Simulation study on microstructure formations in magnetic fluids

We propose the Langevin-type microscopic equations of motion for magnetic fluids. Magnetic fluids are modeled as an ensemble of interacting ferromagnetic nanoparticles suspended in a viscous fluid. The present model is described in terms of position vectors of nanoparticles and orientation vectors of their magnetic dipole moments. In this model, forces and torques arising from the magnetic origin and the surrounding fluid flow are included. Effects of non-spherical particle shape are also taken into account. From the Brownian dynamics simulations of the model, it is found that the present model exhibits various microstructure formation processes in magnetic fluids.     

流体黏性及表面张力对气泡运动特性的影响

基于气泡边界层理论,引入黏性修正,采用边界积分法,考虑黏性效应和表面张力在单气泡以及双气泡耦合作用过程中的影响.首先将建立的数值模型与Rayleigh-Plesset的解析解进行对比,发现二者符合良好,验证了数值模型的有效性;在此基础上,建立考虑流体弱黏性效应的双气泡耦合模型,研究流体黏性和表面张力作用下,气泡表面变形、射流速度、流场能量转换等物理量的变化规律;最后研究雷诺数和韦伯数对于气泡脉动特性的影响规律.结果表明,流体黏性会抑制气泡脉动和气泡射流发展,降低气泡半径和射流速度;表面张力不改变气泡脉动幅值,但缩短了脉动周期,提升气泡势能.     

First-principles calculation of excited states of diatomic molecules: a benchmark for the Gutzwiller conjugate gradient minimisation method

We recently proposed the Gutzwiller conjugate gradient minimisation (GCGM) method for efficient and accurate calculation of the ground state total energy of molecular and bulk systems. The GCGM method is developed under the framework of Gutzwiller wave function but goes beyond the commonly adopted Gutzwiller approximation to improve the accuracy and flexibility in treating the correlation effects. In this conference proceeding, we benchmark the GCGM method with the calculation of excited state potential energy curves of three diatomic molecules, namely H₂, N₂, and O₂. Our calculations demonstrate the flexibility and reasonable accuracy of the method.     

Fallopian tube analysis of the peristaltic-ciliary flow of third grade fluid in a finite narrow tube

The present prospective theoretical investigation deals with analysis of the peristaltic-ciliary transport of a developing embryo within the fallopian tubal fluid in the human fallopian tube. A mathematical model of peristalsis-cilia induced flow of viscoelastic fluid characterized by the third grade fluid model within the fallopian tubal fluid in a finite two dimensional narrow tube is developed. Non-linear partial differential equation resulting from the modelling of the proposed model is solved using perturbation method. Flow variables like axial and radial velocities, appropriate residue time over tube length, pressure difference over wavelength and stream function are analyzed for embedded parameters and constants. Salient features of the pumping characteristics and trapping phenomenon are discussed in detail. The analysis showed that embedded parameters and constants have opposite effects on axial velocity and appropriate residue time over tube length. Moreover, a comparison of the peristaltic flow with the peristaltic-ciliary flow and the third grade fluid with the linearly viscous fluid is made as a special case. The relevance of the current results to the transport of a developing embryo within the fallopian tubal fluid is also explored. It reveals that, third grade fluid instead of the linearly viscous fluid and the inclusion of cilia along with peristalsis help to complete the required mitotic divisions while transporting the developing embryo within the fallopian tubal fluid in the human fallopian tube.     

Flow-thermoelastic vibration and instability analysis of viscoelastic carbon nanotubes embedded in viscous fluid

The flexural vibration of viscoelastic carbon nanotubes (CNTs) conveying fluid and embedded in viscous fluid is investigated by the nonlocal Timoshenko beam model. The governing equations are developed by Hamilton's principle, including the effects of structural damping of the CNT, internal moving fluid, external viscous fluid, temperature change and nonlocal parameter. Applying Galerkin’s approach, the resulting equations are transformed into a set of eigenvalue equations. The validity of the present analysis is confirmed by comparing the results with those obtained in literature. The effects of the main parameters on the vibration characteristics of the CNT are also elucidated. Most results presented in the present investigation have been absent from the literature for the vibration and instability of the CNT conveying fluid.     

Some exact solutions of magnetized viscous model in string cosmology

In this paper, we study anisotropic Bianchi-V Universe with magnetic field and bulk viscous fluid in string cosmology. Exact solutions of the field equations are obtained by using the equation of state (EoS) for a cloud of strings, and a relationship between bulk viscous coefficient and scalar expansion. The bulk viscous coefficient is assumed to be inversely proportional to the expansion scalar. It is interesting to examine the effects of magnetized bulk viscous string model in early and late stages of evolution of the Universe. This paper presents different string models like geometrical (Nambu string), Takabayasi (p-string) and Reddy string models by taking certain physical conditions. We discuss the nature of classical potential for viscous fluid with and without magnetic field. The presence of bulk viscosity stops the Universe from becoming empty in its future evolution. It is observed that the Universe expands with decelerated rate in the presence of viscous fluid with magnetic field whereas, it expands with marginal inflation in the presence of viscous fluid without magnetic field. The other physical and geometrical aspects of each string model are discussed in detail.     

黏性流体中超细长弹性杆的动力学不稳定性

基于坐标基矢摄动的方法研究了黏性流体中超细长弹性杆动力学稳定性判据与失稳后的模态选择,推导出了黏性介质中超细长弹性杆Kirchoff动力学方程的一阶摄动表示,即线性的二阶偏微分方程组.以平面扭转DNA环为例,说明了以上结果的应用,得到了平面扭转DNA环的稳定性判据及其稳定的临界区域,讨论了其失稳后的模态选择及黏性阻力对其的影响.     

汽轮机小长径比静叶片的优化径向积叠

应用粘性流动数值计算对叶轮机械叶片进行设计，能够使设计者对几种不同设计方案进行分析以满足设计要求，并获得最佳设计方案．本文采用三维N．S方程组和Baldwin-Lomax湍流模型，对一个小长径比的汽轮机导叶进行三维粘性流场数值模拟．计算结果表明，采用合适的周向弯曲（优化径向积叠）同样可以提高短叶片的效率．本计算方法可用来分析和研究叶片径向积叠形式对径向和周向流量平均绝热效率的影响，以获得较优的积叠形式．     

An analysis of the semi-analytic solutions of a viscous fluid with old and new definitions of fractional derivatives

In this paper we present the natural convection flow of an incompressible viscous fluid subject to Newtonian heating and constant mass diffusion using a recently developed definition of the Caputo–Fabrizio fractional derivative. Boundary layer equations in dimensionless form are obtained by means of dimensionless variables. The expressions for the temperature, concentration and velocity fields are obtained in the Laplace transformed domain. The inverse Laplace transform for the temperature, concentration and velocity field are found numerically by means of Stehfest's and Tzou's algorithms. A comparative analysis has been carried between the Caputo–Fabrizio and the Caputo fractional model obtained by Vieru (2015) through graphical illustration. At the end, we can see the impact of the flow parameters, including the new fractional parameter, on the flow which is presented graphically. As a result, the fractional viscous fluid model with the Caputo–Fabrizio fractional derivative has a higher velocity than with the Caputo.     

非等温非牛顿黏性流体流动问题的修正光滑粒子动力学方法模拟

为准确、有效地模拟非等温非牛顿黏性流体的流动问题,本文基于一种不含核导数计算的核梯度修正格式和不可压缩条件给出了一种改进光滑粒子动力学(SPH)离散格式,它较传统SPH离散格式具有较高精度和较好稳定性.同时,为准确地描述温度场的演化过程,建立了非牛顿黏性的SPH温度离散模型.通过对等温Poiseuille流、喷射流和非等温Couette流、4:1收缩流进行模拟,并与其他数值结果作对比,分别验证了改进SPH方法模拟非牛顿黏性流动问题的可靠性和提出的SPH温度离散模型求解非等温流动问题的有效性和准确性.随后,运用改进SPH方法结合SPH温度离散模型对环形腔和C形腔内非等温非牛顿黏性流体的充模过程进行了试探性模拟研究,分析了数值模拟的收敛性,讨论了不同位置处热流参数对温度和流动的影响.     

Constraints on the generalized Chaplygin gas model from Gamma-ray bursts

We study the generalized Chaplygin gas model (GCGM) using Gamma-ray bursts as cosmological probes. In order to avoid the so-called circularity problem we use cosmology-independent data set and Bayesian statistics to impose constraints on the model parameters. We observe that a negative value for the parameter α is favoured in a flat Universe and the estimated value of the parameter H₀ is lower than that found in literature.     

Adhesion and fingering in the lifting Hele-Shaw cell: Role of the substrate

The lifting Hele-Shaw cell (LHSC) is used to study adhesion as well as viscous fingering. In the present paper we report a series of observations of development of the interface for different viscous fluids, both Newtonian and non-Newtonian, in a LHSC operated at a constant lifting force. Glass and perspex are used as the plates in two different sets of experiments. The objectives are 1) to measure the time required to separate the plates as a function of the lifting force and 2) to note the force above which viscous fingering appears. We find that for the Newtonian fluids, the plate separation time follows a universal power law with the lifting force, irrespective of fluid and substrate. The non-Newtonian fluids too, with proper scaling obey the same power law. The appearance of fingering, however, depends on the properties of the fluid as well as the substrate. We suggest a modified form of the capillary number which controls the onset of fingering; this new quantity, termed the “fingering parameter” involves the dielectric constants of the substrate and fluid in addition to the viscosity and surface tension.     

Stability analysis of the rotor of ultrasonic motor driving fluid directly

The stability of the rotor of ultrasonic motor driving fluid directly is a key to its applications and control. This paper introduced the acoustic streaming and acoustic viscous stress near the boundary layer. Following this, the effect of acoustic viscous force on the stability of the rotor of ultrasonic motor driving fluid directly was presented in detail. The result showed that this system can be equivalent to a mass-spring and the spring constant can be used to weigh the stability of the rotor. By this model and relevant experiments, factors that affect the stability of the rotor such as the driving frequency, the rotor's weight and radius, the saturated acoustic streaming velocity, the mode number of stator vibration, the fluid's height and type are investigated and useful guidelines for design and application are obtained.     

Effect of the ion slip on the MHD flow of a dusty fluid with heat transfer under exponential decaying pressure gradient

In the present study, the unsteady Hartmann flow with heat transfer of a dusty viscous incompressible electrically conducting fluid under the influence of an exponentially decreasing pressure gradient is studied without neglecting the ion slip. The parallel plates are assumed to be porous and subjected to a uniform suction from above and injection from below while the fluid is acted upon by an external uniform magnetic field applied perpendicular to the plates. The equations of motion are solved analytically to yield the velocity distributions for both the fluid and dust particles. The energy equations for both the fluid and dust particles including the viscous and Joule dissipation terms, are solved numerically using finite differences to get the temperature distributions.     

Viscous quark‐gluon plasma in the early universe

In the present work a study is given for the evolution of a flat, isotropic and homogeneous Universe, which is filled with a causal bulk viscous cosmological fluid. We describe the viscous properties by an ultra‐relativistic equation of state, and bulk viscosity coefficient obtained from recent lattice QCD calculations. The basic equation for the Hubble parameter is derived by using the energy equation obtained from the assumption of the covariant conservation of the energy‐momentum tensor of the matter in the Universe. By assuming a power law dependence of the bulk viscosity coefficient, temperature and relaxation time on the energy density, we derive the evolution equation for the Hubble function. By using the equations of state from recent lattice QCD simulations and heavy‐ion collisions we obtain an approximate solution of the field equations. In this treatment for the viscous cosmology, no evidence for singularity is observed. For example, both the Hubble parameter and the scale factor are finite at t = 0, where t is the comoving time. Furthermore, their time evolution essentially differs from the one associated with non‐viscous and ideal gas. Also it is noticed that the thermodynamic quantities, like temperature, energy density and bulk pressure remain finite. Particular solutions are also considered in order to prove that the free parameter in this model does qualitatively influence the final results.     

A Fictitious Domain,parallel numerical method for rigid particulate flows

In this paper, we develop a Fictitious Domain, parallel numerical method for the Direct Numerical Simulation of the flow of rigid particles in an incompressible viscous Newtonian fluid. A Simultaneous Directions Implicit algorithm is employed which gives the model a high level of parallelization. The projection of the fluid velocity onto rigid motion on the particles is based on a fast computational technique which relies on the conservation of linear and angular momenta. Numerical results are presented which confirm the ability of the proposed method to simulate the sedimentation of one and many particles; the parallel efficiency of the algorithm is also assessed.     

Curvature in causal BD-type inflationary cosmology

We study a closed model of the universe filled with viscous fluid and quintessence matter components in a Brans-Dicke type cosmological model. The dynamical equations imply that the universe may look like an accelerated flat Friedmann-Robertson-Walker universe at low redshift. We consider here dissipative processes which follow a causal thermodynamics. The theory is applied to viscous fluid inflation, where accepted values for the total entropy in the observable universe are obtained.     

I. Formation and rise of a bubble stream in a viscous liquid

The continuous emission of gas bubbles from a single ejection orifice immersed in a viscous fluid is considered. We first present a semi empirical model of spherical bubble growth under constant flow conditions to predict the bubble volume at the detachment stage. In a second part, we propose a physical model to describe the rise velocity of in-line interacting bubbles and we derive an expression for the net viscous force acting on the surrounding fluid. Experimental results for air/water-glycerol systems are presented for a wide range of fluid viscosity and compared with theoretical predictions. An imagery technique was used to determine the bubble size and rise velocity. The effects of fluid viscosity, gas flow rate, orifice diameter and liquid depth on the bubble stream dynamic were analyzed. We have further studied the effect of large scale recirculation flow and the influence of a neighbouring bubble stream on the bubble growth and rising velocity. Received: 23 July 1997 / Revised: 16 December 1997 / Accepted: 11 May 1998     

Signal propagation in the general theory of relativity with viscosity and thermal conductivity: Linear theory

The Eckart-Landau-Lifshitz classical relativistic models of a viscous, heat-conducting fluid are known to lead to an infinite signal propagation velocity. This infinite value contradicts the postulate of a limiting signal velocity, equal to the velocity of light in vacuum. It is suggested that this paradox might be resolved by incorporating internal relaxation processes in the particles of the medium. It has been shown previously that in the special theory of relativity the velocity of a signal in a viscous, heat-conducting fluid with inheritance turns out to be finite. That assertion is proved in the present paper within the framework of the general theory of relativity in the approximation of a weak gravitational field.Institute of Earth Physics, Russian Academy of Sciences. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 13–18, May, 1993.     

Direct pore-level modeling of incompressible fluid flow in porous media

We present a dynamic particle-based model for direct pore-level modeling of incompressible viscous fluid flow in disordered porous media. The model is capable of simulating flow directly in three-dimensional high-resolution micro-CT images of rock samples. It is based on moving particle semi-implicit (MPS) method. We modify this technique in order to improve its stability for flow in porous media problems. Using the micro-CT image of a rock sample, the entire medium, i.e., solid and fluid, is discretized into particles. The incompressible Navier–Stokes equations are then solved for each particle using the MPS summations. The model handles highly irregular fluid–solid boundaries effectively. An algorithm to split and merge fluid particles is also introduced. To handle the computational load, we present a parallel version of the model that runs on distributed memory computer clusters. The accuracy of the model is validated against the analytical, numerical, and experimental data available in the literature. The validated model is then used to simulate both unsteady- and steady-state flow of an incompressible fluid directly in a representative elementary volume (REV) size micro-CT image of a naturally-occurring sandstone with 3.398 μm resolution. We analyze the quality and consistency of the predicted flow behavior and calculate absolute permeability using the steady-state flow rate.