A simple, direct derivation and proof of the validity of the SLLOD equations of motion for generalized homogeneous flows

We present a simple and direct derivation of the SLLOD equations of motion for molecular simulations of general homogeneous flows. We show that these equations of motion (1) generate the correct particle trajectories, (2) conserve the total thermal momentum without requiring the center of mass to be located at the origin, and (3) exactly generate the required energy dissipation. These equations of motion are compared with the g-SLLOD and p-SLLOD equations of motion, which are found to be deficient. Claims that the SLLOD equations of motion are incorrect for elongational flows are critically examined and found to be invalid. It is confirmed that the SLLOD equations are, in general, non-Hamiltonian. We derive a Hamiltonian from which they can be obtained in the special case of a symmetric velocity gradient tensor. In this case, it is possible to perform a canonical transformation that results in the well-known DOLLS tensor Hamiltonian.     

Vapor Nucleation and Droplet Growth: Cluster Distribution Kinetics for Open and Closed Systems

A theory based on cluster distribution kinetics for single-monomer addition and dissociation is presented as a framework for homogeneous and heterogeneous vapor nucleation and growth dynamics. For continuous cluster and monomer distributions in a well-mixed non-steady-state flow system, population (mass) balance equations yield moment equations for the cluster mass moments. Nuclei are either homogeneously generated or heterogeneously seeded, and subsequent cluster growth occurs by reversible condensation of vapor monomers. The zeroth moment is the number (or moles) of clusters, the first moment is cluster mass, and the second moment gives cluster-size variance. Solutions are proposed for steady-state flow (open) and non-steady-state batch (closed) systems. Experimental data are interpreted by recognizing that droplets typically observed in nucleation experiments have grown much larger than their nuclei. This allows resolution of the large temperature-dependent discrepancy between experiment and classical nucleation theory. Copyright 2000 Academic Press.     

Diffusioosmotic flows in slit nanochannels

Diffusioosmotic flows of electrolyte solutions in slit nanochannels with homogeneous surface charges induced by electrolyte concentration gradients in the absence of externally applied pressure gradients and potential differences are investigated theoretically. A continuum mathematical model consisting of the strongly coupled Nernst-Planck equations for the ionic species' concentrations, the Poisson equation for the electric potential in the electrolyte solution, and the Navier-Stokes equations for the flow field is numerically solved simultaneously. The induced diffusioosmotic flow through the nanochannel is computed as functions of the externally imposed concentration gradient, the concentration of the electrolyte solution, and the surface charge density along the walls of the nanochannel. With the externally applied electrolyte concentration gradient, a strongly spatially dependent electric field and pressure gradient are induced within the nanochannel that, in turn, generate a spatially dependent diffusioosmotic flow. The diffusioosmotic flow is opposite to the applied concentration gradient for a relatively low bulk electrolyte concentration. However, the electrolyte solution flows from one end of the nanochannel with a higher electrolyte concentration to the other end with a lower electrolyte concentration when the bulk electrolyte concentration is relatively high. There is an optimal concentration gradient under which the flow rate attains the maximum. The induced flow is enhanced with the increase in the fixed surface charge along the wall of the nanochannel for a relatively low bulk electrolyte concentration.     

Flow of Multicomponent Electrolyte Solutions through Narrow Pores of Nanofiltration Membranes

The slow flow of a multicomponent electrolyte solution in a narrow pore of a nanofiltration membrane is considered. The well-known semiempirical method of subdivision of electrical potential into quasi-equilibrium and streaming parts and the definition of streaming concentrations and pressure are discussed. The usefulness of this tool for solving the electrohydrodynamic equations is shown and justified: the use of a small parameter enables a system of electrohydrodynamic partial differential equations to be reduced to a system of ordinary differential equations for streaming functions. Boundary conditions for streaming functions at both the capillary inlet and outlet are derived. The proposed model is developed for the flow of a multicomponent electrolyte solution with an arbitrary number of ions. This is coupled with (i) the introduction of specific interactions between all ions and the pore wall and (ii) the inclusion of the dissociation of water in both conservation and transport equations. Effective distribution coefficients of ions are introduced that are functions of both the specific interaction potentials and the surface potential of the nanofiltration membrane material. The axial dependency of surface potential is expressed by the use of a charge regulation model from which the discontinuity in electric potential and ion pore concentrations at the pore inlet and outlet can be described.A relation between the frequently used capillary and homogeneous models of nanofiltration membranes is developed. An example of application of the homogeneous model for interpretation of experimental data on nanofiltration separation of electrolyte solutions is presented, which shows a reasonable predictive ability for the homogeneous model.     

Gas dynamics in channels of a gas-feed direct methanol fuel cell: exact solutions

The gas dynamics in channels on both sides of a gas-feed direct methanol fuel cell (DFMC) are considered. The basic equations for the flow velocity and density are derived, taking into account the mass and momentum transfer through the channel/backing layer interface. For the practical case of small inlet velocities the analog of the Bernoulli equation is formulated and the exact solution of nonlinear gas dynamics equations is obtained. It is shown that the flow in both the cathode and anode channels is incompressible (its density is constant) and electrochemical reactions affect only the flow velocity v. Simple formulae for v as a function of local current density and effective water drag coefficient are derived.     

Nonlinear (Fluctuational) dynamics and mathematical modeling of homogenous oxidation of biological substrates

Nonlinear dynamics and mathematical modeling approaches were presented for studying chemical oscillations during homogeneous oxidation of biological substrates in the presence of oxygenated complexes of iron(II). It was shown that examination of fluctuational dynamics is only possible via consistent use of several algorithms for time series processing and that flicker-noise spectroscopic technique is best suited to deriving the most exhaustive information from the patterns of temporal variation of signals. The qualitative analysis was performed, and numerical solution was found for the system of differential equations modeling the reactions kinetics. The nature of the steady state was elucidated, and the possibility of Andronov-Hopf type bifurcation with realization of an oscillatory mode was demonstrated.     

The inelastic hard dimer gas: a nonspherical model for granular matter

We study a two-dimensional gas of inelastic smooth hard dimers. Since the collisions between dimers are dissipative, being characterized by a coefficient of restitution alpha<1, and no external driving force is present, the energy of the system decreases in time and no stationary state is achieved. However, the resulting nonequilibrium state of the system displays several interesting properties in close analogy with systems of inelastic hard spheres, whose relaxational dynamics has been thoroughly explored. We generalize to inelastic systems a recently method introduced [G. Ciccotti and G. Kalibaeva, J. Stat. Phys. 115, 701 (2004)] to study the dynamics of rigid elastic bodies made up of different spheres held together by rigid bonds. Each dimer consists of two hard disks of diameter d, whose centers are separated by a fixed distance a. By describing the rigid bonds by means of holonomic constraints and deriving the appropriate collision rules between dimers, we reduce the dynamics to a set of equations which can be solved by means of event-driven simulation. After deriving the algorithm we study the decay of the total kinetic energy, and of the ratio between the rotational and the translational kinetic energy of inelastic dimers. We show numerically that the celebrated Haff's homogeneous cooling law t(-2), describing how the kinetic energy of an inelastic hard-sphere system with a constant coefficient of restitution decreases in time, holds even in the case of these nonspherical particles. We fully characterize this homogeneous decay process in terms of appropriate decay constants and confirm numerically the scaling behavior of the velocity distributions.     

Kinetic flux vector splitting scheme for solving non-reactive multi-component flows

This paper is about multi-component flow. There is no doubt that multi-component flow has a wide range of applications, specially in aerospace it plays a vital role during reentry of space ship into earth's atmosphere thats why it cannot be neglected for a proper vehicle design. In this paper one- and two-dimensional homogenous multi-component flow models are numerically investigated by using a high resolution splitting scheme and this scheme is known as Kinetic Flux Vector Splitting scheme. This scheme preserves positivity conditions and resolves shocks, rarefaction and contact discontinuity. The scheme is based on splitting of flux functions. Moreover Runge-Kutta time stepping technique with MUSCL-type initial reconstruction is used to guarantee higher order accurate solution. This work is first done by Qamar and Warnecke (2004) for the homogeneous multi-component flow equations using central scheme, here we investigate the same work using kinetic flux vector splitting scheme (KFVS) and compared the results with central scheme to verify the efficiency of studied scheme.     

On the Phase Shifts in the Dynamics of the H2O2–Na2S2O3–H2SO4–CuSO4 Oscillator Revealed by Comparison of Potentiometric Responses of Different Indicator Electrodes

The dynamics of the H₂O₂–Na₂S₂O₃–H₂SO₄–CuSO₄ homogeneous pH oscillator was studied in the flow reactor potentiometrically using different sensors: platinum electrode, Cu(II) ion‐selective electrode (Cu‐ISE), and pH‐electrode. It was found that for the flow rates close to two bifurcation values, between which the oscillations exist, there is a detectable phase shift between the response of the Cu‐ISE and other electrodes, while it practically vanishes for the intermediate flow rates. To explain both the oscillations of the Cu‐ISE potential and the relevant phase shift, the system's dynamics was studied both experimentally and numerically. The literature kinetic mechanism of the pH oscillator was extended for the dynamics of the copper(II) and copper(I) species in the form of thiosulfate complexes, and kinetic parameters of the redox equilibria, ensuring the oscillations, were estimated. It was found that the phase shift at the relatively low flow rates occurs due to limited efficiency of the supply of CuSO₄ catalyst, as the species of lowest concentration, to the reactor, and therefore it can be minimized either by increasing the flow rate of all reactants or, alternatively, by enhancing the model concentration of CuSO₄ in the feeding stream, for its fixed flow rate. This work is one more proof that it is useful to monitor the dynamics of the homogeneous oscillatory systems with more than one electrode, if the experimental potential–time courses are to be explained in terms of an appropriate kinetic mechanism.     

Operator splitting algorithm for isokinetic SLLOD molecular dynamics

We apply an operator splitting method to develop a simulation algorithm that has complete analytical solutions for the Gaussian thermostated SLLOD equations of motion [D. J. Evans and G. P. Morriss, Phys. Rev. A 30, 1528 (1984)] for a system under shear. This leads to a homogeneous algorithm for performing both equilibrium and nonequilibrium isokinetic molecular dynamics simulation. The resulting algorithm is computationally efficient. In particular, larger integration time steps can be used compared to simulations with regular Gaussian thermostated SLLOD equations of motion. The utility and accuracy of the algorithm are demonstrated through application to the Weeks-Chandler-Anderson fluid. Although strict conservation of the kinetic energy suppresses thermal fluctuations in the system, this algorithm does not allow simulations at lower shear rates than those normally afforded by older nonequilibrium molecular dynamics simulations.     

动力学方程控制表面反应的模拟模型和方法

提出了动力学方程控制表面反应的模拟模型和方法.该模型从最基本的质量作用定律出发,获得表面反应的动力学方程.而表面反应通过格子模拟反应器进行.通过表面催化样板反应"CO表面催化氧化"检验了该模拟模型和方法,与实验结果吻合.该模型可在其它复杂的表面催化反应体系中推广应用.     

Hydrodynamics of nearly smooth granular gases

Hydrodynamic equations of motion for a monodisperse collection of nearly smooth homogeneous spheres have been derived from the corresponding Boltzmann equation, using a Chapman-Enskog expansion around the elastic smooth spheres limit. Because in the smooth limit the rotational degrees of freedom are uncoupled from the translational ones, it turns out that the required hydrodynamic fields include (in addition to the standard density, velocity, and translational granular temperature fields) the (infinite) set of number densities, n(s,r, t), corresponding to the continuum of values of the angular velocities. The Chapman-Enskog expansion was carried out to high (up to 10th) order in a Sonine polynomial expansion by using a novel computer-aided method. One of the consequences of these equations is that the asymptotic spin distribution in the homogeneous cooling state for nearly smooth, nearly elastic spheres, is highly non-Maxwellian. The simple sheared flow possesses a highly non-Maxwellian distribution as well. In the case of wall-bounded shear, it is shown that the angular velocity injected at the boundaries has a finite penetration length.     

On-the-fly localization of electronic orbitals in Car-Parrinello molecular dynamics

The ab initio molecular-dynamics formalism of Car and Parrinello is extended to preserve the locality of the orbitals. The supplementary term in the Lagrangian does not affect the nuclear dynamics, but ensures "on the fly" localization of the electronic orbitals within a periodic supercell in the Gamma-point approximation. The relationship between the resulting equations of motion and the formation of a gauge-invariant Lagrangian combined with a gauge-fixing procedure is briefly discussed. The equations of motion can be used to generate a very stable and easy to implement numerical integration algorithm. It is demonstrated that this algorithm can be used to compute the trajectory of the maximally localized orbitals, known as Wannier orbitals, in ab initio molecular dynamics with only a modest increase in the overall computer time. In the present paper, the new method is implemented within the generalized gradient approximation to Kohn-Sham density-functional theory employing plane wave basis sets and atomic pseudopotentials. In the course of the presentation, we briefly discuss how the present approach can be combined with localized basis sets to design fast linear scaling ab initio molecular-dynamics methods.     

Generation of dynamic temporal and spatial concentration gradients using microfluidic devices

This paper describes a microfluidic approach to generate dynamic temporal and spatial concentration gradients using a single microfluidic device. Compared to a previously described method that produced a single fixed gradient shape for each device, this approach combines a simple "mixer module" with gradient generating network to control and manipulate a number of different gradient shapes. The gradient profile is determined by the configuration of fluidic inputs as well as the design of microchannel network. By controlling the relative flow rates of the fluidic inputs using separate syringe pumps, the resulting composition of the inlets that feed the gradient generator can be dynamically controlled to generate temporal and spatial gradients. To demonstrate the concept and illustrate this approach, examples of devices that generate (1) temporal gradients of homogeneous concentrations, (2) linear gradients with dynamically controlled slope, baseline, and direction, and (3) nonlinear gradients with controlled nonlinearity are shown and their limitations are described.     

Homogeneous nucleation of particles from the vapor phase in thermal plasma synthesis

Particle nucleation and growth are simulated for iron vapor in a thermal plasma reactor with an assumed one-dimensional flow field and decoupled chemistry and aerosol dynamics. Including both evaporation and coagulation terms in the set of cluster-balance rate equations, a sharply defined homogeneous nucleation event is calculated. Following nucleation the vapor phase is rapidly depleted by condensation, and thereafter particle growth occurs purely by Browntan coagulation. The size and number of nucleated particles are found to be affected strongly by the cooling rate and by the initial monomer concentration. An explanation is presented in terms of the response time of the aerosol to changing thermodynamic conditions.This work appears in abbreviated from in the proceedings of the International Symposium on Combustion and Plasma Synthesis of High Temperature Materials, San Francisco, Oct. 24–26, 1988, to be published asCombustion and Plasma Synthesis of Hig Temperature Materials, Z. A. Munir and J. B. Holt (eds.), VCH, New York (in press).     

Langevin dynamics in constant pressure extended systems

The advantages of performing Langevin dynamics in extended systems are discussed. A simple Langevin dynamics scheme for producing the canonical ensemble is reviewed, and is then extended to the Hoover ensemble. We show that the resulting equations of motion generate the isobaric-isothermal ensemble. The Parrinello-Rahman ensemble is then discussed and we show that despite the presence of intrinsic probability gradients in this system, a Langevin dynamics approach samples the extended phase space in the correct fashion. The implementation of these methods in the ab initio plane wave density functional theory code CASTEP [M. D. Segall, P. L. D. Lindan, M. J. Probert, C. J. Pickard, P. J. Hasnip, S. J. Clarke, and M. C. Payne, J. Phys.: Condens. Matter 14, 2717 (2003)] is demonstrated.     

Molecular simulation study of cavity-generated instabilities in the superheated Lennard-Jones liquid

Previous equilibrium-based density-functional theory (DFT) analyses of cavity formation in the pure component superheated Lennard-Jones (LJ) liquid [S. Punnathanam and D. S. Corti, J. Chem. Phys. 119, 10224 (2003); M. J. Uline and D. S. Corti, Phys. Rev. Lett. 99, 076102 (2007)] revealed that a thermodynamic limit of stability appears in which no liquidlike density profile can develop for cavity radii greater than some critical size (being a function of temperature and bulk density). The existence of these stability limits was also verified using isothermal-isobaric Monte Carlo (MC) simulations. To test the possible relevance of these limits of stability to a dynamically evolving system, one that may be important for homogeneous bubble nucleation, we perform isothermal-isobaric molecular dynamics (MD) simulations in which cavities of different sizes are placed within the superheated LJ liquid. When the impermeable boundary utilized to generate a cavity is removed, the MD simulations show that the cavity collapses and the overall density of the system remains liquidlike, i.e., the system is stable, when the initial cavity radius is below some certain value. On the other hand, when the initial radius is large enough, the cavity expands and the overall density of the system rapidly decreases toward vaporlike densities, i.e., the system is unstable. Unlike the DFT predictions, however, the transition between stability and instability is not infinitely sharp. The fraction of initial configurations that generate an instability (or a phase separation) increases from zero to unity as the initial cavity radius increases over a relatively narrow range of values, which spans the predicted stability limit obtained from equilibrium MC simulations. The simulation results presented here provide initial evidence that the equilibrium-based stability limits predicted in the previous DFT and MC simulation studies may play some role, yet to be fully determined, in the homogeneous nucleation and growth of embryos within metastable fluids.     

Impact of homogeneous–heterogeneous reactions on heat and mass transfer flow of Au–Eg and Ag–Eg Maxwell nanofluid past a horizontal stretched cylinder

The object of this study is to analyze the impact of heterogeneous and homogeneous reactions on the flow, heat and mass transfer analysis of Maxwell nanofluid of Tiwari–Das kind over a stretched cylinder by considering convective boundary condition and velocity slip. Ethylene glycol (Eg) is used as base fluid; while gold (Au) and silver (Ag) are taken as nanoparticles. The governing equations represent nanofluid momentum, and energy and mass are reduced to system of nonlinear ordinary differential equations by utilizing similarity transformation procedure and are numerically evaluated by using finite element method. The sway of several pertinent parameters on the sketches of velocity, temperature and concentration is plotted through graphs. In addition to that the values of rate of heat transfer and skin-friction coefficient are calculated and presented through tables. The values of skin-friction coefficient are intensified as the values of homogeneous–heterogeneous reaction parameters rises. The velocity and concentration scatterings are both declines as the strength of Maxwell parameter raises.