Simulation of a confined polymer in solution using the dissipative particle dynamics method

The dynamics of a bead-and-spring polymer chain suspended in a sea of solvent particles are examined by dissipative particle dynamics (DPD) simulations. The solvent is treated as a structured medium, comprised of particles subject to both solvent-solvent and solvent-polymer interactions and to stochastic Brownian forces. Thus hydrodynamic interactions among the beads of the polymer evolve naturally from the dynamics of the solvent particles. DPD simulations are about two orders of magnitude faster than comparable molecular dynamics simulations. Here we report the results of an investigation into the effects of confining the dissolved polymer chain between two closely spaced parallel walls. Confinement changes the polymer configuration statistics and produces markedly different relaxation times for chain motion parallel and perpendicular to the surface. This effect may be partly responsible for the gap width-dependent theological properties observed in nanoscale rheometry.Paper presented at the Twelfth Symposium on Thermophysical Properties, June 19–24, 1994, Boulder, Colorado, U.S.A.     

杜仲胶/天然橡胶共混物的分子动力学模拟和耗散粒子动力学模拟

应用分子动力学(MD)和耗散粒子动力学(DPD)模拟方法对杜仲胶(TPI)、天然橡胶(NR)的相容性进行了研究。采用MD模拟方法,在COMPASS力场下,对纯物质在不同聚合度下的溶度参数、一系列共混比的TPI/NR共混物内聚能密度、Flory-Huggins作用参数进行了模拟计算,确定了纯物质单链的聚合度,经判断各比例共混物的相容性均较好;采用DPD模拟方法对TPI/NR共混体系的相结构进行了研究,从等密度图可以进一步判断共混体系的相容性;分析比较两种纯物质的径向分布函数,揭示了其相互作用的本质;经过分析比较静态力学性能,发现共混比为1/3的TPI/NR共混物性能最佳,其结论与实验结果一致。     

An implementation of no-slip boundary conditions in DPD

We report an implementation of the no-slip boundary condition in the modeling of solid boundaries by dissipative particle dynamics (DPD) method. Stimulated by a model for several types of solid boundaries, we develop an implementation that satisfies no-slip boundary condition with practically no-density distortion near the boundaries. The model is implemented to simulate the planar Poiseuille and Couette flows, as well as the flow through a contraction and diffusion channel. Results compare excellently with the previous methods.     

Influence of inelastic collision on the dynamic behavior of particle sedimentation in high-viscosity fluids

To further understand the characteristics of particle–fluid flow, the particle sedimentation process in a high-viscosity fluid is conducted with both experimental and numerical methods. In this work, inelastic collisions between particles during the sedimentation process are observed. Different from the sedimentation in a low-viscosity fluid, the increase of particle sedimentation velocity can be found due to the inelastic collisions in a high-viscosity fluid. This phenomenon is more obvious with the increase of the particle volume fractions and the viscosity of the fluid. The necessary conditions for the inelastic collision phenomenon are determined based on the viscous dissipative dynamics of particle collisions. According to the experimental and numerical results, the interactions between particles in high-viscosity liquids are mainly the inelastic collisions which caused the particle aggregation. The correction coefficient of particle sedimentation velocity equation is obtained, and the applicability of the equation for the sedimentation in a high-viscosity fluid is improved.     

Liquid-crystalline ordering in rod-coil diblock copolymers studied by mesoscale simulations

Using mesoscale dissipative particle dynamics (DPD) simulations, which ignore all atomistic details, we show the formation of lamella mesophases by cooling a fully disordered system composed of symmetric (A7B7) rod-coil diblock copolymers. Equilibration is achieved very rapidly using DPD, and isotropic, smectic A and crystalline phases of the rod-like blocks can be observed either by heating or cooling. An interesting pseudo-smectic phase can be characterized when the order-disorder transition temperature is above the clearing temperature. This phase gradually fades into a normal microphase-separated structure as the system is heated through the clearing temperature. Simulations of pure rods, however, show the formation of isotropic, nematic, smectic A and crystalline phases.     

剪切场作用下短纤维复合材料纤维取向的耗散粒子动力学研究

为了描述短纤维复合材料注射充模过程的介观结构生成、演化规律,借鉴硬棒模型和粒子模型,建立了一种修正的耗散粒子动力学模型,采用修正的Verlet算法对剪切场作用下短纤维复合材料熔体纤维取向进行研究,模拟结果与实际基本符合.     

Extension of nonlinear Onsager theory of irreversibility

Nonlinear Onsager theory in combination with Wang’s representation theorem is utilized to obtain nonlinear constitutive equations for fluid. The constitutive equations can be derived using the derivative of a dissipative function according to nonlinear Onsager’s theory. The requirement of the dissipative function is convexity in thermodynamic force and continuity in thermodynamic flux. An isothermal fluid is provided as an example. Objectivity is required for the constitutive equations of the fluid. Such an axiom permits that all response functions are isotropic functions and can be expressed by Wang’s representation theorem. Therefore, the dissipative part of Cauchy stress is obtained using (i) Wang’s representation theorem only and (ii) both nonlinear Onsager theory and Wang’s representation theorem. In method (i), the coefficients for the constitutive equations are only constrained by the Clausius–Duhem inequality, while in method (ii), these are not only constrained by Clausius–Duhem inequality but also by the positive semidefiniteness of the Hessian matrix of the dissipative function (convexity of the dissipative function).     

The velocity autocorrelation function of nanoparticles in a hard-sphere molecular system

The diffusion of nanoparticles in a dense molecular medium representing a fluid (liquid or gas) composed of hard absolutely elastic spheres was studied by the molecular dynamics method in a broad range of the medium density. It was established that relaxation of the velocity autocorrelation function of the particles is well described by a superposition of two exponents with different characteristic relaxation times. Dependence of the velocity autocorrelation function on the particle and radius and on the carrying fluid density was studied.     

Concerning the alternating-sign dissipation of energy in a fluid with relaxing viscous stresses

Total equations of motion of an incompressible fluid are investigated taking account of relaxation phenomena for viscous stresses and heat flux. In the K. I. Strakhovich class of solutions the fluid flows are considered that contain a strong hydrodynamic discontinuity. The conditions of motion are analyzed under which the dissipative function is negative. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 70, No. 6, pp. 967–974, November–December, 1997.     

Influence of particle elasticity in shear testers

Two dimensional simulations of non-cohesive granular matter in a biaxial shear tester are discussed. The effect of particle elasticity on the mechanical behavior is investigated using two complementary distinct element methods (DEM): Soft particle molecular dynamics simulations (Particle Flow Code, PFC) for elastic particles and contact dynamics simulations (CD) for the limit of perfectly rigid particles. As soon as the system dilates to form shear bands, it relaxes the elastic strains so that one finds the same stresses for rigid respectively elastic particles in steady state flow. The principal stresses in steady state flow are determined. They are proportional to each other, giving rise to an effective macroscopic friction coefficient which is about 10% smaller than the microscopic friction coefficient between the grains.     

Simulation of granular packing of particles with different size distributions

The study of granular matter composed of spherical particles is of interest in manufacturing, material, and metallurgy. The viscoelastic and frictional contacts between the particles are the cause of forming the agglomeration. We present a numerical simulation for particles packing with three different kinds of size distributions: monosize, bimodal, and Gaussian, using distinct element method (DEM). The particles are initially put randomly but without any overlap, and then fall down due to the gravity force and collide with neighbor particles. Because of the dissipative factors of viscoelastic collision and frictional force, all the particles finally come together to form an agglomeration. Coordination number, porosity, radial distribution function, and force distribution are calculated for different size distributions. It is demonstrated that particle size distribution does affect the granular packing structure.     

Viscous dissipative power density function for poroelastic saturated materials at high frequencies

A viscous dissipative power density function is defined for poroelastic saturated materials at high frequencies. In the framework of Biot’s general theory of acoustics of poroelastic materials, the correction factor of the flow resistance of the fluid from low to high frequencies is derived from the power density function. For this aim the dissipative forces per unit volume are obtained from the viscous dissipative power density. The complex dynamic correction function of the viscosity is derived for the motion of a fluid limited by two parallel planes’ boundaries. It is also derived for the motion of a fluid in a cylindrical duct. Analytical solutions and impedance tube test results on air saturated porous metals are compared to validate the viscous dissipative power density up to frequencies of 6 kHz. A second comparison is performed for kerosene saturated porous metals. Finally, a validation is performed using ultrasonic experiments on water saturated bones.     

Simulation of Sheared Suspensions With a Parallel Implementation of QDPD

A parallel quaternion-based dissipative particle dynamics (QDPD) program has been developed in Fortran to study the flow properties of complex fluids subject to shear. The parallelization allows for simulations of greater size and complexity and is accomplished with a parallel link-cell spatial (domain) decomposition using MPI. The technique has novel features arising from the DPD formalism, the use of rigid body inclusions spread across processors, and a sheared boundary condition. A detailed discussion of our implementation is presented, along with results on two distributed memory architectures. A parallel speedup of 24.19 was obtained for a benchmark calculation on 27 processors of a distributed memory cluster.     

The Effect of Frequency Sweeping and Fluid Flow on Particle Trajectories in Ultrasonic Standing Waves

Particle concentration and separation in ultrasonic standing waves through the action of the acoustic radiation force on suspended particles are discussed. The acoustic radiation force is a function of the density and compressibility of the fluid and the suspended particles. A two-dimensional theoretical model is developed for particle trajectory calculations. An electroacoustic model is used to predict the acoustic field in a resonator, driven by a piezoelectric transducer. Second, the results of the linear acoustic model are used to calculate the acoustic radiation force acting on a particle suspended in the resonator. Third, a particle trajectory model is developed that integrates the equation of motion of a particle subjected to a buoyancy force, a fluid drag force, and the acoustic radiation force. Computational fluid dynamics calculations are performed to calculate the velocity field that is subsequently used to calculate fluid drag. For a fixed frequency excitation, the particles are concentrated along the stable node locations of the acoustic radiation force. Through a periodic sweeping of the excitation frequency particle translation is achieved. Two types of frequency sweeps are considered, a ramp approach and a step-change method. Numerical results of particle trajectory calculations are presented for two configurations of flow-through resonators and for two types of frequency sweeping. It is shown that most effective particle separation occurs when the fluid drag force is orthogonal to the acoustic radiation force.     

Efficient direct position determination of orthogonal frequency division multiplexing signals

The authors present an efficient method for positioning of orthogonal frequency division multiplexing (OFDM) signals. The method, called direct position determination (DPD), enables one to determine the emitter position in a single search operation. In formerly published articles on DPD, the signal was assumed to be a narrowband Gaussian source, which was subjected to a rather simple flat-fading channel model. Here, the authors extend the DPD algorithm to handle the OFDM signals that propagate through a frequency-selective channel, and derive the least squares estimator (LSE) for the problem. In addition, the authors present a method for a fine 2D position estimation, which enables one to reduce the DPD computational complexity without compromising on its estimation accuracy.     

An efficient algorithm for granular dynamics simulations with complex-shaped objects

One of the most difficult aspect of the realistic modeling of granular materials is how to capture the real shape of the particles. Here we present a method to simulate two-dimensional granular materials with complex-shaped particles. The particle shape is represented by the classical concept of a Minkowski sum, which permits the representation of complex shapes without the need to define the object as a composite of spherical or convex particles. A well defined interaction force between these bodies is derived. The algorithm for identification of neighbor particles reduces force calculations to O(N), where N is the number of particles. The method is much more efficient, accurate and easier to implement than other models. We prove that the algorithm is consistent with energy conservation, which is numerically verified using non-dissipative granular dynamics simulations. Biaxial test simulations on dissipative granular systems demonstrate the relevance of shape in the strength and stress fluctuations at the critical state.     

强耦合流激振动的建模及求解的预测多修正算法

将基于Lagrangian描述的结构振动问题与基于Eulerian描述的不可压缩粘性流动问题通过流-固系统的功率耗散平衡在广义变分原理的框架下统一,建立了描述强耦合流激振动的有限元控制方程。采用将Newmark法和Hughes预测多修正法相结合的求解策略,提出了基于稳定有限元法求解小变形弹性结构强耦合流激振动的计算方法,用于计算复杂边界条件下的流激振动问题。以三维混流式水轮机叶道为例的数值算例表明,模拟结果与试验实测结果吻合较好。     

Nearly exact solution for coupled continuum/MD fluid simulation

A general statistical approach is described to couple the continuum with molecular dynamics in fluid simulation. Arbitrary thermodynamic field boundary conditions can be imposed on an MD system while minimally disturbing the particle dynamics of the system. And by acting away from the region of interest through a feedback control mechanism, across a buffer zone where the disturbed dynamics are allowed to relax, we can eliminate that disturbance entirely. The field estimator, based on maximum likelihood inference, serves as the detector of the control loop, which infers smooth instantaneous fields from the particle data. The optimal particle controller, defined by an implicit relation, can be proved mathematically to give the correct distribution with least disturbance to the dynamics. A control algorithm compares the estimated current fields with the desired fields at the boundary and modifies the action of the particle controller far way, until they eventually agree. This method, combined with a continuum code in a Schwarz iterative domain-decomposition formalism, provides a mutually consistent solution for steady-state problems, as particles in the MD region of interest have no way to tell any difference from reality. Finally, we explain the importance of using a higher order single-particle distribution function, in light of the Chapman–Enskog development for shear flow. This revised version was published online in July 2006 with corrections to the Cover Date.     

Collective drag and sedimentation: comparison of simulation and experiment in two and three dimensions

We simulate systems of particles immersed in fluid at Reynolds numbers on the particle scale of 0.1 to 20. Our simulation method is based on a finite differencing multi-grid Navier-Stokes solver for the fluid and a molecular dynamics technique for the particle motion. The mismatch between the fixed rectangular grid and the spherical particle shape is taken into account by considering analytical series expansions of the pressure and velocity of the fluid in the vicinity of the particle surface. We give an expression for the force on a particle in terms of the expansion coefficients. At each time step these coefficients are determined from pressure and velocity values on the fluid grid. We demonstrate the validity of our approach by performing numerical simulations of flow through porous solid beds and of bulk sedimentation in two and three spatial dimensions. We compare our results to experimental data and analytical results. Quantitative agreement is found in situations where the volume fraction remains below approximately 0.25 both in two and three dimensions, provided that at the same time the Reynolds number remains below about 10. In contrast, e.g., to finite-element techniques the method remains fast enough to allow dynamical simulations of particle-fluid systems with several hundred spheres on workstations taking all inertial effects into account.     

Response of multilayered composite laminates to dynamic surface loads

A theoretical investigation of the response of multilayered composite laminates to concentrated and distributed dynamic surface loads is carried out. Each layer of the laminate is assumed to be transversely isotropic and dissipative with arbitrarily oriented symmetry axis. The dissipative property of the material is modeled approximately through the introduction of a frequency-dependent damping function. A multiple transform technique is used to calculate the spectra and time histories of the displacements and stresses produced by a variety of dynamic loads, and the quantitative features of the waves produced in the laminate are determined. The methodology developed in this work is expected to be useful in the prediction of the response of composite laminates to impact loads and also in the characterization of acoustic emission (AE) sources in these materials under static and dynamic loads.