Crucial properties of the moment closure model FENE-QE

We investigate four crucial properties for testing and evaluating a moment closure approximation of the FENE dumbbell model for dilute polymer solutions: non-negative configuration distribution function, energy dissipation, accuracy of approximation and computational expense. Through mathematical analysis, numerical experiments and comparisons with closure model FENE-P and FENE-YDL, we prove that the FENE-QE approximation has non-negative configuration distribution function, approximates the energy dissipation behavior of original kinetic theory and provides good accuracy. To improve the efficiency of this closure approximation, we introduce a piecewise linear approximation technique that greatly reduces the computational cost. This extension of FENE-QE, FENE-QE-PLA, is the closure model we recommend for simulating dilute polymer solutions.     

Direct modeling of flow of FENE fluids

Direct simulations of macromolecular fluids are carried out for flows between parallel plates and in expanding and contracting channels. The macromolecules are modeled as FENE dumbbells with soft disks or Lennard-Jones dumbbell-dumbbell interactions. The results are presented in terms of profiles and contour plots of velocity, pressure, temperature, density, and flow fields. In addition the data for potential energy, shear stress, and the normal components of the stress tensor are collected. In general, an excellent agreement is found between the simulated profiles and the well-known flow structures, such as flow separation and formation of viscous eddies, indicating that micro-hydrodynamics is a viable tool in linking macroscopic phenomena with the underlying physical mechanisms. The simulations are performed in the Newtonian regime, for medium-size systems comprising up to 3888 dumbbells. This number is sufficiently large to control boundary and particle number effects. The flow is induced by gravity. The traditional stochastic (thermal) and periodic boundary conditions are employed. Also, diffusive boundary conditions, which could include a stagnant fluid layer and repulsive potential walls, are developed. The scaling problems, which are related to the application of a large external force in a microscopic system (of the size of the order 100 Å), result in extreme pressure and temperature gradients. In addition, the viscosity and thermal conductivity coefficients obtained from velocity and temperature profiles of the channel flow are presented. These results are confirmed independently from modeling of Couette flow by the SLLOD equations of motion and from the Evans algorithm for thermal conductivity.     

Transient free convection of non-Newtonian fluids along a wavy vertical plate including the magnetic field effect

A Prandtl transformation method is applied to study the transient free convection of non-Newtonian fluids along a wavy vertical plate in the presence of a magnetic field. A simple transformation is proposed to transform the governing equations into the boundary-layer equations and solved numerically by the cubic spline approximation. A simple coordinate transformation is employed to transform the complex wavy surface to a vertical flat plate for a constant wall temperature by the numerical method. The effects of the magnetic field parameter, the wavy geometry and the non-Newtonian nature of the fluids on the flow characteristics and heat transfer are discussed in detail.     

Transportation of heat through Cattaneo-Christov heat flux model in non-Newtonian fluid subject to internal resistance of particles

Thermal conduction which happens in all phases(liquid,solid,and gas) is the transportation of internal energy through minuscule collisions of particles and movement of electrons within a working body.The colliding particles comprise electrons,molecules,and atoms,and transfer disorganized microscopic potential and kinetic energy,mutually known as the internal energy.In engineering sciences,heat transfer comprises the processes of convection,thermal radiation,and sometimes mass transportation.Typi...     

A modified SPH method to model the coalescence of colliding non-Newtonian liquid droplets

This paper develops a modified smoothed particle hydrodynamics (SPH) method to model the coalescence of colliding non-Newtonian liquid droplets. In the present SPH, a van der Waals (vdW) equation of state is particularly used to represent the gas-to-liquid phase transition similar to that of a real fluid. To remove the unphysical behavior of the particle clustering, also known as tensile instability, an optimized particle shifting technique is implemented in the simulations. To validate the numerical method, the formation of a Newtonian vdW droplet is first tested, and it clearly demonstrates that the tensile instability can be effectively removed. The method is then extended to simulate the head-on binary collision of vdW liquid droplets. Both Newtonian and non-Newtonian fluid flows are considered. The effect of Reynolds number on the coalescence process of droplets is analyzed. It is observed that the time up to the completion of the first oscillation period does not always increase as the Reynolds number increases. Results for the off-center binary collision of non-Newtonian vdW liquid droplets are lastly presented. All the results enrich the simulations of the droplet dynamics and deepen understandings of flow physics. Also, the present SPH is able to model the coalescence of colliding non-Newtonian liquid droplets without tensile instability.     

Comparison of a new internal viscosity model with other constrained-connector theories of dilute polymer solution rheology

Complex viscosity ^* = -i predictions of the Dasbach-Manke-Williams (DMW) internal viscosity (IV) model for dilute polymer solutions, which employs a mathematically rigorous formulation of the IV forces, are examined in the limit of infinite IV over the full range of frequency number of submolecules N, and hydrodynamic interaction h ^*. Although the DMW model employs linear entropic spring forces, infinite IV makes the submolecules rigid by suppressing spring deformations, thereby emulating the dynamics of a freely jointed chain of rigid links. The DMW () and () predictions are in close agreement with results for true freely jointed chain models obtained by Hassager (1974) and Fixman and Kovac (1974 a, b) with far more complicated formalisms. The infinite-frequency dynamic viscosity predicted by the DMW infinite-IV model is also found to be in remarkable agreement with the calculations of Doi et al. (1975). In contrast to the other freely jointed chain models cited above, however, the DMW model yields a simple closed-form solution for complex viscosity expressed in terms of Rouse-Zimm relaxation times.     

Molecular dynamical study of the energy relaxation processes after heating the vibrational degree of freedom in a diatomic molecular crystal

Energy relaxation processes initiated by sudden heating of the vibrational degree of freedom were studied with molecular dynamical method. A unit cell of bee structure containing 128 diatomic molecules with periodic boundary conditions was considered. Compound Morse potential was assumed as the atom-atom interactions. It was found that the logarithra of the equilibration time depends linearly upon a factorf ₂₁ which is proportional to the frequency ratio of the intra- and inter-molecular vibrations. The project is supported by the National Natural Science Foundation of China.     

Effect of inelastic collisions on the first-order slip coefficients for a diatomic gas with rotational degrees of freedom

When solving problems of inhomogeneous gas dynamics in the slip regime, it is necessary to know the boundary conditions for the velocity, temperature, heat fluxes, etc., that is, the boundary conditions for the gas macroparameters. In particular, such problems arise in developing the theory of thermophoresis of moderately large aerosol particles [1].The problem of monatomic and molecular (di- and polyatomic) gas slip along a boundary surface is considered in many publications (see, for example, [2–8]). The first-order effects include the isothermal and thermal gas slips characterized by the coefficients C_m and K_TS, respectively.In contrast to a monatomic gas, the molecules of diatomic and polyatomic gases have internal degrees of freedom, which considerably complicates the kinetic equation [9]. The lack of reliable models for the intermolecular interaction potential predetermines the need to construct model kinetic equations [10].In this study, for a diatomic gas whose molecules have rotational degrees of freedom, we propose a model kinetic equation obtained by developing the approach described in [6]. With the use of this model equation, the problem of diatomic gas slip along a plane surface is solved. As a result, for diatomic gases the coefficients C_m and K_TS, which depend on the thermophysical gas parameters and the intensity of inelastic collisions, are obtained.Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, 2004, pp. 176–182. Original Russian Text Copyright © 2004 by Poddoskin.     

Nonequilibrium excitation of internal molecular degrees of freedom in the shock layer during hypersonic flight

A kinetic scheme of processes including the formation and quenching of electronically and vibrationally excited particles is proposed for the shock layer adjacent to the surface of a body flying at hypersonic speed. We present results of a numerical calculations for the stagnation point obtained under the thin viscous shock layer approximation for space shuttle flight conditions.We show that the release of atom recombination energy into the internal molecular degrees of freedom and the finite rate of relaxation reduce the calculated heat flux by 20 %.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1.0 and the AMS fonts, developed by the American Mathematical Society.     

Rheology of dense model fluids via nonequilibrium molecular dynamics: Shear thinning and ordering transition

Nonequilibrium molecular dynamics computer simulations are employed to investigate the rheology of dense simple model fluids. Besides the non-Newtonian behavior of the viscosity functions a shear-induced ordering transition is an essential feature of this presentation. Its occurrence in the simulation is supported by a hydrodynamic stability analysis. To illustrate the scenario preceding the instability, density and velocity profiles of the flow are considered as well as the static structure factor which enables a comparison with recent experimental results for dense suspensions. Problems related to experimental evidence of the ordering transition into layers are discussed in light of the derived stability criterion.

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Zusammenfassung Nichtgleichgewichts-Molekulardynamik Computersimulationen werden zur Untersuchung der rheologischen Eigenschaften von dichten einfachen Modell-Fluiden herangezogen. Neben dem nicht-Newtonschen Verhalten der Viskositätsfunktionen steht ein scherinduzierter Ordnungsübergang im Vordergrund der Betrachtungen. Sein Auftreten in der Simulation wird durch eine hydrodynamische Stabilitätsanalyse untermauert. Dichte- und Geschwindigkeitsprofile der Strömung werden zur Veranschaulichung des der Instabilität vorausgehenden Szenarios ebenso herangezogen wie der statische Strukturfaktor, der einen Vergleich mit neuen experimentellen Beobachtungen an dichten Suspensionen ermöglicht. Probleme beim experimentellen Nachweis dieses sich als Schichtenbildung manifestierenden Ordnungsüberganges werden anhand des abgeleiteten Stabilitätskriteriums diskutiert.

     

The boundary layer contribution to intertropical convergence zones in the quasi-equilibrium tropical circulation model framework

Theories for the position and intensity of precipitation over tropical oceans on climate time scales have a perplexing disagreement between those that focus on the momentum budget of the atmospheric boundary layer (ABL) and those that focus on thermodynamic factors. In the case of narrow intertropical convergence zones (ITCZs), there is some evidence for both classes of theories, and there are large open questions on the interpretation of the moist static energy (MSE) and momentum budgets of these regions. We develop a model in which both types of mechanisms can operate and the interaction between them can be analyzed. The model includes a mixed-layer ABL, coupled to a free troposphere whose vertical structure follows the quasi-equilibrium tropical circulation model (QTCM) of Neelin and Zeng. The case analyzed here is axisymmetric, using a fixed sea surface temperature (SST) lower boundary condition with an idealized off-equatorial SST maximum. We examine a regime with small values of the gross moist stability associated with tropospheric motions, which is realistic but poses theoretical challenges. In both rotating (equatorial β-plane) and nonrotating cases, the model ITCZ width and intensity are substantially controlled by the horizontal diffusion of moisture, which is hypothesized to be standing in for nonaxisymmetric transients. The inclusion of the ABL increases the amplitude and sharpness of the ITCZ, contributing to the importance of diffusion. Analytical solutions under simplifying assumptions show that the ABL contribution is not singular in the nondiffusive limit; it just features an ITCZ more intense than observed. A negative gross moist stability contribution associated with the flow component driven by ABL momentum dynamics plays a large role in this. Because of the ABL contribution, the flow imports, rather than exports, MSE in the ITCZ, but we show that this can be understood rather simply. The ABL contribution can be approximately viewed as a forcing to the tropospheric thermodynamics. The ABL forcing term is in addition to thermodynamic forcing by net flux terms in the MSE budget, which otherwise is much as in the standard QTCM. The ABL momentum budget suggests that divergent flow in the ABL is controlled to a significant extent by the pressure gradient imprinted on the ABL by the SST gradient—termed the Lindzen–Nigam contribution—although we also find that the thermodynamics mediating this is nontrivial, especially in the rotating case. Nonetheless, when this component of the pressure gradient is artificially removed, the peak ITCZ precipitation is reduced by a fraction on the order of 15 to 25%, less than might have been expected based on the diagnosis of the ABL momentum budget.     

Testing viscometric predictions of the internal viscosity model,using dilute viscous theta solutions

A stress-symmetrized internal viscosity (I.V.) model for flexible polymer chains, proposed by Bazua and Williams, is scrutinized for its theoretical predictions of complex viscosity ^* () = – i and non-Newtonian viscosity (), where is frequency and is shear stress. Parameters varied are the number of submolecules,N (i.e., molecular weightM = NM _s ); the hydrodynamic interaction,h ^*; and/f, where andf are the I.V. and friction coefficients of the submolecule. Detailed examination is made of the eigenvalues _p (N, h ^*) and how they can be estimated by various approximations, and property predictions are made for these approximations.Comparisons are made with data from our preceding companion paper, representing intrinsic properties [], [], [] in very viscous theta solutions, so that theoretical foundations of the model are fulfilled. It is found that [ ()] data can be predicted well, but that [ ()] data cannot be matched at high. The latter deficiency is attributed in part to unrealistic predictions of coil deformation in shear.     

The influence of matrix viscoelasticity on the rheology of polymer blends

We examine the effects of matrix phase viscoelasticity on the rheological modeling of polymer blends with a droplet morphology. Two contravariant, second-rank tensor variables are adopted along with the translational momentum density of the fluid to account for viscoelasticity of the matrix phase and the ellipsoidal droplet shapes. The first microstructural variable is a conformation tensor describing the average extension and orientation of the molecules in the matrix phase. The other microstructural variable is a configuration tensor to account for the average shape and orientation of constant-volume droplets. A Hamiltonian framework of non-equilibrium thermodynamics is then adopted to derive a set of continuum equations for the system variables. This set of equations accounts for local conformational changes of the matrix molecules due to droplet deformation and vice versa. The model is intended for dilute blends of both oblate and prolate droplets, and droplet breakup and coalescence are not taken into account. Only the matrix phase is considered as viscoelastic; i.e., the droplets are assumed to be Newtonian. The model equations are solved for various types of homogeneous deformations, and microstructure/rheology relationships are discussed for transient and steady-state conditions. A comparison with other constrained-volume rheological models and experimental data is made as well.     

The influence of measurement errors on the determination of the degrees of freedom of dynamic systems

We consider the influence of measurement errors on the experimental calculation of dimensions of possible turbulent flow attractors. For this purpose we considered a Gaussian noise and we carried out some tests showing the existence of a lower limit below which the operational definition of dimension is not reliable.

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Sommario In questo lavoro viene presentata una valutazione della influenza degli errori di misura sulla determinazione sperimentale delle dimensioni di eventuali attrattori di deflussi turbolenti. A tale scopo si considera un rumore Gaussiano. I test effettuati permettono di definire l'esistenza di un minimo al di sotto del quale la definizione operativa di dimensione formisce valori non attendibili.

     

Separation strain rate dependence on the failure of polymer adhesion with mobile promoters

Comprehensive molecular dynamics simulations, employing a coarse-grained bead-spring model, are conducted to study the failure of adhesion between two immiscible polymers stitched together via mobile promoters. A realistic model under separating tension is constructed that enables both chain pulling out viscously and bulk dissipation in two dissimilar glassy polymers that one is dense melt and another is loose. The contributions to the adhesion energy from thermodynamics and chain suction are studied for dependence of the strain rate at fixed basic molecular parameters. With low density of connectors, either adhesion toughness or strength changes slightly with separation strain rate as viscous loss is negligible. But rate effects become evident for long connectors with high density, viscoelastic sliding friction and reptation of chains dominate and the fracture energy increases with strain rate. The results provide insights into the evolution of adhesion surfaces coupled with promoter molecular slipping out of bulk melts, which are useful for future developments of continuum models for failure of polymeric interfaces.     

爆轰等离子体非平衡区的双流体模型

在爆轰等离子体中存在一个由化学反应放热非平衡导致的非平衡电离区。由于电子质量远小于重粒子质量,使得在电离区中电子与重粒子的能量与动量交换效率较低,这也加剧了这种非平衡特性。建立了爆轰等离子体非平衡电离区中的电子和重粒子的双流体模型,并通过该模型研究爆轰等离子体中的非平衡现象。以氢氧爆轰为例计算不同氢氧摩尔比和初始压力条件下,爆轰非平衡区中重粒子参数和电子参数的变化情况。     

Generalization of the Lorenz model to the two-dimensional convection of second-grade fluids

We apply the truncation of the Navier-Stokes-Fourier equations which leads to the Lorenz model, to the investigation of second-grade fluids. The new set of equations proves to work as an approximated approach to 2D-convective dynamics, under the same restrictions as for Newtonian fluids. The different behaviour depends only on α₁ and consists in a “modified” Prandtl number.     

The equations of Reissner-Mindlin plates obtained by the method of internal constraints

The aim of this paper is to give the title theory of shearable plates a precise and exact position with respect to three-dimensional linear elasticity. We assume that the Reissner-Mindlin representation of the displacement field hold in a 3-D body in the shape of a plate, and discuss how a constitutive response consistent with such a representation should be chosen. We find that the Reissner-Mindlin plate theory results from mere integration over the thickness of the equilibrium equations of a cylindrical body made of a linearly elastic material which is both transversely inextensible and transversely isotropic.

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Sommario Scopo di questo articolo è fornire una deduzione esatta, nell'ambito dell'elasticità lineare tridimensionale, della teoria delle piastre deformabili a taglio menzionata nel titolo. Ammesso che la rappresentazione di Reissner-Mindlin per il campo di spostamento valga in una regione tridimensionale a forma di piastra, si discute come scegliere la risposta costitutiva in maniera coerente con quella rappresentazione. Si trova che la teoria delle piastre di Reissner-Mindlin si ottiene per semplice integrazione sullo spessore delle equazioni di equilibrio di un corpo cilindrico che sia costituito di un materiale linearmente elastico tanto trasversalmente inestensibile che trasversalmente isotropo.

     

Numerical investigation from rarefied flow to continuum by solving the Boltzmann model equation

Based on the Bhatnagar–Gross–Krook (BGK) Boltzmann model equation, the unified simplified velocity distribution function equation adapted to various flow regimes can be presented. The reduced velocity distribution functions and the discrete velocity ordinate method are developed and applied to remove the velocity space dependency of the distribution function, and then the distribution function equations will be cast into hyperbolic conservation laws form with non‐linear source terms. Based on the unsteady time‐splitting technique and the non‐oscillatory, containing no free parameters, and dissipative (NND) finite‐difference method, the gas kinetic finite‐difference second‐order scheme is constructed for the computation of the discrete velocity distribution functions. The discrete velocity numerical quadrature methods are developed to evaluate the macroscopic flow parameters at each point in the physical space. As a result, a unified simplified gas kinetic algorithm for the gas dynamical problems from various flow regimes is developed. To test the reliability of the present numerical method, the one‐dimensional shock‐tube problems and the flows past two‐dimensional circular cylinder with various Knudsen numbers are simulated. The computations of the related flows indicate that both high resolution of the flow fields and good qualitative agreement with the theoretical, DSMC and experimental results can be obtained. Copyright © 2003 John Wiley & Sons, Ltd.