A proper approach for nonequilibrium molecular dynamics simulations of planar elongational flow

We present nonequilibrium molecular dynamics simulations of planar elongational flow (PEF) by an algorithm proposed by Tuckerman et al. [J. Chem. Phys. 106, 5615 (1997)] and theoretically elaborated by Edwards and Dressler [J. Non-Newtonian, Fluid Mech. 96, 163 (2001)], which we shall call the proper-SLLOD algorithm, or p-SLLOD for short. [For background on names of algorithms see W. G. Hoover, D. J. Evans, R. B. Hickman, A. J. C. Ladd, W. T. Ashurst, and B. Moran, Phys. Rev. A 22, 1690 (1980) and D. J. Evans and G. P. Morriss, Phys. Rev. A 30, 1528 (1984).] We show that there are two sources for the exponential growth in PEF of the total linear momentum of the system in the contracting direction, which has been previously observed using the so-called SLLOD algorithm. The first comes from the SLLOD algorithm itself, and the second from the implementation of the Kraynik and Reinelt [Int. J. Multiphase Flow 18, 1045 (1992)] boundary conditions. Using the p-SLLOD algorithm (to eliminate the first source) implemented with our simulation strategy (to eliminate the second) in PEF simulations, we no longer observe the exponential growth. By analyzing the equations of motion, we also demonstrate that both the SLLOD and the DOLLS algorithms are intrinsically unsuitable for representing a nonequilibrium system with elongational flow. However, the p-SLLOD algorithm has a rigorously canonical structure in laboratory phase space, and thus can represent a nonequilibrium system not only for elongational flow but also for a general flow.     

Molecular dynamics simulation of planar elongational flow at constant pressure and constant temperature

Molecular dynamics simulations of liquid systems under planar elongational flow have mainly been performed in the NVT ensemble. However, in most material processing techniques and common experimental settings, at least one surface of the fluid is kept in contact with the atmosphere, thus maintaining the sample in the NpT ensemble. For this reason, an implementation of the Nose-Hoover integral-feedback mechanism for constant pressure is presented, implemented via the SLLOD algorithm for elongational flow. The authors test their procedure for an atomic liquid and compare the viscosity obtained with that in the NVT ensemble. The scheme is easy to implement, self-starting and reliable, and can be a useful tool for the simulation of more complex liquid systems, such as polymer melts and solutions.     

Viscosity of confined inhomogeneous nonequilibrium fluids

We use the nonlocal linear hydrodynamic constitutive model, proposed by Evans and Morriss [Statistical Mechanics of Nonequilibrium Liquids (Academic, London, 1990)], for computing an effective spatially dependent shear viscosity of inhomogeneous nonequilibrium fluids. The model is applied to a simple atomic fluid undergoing planar Poiseuille flow in a confined channel of several atomic diameters width. We compare the spatially dependent viscosity with a local generalization of Newton's law of viscosity and the Navier-Stokes viscosity, both of which are known to suffer extreme inaccuracies for highly inhomogeneous systems. The nonlocal constitutive model calculates effective position dependent viscosities that are free from the notorious singularities experienced by applying the commonly used local constitutive model. It is simple, general, and has widespread applicability in nanofluidics where experimental measurement of position dependent transport coefficients is currently inaccessible. In principle the method can be used to predict approximate flow profiles of any arbitrary inhomogeneous system. We demonstrate this by predicting the flow profile for a simple fluid undergoing planar Couette flow in a confined channel of several atomic diameters width.     

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.     

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.     

Flow mechanisms in the face-centred cubic micellar gel of a diblock copolymer

The mechanisms of flow of a face-centred cubic micellar phase were investigated using small-angle X-ray scattering (SAXS) for samples under either steady or oscillatory shear in two different geometries: Couette cell and planar shear sandwich. The system studied was a gel formed by a poly(oxyethylene)–poly(oxypropylene) diblock copolymer in water. SAXS indicated that under steady shear in a Couette cell, flow occurs via sliding of hexagonal close-packed (hcp) layers with a close-packed [110] direction along the shear direction. Under oscillatory shear in the planar shear sandwich, coexistence between this orientation and one in which the hcp layers are rotated by 30° (and flow is in a [211] direction) was observed; however, when subject to oscillatory shear in the Couette cell, flow only occurred along a [110] direction. This observation of flow in a non-close-packed direction may be due to alignment induced by the walls of the shear sandwich. Received: 24 February 2001 Accepted: 21 March 2001     

Electroosmotic Flows Created by Surface Defects in Capillary Electrophoresis

We compute the electroosmotic flow in nonuniformly charged planar and cylindrical capillaries for the limit of low-Reynolds-number flows and thin Debye layers. Analytical formulae for the velocity field are provided for the general case of an arbitrary surface inhomogeneity but we also focus on various specific defect geometries. Many important features can be obtained from the simple lubrication approximation. The pressure jump induced by the presence of such surface defects is calculated and the possible occurrence of recirculating flows is discussed, as are effects of the flow perturbations on dispersion in capillary electrophoresis. Copyright 1999 Academic Press.     

Planar mixed flow and chaos: Lyapunov exponents and the conjugate-pairing rule

In this work we characterize the chaotic properties of atomic fluids subjected to planar mixed flow, which is a linear combination of planar shear and elongational flows, in a constant temperature thermodynamic ensemble. With the use of a recently developed nonequilibrium molecular dynamics algorithm, compatible and reproducible periodic boundary conditions are realized so that Lyapunov spectra analysis can be carried out for the first time. Previous studies on planar shear and elongational flows have shown that Lyapunov spectra organize in different ways, depending on the character of the defining equations of the system. Interestingly, planar mixed flow gives rise to chaotic spectra that, on one hand, contain elements common to those of shear and elongational flows but also show peculiar, unique traits. In particular, the influence of the constituent flows in regards to the conjugate-pairing rule (CPR) is analyzed. CPR is observed in homogeneously thermostated systems whose adiabatic (or unthermostated) equations of motion are symplectic. We show that the component associated with the shear tends to selectively excite some of those degrees, and is responsible for violations in the rule.     

A new algorithm for extended nonequilibrium molecular dynamics simulations of mixed flow

In this work, we develop a new algorithm for nonequilibrium molecular dynamics of fluids under planar mixed flow, a linear combination of planar elongational flow and planar Couette flow. To date, the only way of simulating mixed flow using nonequilibrium molecular dynamics techniques was to impose onto the simulation box irreversible transformations. This would bring the simulation to an end as soon as the minimum lattice space requirements were violated. In practical terms, this meant repeating the short simulations to improve statistics and extending the box dimensions to increase the total simulation time. Our method, similar to what has already been done for pure elongational flow, allows a cuboid box to deform in time following the streamlines of the mixed flow and, after a period of time determined by the elongational field, to be mapped back and recover its initial shape. No discontinuity in physical properties is present during the mapping and the simulation can, in this way, be extended indefinitely. We also show that the most general form of mixed flow, in which the angle between the expanding (or contracting) direction and the velocity gradient axis varies, can be cast in a so-called canonical form, in which the angle assumes values that are multiples of π (when a mixed flow exists), by an appropriate choice of the field parameters.     

Analysis of the shape of dendrimers under shear

Nonequilibrium molecular-dynamics simulations are used to investigate the molecular shape of dendrimers and linear polymers in a melt and under shear. Molecules are modeled at the coarse-grained level using a finitely extensible nonlinear elastic bead-spring model. The shape of dendrimers and linear polymers at equilibrium and undergoing planar Couette flow is analyzed quantitatively and it is related to the shear viscosity. The shape of dendrimers responds differently to the influence of shear compared with linear polymers of equivalent molecular mass. However, in both cases the transition from Newtonian to non-Newtonian viscosity behavior corresponds to significant changes in molecular symmetry. This suggests that a shape analysis could be used to estimate the onset of shear thinning in polymers.     

A validation of the p-SLLOD equations of motion for homogeneous steady-state flows

A validation of the p-SLLOD equations of motion for nonequilibrium molecular dynamics simulation under homogeneous steady-state flow is presented. We demonstrate that these equations generate the correct center-of-mass trajectory of the system, are completely compatible with (and derivable from) Hamiltonian dynamics, satisfy an appropriate energy balance, and require no fictitious external force to generate the required homogeneous flow. It is also shown that no rigorous derivation of the SLLOD equations exists to date.     

Theoretical and Experimental Study of an Electrochemical Converter of a Pulsing Electrolyte Flow

A pulsing electrolyte flow through an electrochemical cell with planar gauze electrodes is studied theoretically and experimentally. The presence of steady flows in the cell increases its conversion coefficient and significantly decreases nonlinear distortions in its output current. The upper limiting frequency of a diffusion converter depends on the electrolyte's steady flow rate; at high fluxes, the dependence is quadratic. The adequacy of a quasi-unidimensional model intended for the calculation of basic parameters of real converters is demonstrated experimentally.     

Phase behavior of a simple dipolar fluid under shear flow in an electric field

Nonequilibrium molecular dynamics simulations are performed on a dense simple dipolar fluid under a planar Couette shear flow. Shear generates heat, which is removed by thermostatting terms added to the equations of motion of the fluid particles. The spatial structure of simple fluids at high shear rates is known to depend strongly on the thermostatting mechanism chosen. Kinetic thermostats are either biased or unbiased: biased thermostats neglect the existence of secondary flows that appear at high shear rates superimposed upon the linear velocity profile of the fluid. Simulations that employ a biased thermostat produce a string phase where particles align in strings with hexagonal symmetry along the direction of the flow. This phase is known to be a simulation artifact of biased thermostatting, and has not been observed by experiments on colloidal suspensions under shear flow. In this paper, we investigate the possibility of using a suitably directed electric field, which is coupled to the dipole moments of the fluid particles, to stabilize the string phase. We explore several thermostatting mechanisms where either the kinetic or configurational fluid degrees of freedom are thermostated. Some of these mechanisms do not yield a string phase, but rather a shear-thickening phase; in this case, we find the influence of the dipolar interactions and external field on the packing structure, and in turn their influence on the shear viscosity at the onset of this shear-thickening regime.     

Molecular dynamic simulations of systems undergoing shear

Non-equilibrium molecular dynamics have been used to simulate, at a molecular level, fluids undergoing planar Couette flow. The results give a microscopic picture of the processes involved in viscoelasticity, shear dilatancy, shear birefringence, normal stress effects and shear thinning behavior. The calculations prove that shear dilatant fluids are not necessarily shear thickening. The results also suggest that the constitutive relations governing non-Newtonian behavior are non-analytic functions of strain rate.The calculations have led directly to the development of non-linear irreversible thermodynamics. This generalization of thermodynamics provides a macroscopic understanding of such processes as shear induced phase changes and the relation of shear dilatancy to shear induced energy changes.     

拉格朗日欧拉计算机模拟方法——对牛顿流体的解

用拉格朗日 欧拉方法模拟计算了各种流场中牛顿流体的流动问题 ,并以此来验证该算法的正确性 .其中 ,对具有准确解的二维Poiseuille流动、Couette流动以及同心圆筒间的流动 ,将模拟得到的数值解与数学解析解直接加以比较 ;对没有准确解的绕圆柱的平面流动、平面收缩和扩张流动 ,将模拟结果同一些已经发表的模拟或实验结果相比较 .从文中可见 ,该方法得到的各种结果都是合理、准确的 .     

The bis(p-sulfonatophenyl)phenylphosphine-assisted synthesis and phase transfer of ultrafine gold nanoclusters

The behavior of Couette flow of nanofluids composed of negatively-charged nanoparticles dispersed in aqueous NaCl solutions is studied theoretically. The equation for calculating the Couette flow velocity profiles is derived. The induced electric fields and velocity profiles are calculated as a function of key parameters including nanoparticle size and volume fraction. We have found for the first time that the velocity profile of nanofluids containing charged nanoparticles deviates significantly from the classical linear velocity profile for Couette flow. This previously unseen flow phenomenon is attributed to the dominance of the electric field strength induced by the flow of charged nanoparticles. This new mechanism of nanoparticle-induced microfluidic transport could lead to novel microfluidic and tribological applications.     

The theory of absolute surface shear viscosity V. The effect of finite ring thickness

In the theory of Couette surface viscometers it is convenient to idealize a rotating ring thrust into a fluid interface supporting an adsorbed surface film as making a knife-edge contact of zero thickness. The validity of this assumption is examined by calculating from theory the flow patterns to be expected when the ring makes a contact of finite thickness with the interface. The zero thickness idealization is found to be valid for films of moderate to large surface viscosity, but it fails badly for films of low surface viscosity and places a limit upon the sensitivity of the ring method.     

Internal structure of dendrimers in the melt under shear: a molecular dynamics study

The molecular structure of fluids composed of dendrimers of different generations is studied using nonequilibrium molecular dynamics (NEMD). NEMD results for dendrimer melts undergoing planar Couette flow are reported and analyzed with particular attention paid to the shear-induced changes in the internal structure of dendrimers. The radii of gyration, pair distribution functions and the fractal dimensionality of the dendrimers are determined at different strain rates. The location of the terminal groups is analyzed and found to be uniformly distributed throughout the space occupied by the molecules. The fractal dimension as a function of strain rate displays crossover behavior analogous to the Newtonian/non-Newtonian transition of shear viscosity.     

Electroosmotic flow in microchannels with arbitrary geometry and arbitrary distribution of wall charge

General solutions are developed for direct current (DC) and alternating current (AC) electroosmotic flows in microfluidic channels with arbitrary cross-sectional geometry and arbitrary distribution of wall charge (zeta potential). The applied AC electric field can also be of arbitrary waveform. By proposing a nondimensional time scale varpi defined as the ratio of the diffusion time of momentum across the electric double-layer thickness to the period of the applied electric field, we demonstrate analytically that the Helmholtz-Smoluchowski electroosmotic velocity is an appropriate slip condition for AC electroosmotic flows in typical microfluidic applications. With this slip condition approach, electroosmotic flows in rectangular and asymmetric trapezoidal microchannels with nonuniform wall charge, as examples, are investigated. The unknown constants in the proposed general solutions are numerically determined with a least-squares method through matching the boundary conditions. We find that the wall charge affects significantly the electroosmotic flow while the channel geometry does not. Moreover, the flow feature is characterized by another nondimensional time scale Omega defined as the ratio of the diffusion time of momentum across the channel hydraulic radius to the period of the applied electric field. The onset of phase shift between AC electroosmotic velocity and applied electric field is also examined analytically.     

Oscillating laminar electrokinetic flow in infinitely extended rectangular microchannels

This paper has addressed analytically the problem of laminar flow in microchannels with rectangular cross-section subjected to a time-dependent sinusoidal pressure gradient and a sinusoidal electric field. The analytical solution has been determined based on the Debye-Hückel approximation of a low surface potential at the channel wall. We have demonstrated that Onsager's principle of reciprocity is valid for this problem. Parametric studies of streaming potential have shown the dependence of the electroviscous effect not only on the Debye length, but also on the oscillation frequency and the microchannel width. Parametric studies of electroosmosis demonstrate that the flow rate decreases due to an increase in frequency. The obtained solutions for both the streaming potential and electroosmotic flows become those for flow between two parallel plates in the limit of a large aspect ratio.