force on the obstacle. The Brownian motion of an obstacle was reproduced using this model. Some examples of flow simulations are presented.
The second is a model of deformable colloidal particles such as droplets. Droplets covered with amphiphilic molecules can hardly coalesce into one big droplet. The system is called an emulsion.
We have developed the immiscible multi-phase fluid to simulate flows of emulsions. The kernel algorithm is Rothman-Keller type dynamics of colored particles. The stable dispersion or aggregation of immiscible droplets could be controlled by a model parameter. The flow simulation of immiscible droplets in porous media is presented.
Surfactants are substances that preferentially accumulate at interfaces between two fluids, altering the local surface tension. Non-uniform distribution of surfactant on an interface induces a Marangoni force tangential to the interface, in addition to the usual normal surface tension force. This Marangoni force tends to make the surfactant distribution uniform, as does diffusion of surfactant along the interface. External imposition of a tangential flow of sufficient strength can counteract this tendency toward uniformity by dragging the surfactant toward a single location on the interface. In regions of high surfactant concentration the surface tension is low, so the interface offers less resistance to deformation and can become highly curved. This work is primarily focused on applications involving the formation of such regions and the subsequent pinch-off of very small droplets or bubbles.
A numerical method to simulate interfacial surfactant mechanics within a volume of fluid method has been developed. Two important features of this new method are that it conserves surfactant mass exactly and the form of the equation of state is not restricted, i.e. the relation between surfactant concentration and surface tension can be linear or nonlinear. To conserve surfactant, the surfactant mass and the interfacial surface area are tracked as the interface evolves, and then the surfactant concentration is reconstructed. The algorithm is coupled to an incompressible Navier-Stokes solver that uses a continuum method to incorporate both the normal and tangential components of the surface tension force into the momentum equation.
Numerical simulations demonstrate the effect of surfactant on the dynamics of several problems by comparison to surfactant-free simulations. First, the buoyant rise of a bubble is examined. Next, the evolution of a drop in an extensional flow is studied. Finally, the motion of a drop through a constriction is investigated. In each of these problems surfactant accumulation allows high interface curvature and the formation of small secondary drops or bubbles.
A sketch of the Multi-Particle Collision Model will be given. In this model mesoscopic particle dynamics consists of free streaming interrupted by multi-particle collisions. The multi-particle collisions are carried out by performing random rotations of particle velocities in predetermined cells in a manner that conserves mass, momentum, and energy. The algorithmic implementation of the method will be described and its theoretical basis will be justified. An indication of how hydrodynamic equations may be obtained from the model and hydrodynamic flows can be simulated will be given.
A hybrid molecular dynamics multi-particle collision model, where full molecular dynamics of molecules is combined with the mesoscopic dynamics of the surrounding fluid, will be described. An application of this hybrid model to the study the influence of diffusion on the rate constants of the A+C <--> B+C reaction will be described. Reactive and non-reactive interactions with catalytic solute particles are described by full molecular dynamics and the remainder of the dynamics by the multi-particle collision model. Results of three-dimensional simulations will be presented. In the limit of a dilute solution of catalytic C particles, the simulation results will be compared with diffusion equation approaches for both the irreversible and reversible reaction cases. Simulation results for systems where the volume fraction of catalytic spheres is high will also be presented, and collective interactions among reactions on catalytic spheres that introduce volume fraction dependence in the rate constants will be discussed. Finally, generalizations of the multi-particle collision model to pattern-forming reactive systems will be described briefly.
Brownian Dynamics (BD) is a stochastic simulation method that can quantitatively describe the behavior of polymers in flow and electric fields. With the increasing use of nano- and microfluidic devices for the handling of biopolymers such as DNA, BD has the potential to be a powerful design tool for the separation and transport processes carried out in these devices. As a coarse-grained simulation method, BD also serves as a natural bridge between atomistic and continuum modeling. In this talk, an introduction to the Brownian Dynamics simulation method will be given along with simulation results for some nano- and microfluidic systems of current interest. The introduction will review basic molecular models for polymers (bead-rod, bead-spring) and the stochastic differential equations used to describe their dynamics. The applications will focus on polymer stretching and transport in complex electroosmotic flows and polymer electrophoresis in narrow channels.
Break up and coalescence between liquid volumes are typically initiated and driven by instabilities and motions that occur at macroscopic scales. The actual transitions in interface topology occur, however, at microscopic scales. Although a number of instabilities leading to breakup are fairly well characterized, this is not true for coalescence. Also, the microscopic mechanisms leading to the actual break or coalescence between volumes are not understood. Finally, it is unclear how to couple the macroscopic and microscopic behaviors into physically meaningful and accurate models useful for practical applications. The status of knowledge in these areas will be outlined, and some suggestions for future research directions will be given.
Because polymers are very large molecules their dynamics are by, by atomic standards, very slow. To access time-scales long enough to calculate the real (long-time, or low frequency) transport coefficients we need to be able to simulate polymeric systems on times approaching seconds. We also need to model hydrodynamic interactions, which significantly influence polymer dynamics, and fluctuations that cause the instantaneous shape to fluctuate. To do so we use a simple off-lattice particle model solvent that I will show does a surprisingly good job of this. Reaching the time-scale we are interested in is only possible, however, if we represent real long polymers with polymers modelled using a vastly smaller number of repeating units. This raises the issue, can we show that in any meaningful way we model the dynamic behaviour of a real long polymer with such a short model one? After all, the dynamics of short and long polymers normally differ significantly. Putting things together I will argue that we can indeed claim to study long time dynamics of long polymers with simulations of chains composed of only a few beads. We have used the method to calculate the low frequency visco-elastic response of dilute and semi-dilute polymer solutions in the long chain limit. The simulations shed light on how hydrodynamic interactions propagate, the role of interpolymer hydrodynamics and the limitations of theories that neglect the time dependence of these interactions.
In many practical applications polymer solutions are moving through confined geometries. Modeling confined geometries with an off-lattice particle model solvent has proved problematic. I will describe how we have tackled this problem in such a way that we can locate a boundary in continuous space and reproduce correct hydrodynamic behaviour right up to the solid/solvent interface. We have used this method to calculate flow velocities for polymers in confined geometries. These are size dependent and differ from the solvent flow velocities (a principle used in hydrodynamic chromatography). These results allow us to determine the successes and failures of simple excluded volume models used to predict the magnitude of this effect.
The proper inclusion of hydrodynamic interactions is fundamental in simulation of complex fluids. We investigate fluids with embedded particles described by a mesoscopic simulation technique called Multi-Particle-Collision Dynamics (MPCD). We find two dynamical regimes for a fluid simulated by MPCD. In the .particle. regime the system displays gas-like behavior, the hydrodynamic interactions are weak and diffusion dominates the dynamic. In the .collective. regime the system exhibits a fluid-like behavior and the hydrodynamic interactions are fully developed. We study how hydrodynamic interactions appear in a simple fluid and which are the consequences for some relevant properties as the diffusion coefficient. These results are then used to study the dynamics of short polymer chains in solution. In the .collective. regime of the solvent, we obtain excellent agreement of our simulation results with the predictions of Zimm theory for the center-of-mass diffusion coefficient and the relaxation times of the Rouse modes.
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