Force between the plates of a plane capacitor in a fluid: a rigorous thermodynamic analysis

Summary A critical analysis of the literature on the deduction of the well-known expression of the attractive force between the plates of a plane-parallel capacitor completely immersed in a linear dielectric fluid is presented. Then, rigorous deductions of this force are proposed. It is shown that, contrary to the statement reported in most references, no pressure difference exists between the fluid within the plates and the external fluid.     

磁流体中Helmholtz和Kelvin力的界定

磁流体磁彻体力的两种简化形式Helmholtz力和Kelvin力具有一定的适用范围.在推导磁流体中的磁彻体力表达式基础上,分析Helmholtz力和Kelvin力在磁流体中的起源,得出两种形式的成立条件.计算结果表明:当磁流体磁导率与外磁场强度无关时,磁流体磁彻体力可由Helmholtz力表示;当磁流体中磁性颗粒的平均磁矩与磁流体比体积无关时,Kelvin力为磁彻体力的简化形式;在磁流体磁化系数与其密度成正比情况下,Helmholtz力可转换为Kelvin力. 关键词： 磁流体 磁彻体力 Helmholtz力 Kelvin力     

The mechanism of the attracting acoustic radiation force on a polymer-coated gold sphere in plane progressive waves

Acoustic plane progressive waves incident on a sphere immersed in a nonviscous fluid exert a steady force acting along the direction of wave motion. It is shown here that when an elastic gold sphere is coated with a polymer-type (polyethylene) viscoelastic layer, this force becomes a force of attraction in the long wavelength limit. Kinetic, potential and Reynolds stress energy densities are defined and evaluated with and in the absence of absorption in the layer. Without absorption, the mechanical energy density counteracts the Reynolds stress energy density, which causes a repulsive force. However, in the case of absorption, the attractive force is predicted to be a physical consequence of a mutual contribution of both the mechanical and the Reynolds stress energy densities. This condition provides an impetus for further designing acoustic tweezers operating with plane progressive waves as well as fabricating polymer-coated gold particles for specific biophysical and biomedical applications.     

负绝对温度下的勒夏忒列原理

本文指出,在负绝对温度下的勒夏忒列原理其形式可以不变,唯关于副“力”作用的内容却与正绝对温度情况的相反。并附带指出,关于麦氏关系问题应满足什么条件才能符合勒夏忒列原理的推论。     

A boundary condition capturing immersed interface method for 3D rigid objects in a flow

To simulate the flow around an object, we can replace the object with the fluid enclosed by a singular force. We can then simulate the flow on a fixed domain with a fluid–fluid interface supporting the singular force. In this paper, we present a boundary condition capturing approach to determine the singular force for a 3D rigid object. We apply a discontinuous body force to enforce the rigid motion of the fluid replacing the object and compute the singular force based on the kinematics of the object. Due to the singular force and the body force, the flow is not smooth across the interface. We solve the flow using the immersed interface method. Our boundary condition capturing immersed interface method is very efficient and stable, and its accuracy based on the infinity norm is near second order for the velocity and above first order for the pressure.     

A class of Cartesian grid embedded boundary algorithms for incompressible flow with time-varying complex geometries

We present a class of numerical algorithms for simulating viscous fluid problems of incompressible flow interacting with moving rigid structures. The proposed Cartesian grid embedded boundary algorithms employ a slightly different idea from the traditional direct-forcing immersed boundary methods: the proposed algorithms calculate and apply the force density in the extended solid domain to uphold the solid velocity and hence the boundary condition at the rigid-body surface. The principle of the embedded boundary algorithm allows us to solve the fluid equations on a Cartesian grid with a set of external forces spread onto the grid points occupied by the rigid structure. The proposed algorithms use the MAC (marker and cell) algorithm to solve the incompressible Navier-Stokes equations. Unlike projection methods, the MAC scheme incorporates the gradient of the force density in solving the pressure Poisson equation, so that the dipole force, due to the jump of pressure across the solid-fluid interface, is directly balanced by the gradient of the force density. We validate the proposed algorithms via the classical benchmark problem of flow past a cylinder. Our numerical experiments show that numerical solutions of the velocity field obtained by using the proposed algorithms are smooth across the solid-fluid interface. Finally, we consider the problem of a cylinder moving between two parallel plane walls. Numerical solutions of this problem obtained by using the proposed algorithms are compared with the classical asymptotic solutions. We show that the two solutions are in good agreement.     

Buoyancy Force in Liquid Fluidized Beds of Mixed Particles

The literature represents the buoyancy force on particles in a fluidized bed in two different ways: one is based on the density of the fluid alone and the other is based on the density of the suspension comprised of the fluid and solid. To clarify this problem is especially important for mixing/segregation phenomena in fluidized beds of mixed particles. This paper, presents a brief review of the literature and provides experimental evidence to conclude for the correct expression of the buoyancy force in fluidized beds.     

纳米通道滑移流动的分子动力学模拟研究

本文采用非平衡分子动力学方法对平板纳米通道滑移流动进行了非平衡分子动力学模拟,获得了不同壁面势能和不同温度时流体的速度分布及密度分布。研究结果表明滑移速度在很大程度上决定于流体温度和壁面吸引力作用强度的大小。由于不同壁面吸引力时流体的密度分布受温度的影响规律不同,使得不同壁面吸引力时流体的滑移速度受温度影响规律也不一致。而且,流体结构受壁面流速的影响要受到壁面势能的制约。     

Visualization study on the layer formation of electro-rheological fluid

The visualization study on the microstructure of the Electro-Rheological (ER) fluid was carried out. The dense particle motion was difficult to visualize because of the severe light scattering by the particle itself. In this study, the laser light sheet was illuminated to visualize the dense particle condition, 10 wt%. As the ER fluid, the cholesterol particles (∼20 mm) were dispersed into the silicone oil (10 cS). The humidity of particle was controlled to be 4%. The particle density was set to be 10 wt%. Under this condition, individual particle could not be distinguished. However, the particle cluster motion could be clearly visualized. With the electrical field, the chains of the particles were formed. The ER fluid with the chain was recorded onto the video camera. With higher electrical field, the layer of the particle was formed at the top and bottom electrode. The layer caused the decrease of the fluid channel width, resulting in the resistance to be increased. The effects of electrical field on the layer formation were experimentally investigated. The Mason number, which is the ratio of shear force to electrical force, was found to be the key parameter of the layer formation.     

An immersed boundary energy-based method for incompressible viscoelasticity

Incompressible viscoelastic materials are prevalent in biological applications. In this paper we present a method for incompressible viscoelasticity in which the elasticity of the material is described in Lagrangian form (i.e. in material coordinates), and Eulerian (spatial) coordinates are used for the equations of motion and to enforce the incompressibility condition. The elastic forces are computed directly from an energy functional without the use of stress tensors, and the immersed boundary method is used to communicate between Lagrangian and Eulerian variables. The method is first applied to a warm-up problem, in which a viscoelastic incompressible material fills a two-dimensional periodic domain. For this problem, we study convergence of the velocity field, the deformation map, and the Eulerian force density. The numerical results indicate that the velocity field and deformation map converge strongly at second order and the Eulerian force density converges weakly at second order. Incompressibility is well maintained, as indicated by area conservation in this 2D problem. Finally, the method is applied to a three-dimensional fluid–structure interaction problem with two different materials: an isotropic neo-Hookean model and an anisotropic fiber-reinforced model.     

Convective motion and transfer of force by many-body hydrodynamic interaction

We consider hydrodynamic interactions between N rigid bodies of arbitrary shape immersed in an incompressible fluid. When the bodies are carried along by an incident flow without exerting forces or torques on the fluid then their translational and rotational velocities are linearly related to the incident flow velocity by convection kernels. In the absence of an incident flow, but with applied forces and torques, the force density acting on the fluid is linearly related to the forces and torques by transfer kernels. We show that the convection and transfer kernels are simply related by a symmetry relation. For freely moving bodies the force density exerted on the fluid is related to the incident flow by a convective friction kernel. We show that this kernel is symmetric.     

Axial radiation force of a bessel beam on a sphere and direction reversal of the force

An expression is derived for the radiation force on a sphere placed on the axis of an ideal acoustic Bessel beam propagating in an inviscid fluid. The expression uses the partial-wave coefficients found in the analysis of the scattering when the sphere is placed in a plane wave traveling in the same external fluid. The Bessel beam is characterized by the cone angle beta of its plane wave components where beta=0 gives the limiting case of an ordinary plane wave. Examples are found for fluid spheres where the radiation force reverses in direction so the force is opposite the direction of the beam propagation. Negative axial forces are found to be correlated with conditions giving reduced backscattering by the beam. This condition may also be helpful in the design of acoustic tweezers for biophysical applications. Other potential applications include the manipulation of objects in microgravity. Islands in the (ka, beta) parameter plane having a negative radiation force are calculated for the case of a hexane drop in water. Here k is the wave number and a is the drop radius. Low frequency approximations to the radiation force are noted for rigid, fluid, and elastic solid spheres in an inviscid fluid.     

Electric Field-Induced Fluid Velocity Field Distribution in DNA Solution

We present an analytical solution for fluid velocity field distribution of polyelectrolyte DNA. Both the electric field force and the viscous force in the DNA solution are considered under a suitable boundary condition. The solution of electric potential is analytically obtained by using the linearized Poisson-Boltzmann equation. The fluid velocity along the electric field is dependent on the cylindrical radius and concentration. It is shown that the electric field-induced fluid velocity will be increased with the increasing cylindrical radius, whose distribution also varies with the concentration     

Hydrodynamic fluctuation forces

We consider the fluctuating hydrodynamics of Landau and Lifshitz for a fluid confined by hard walls at finite distance. By considering the non-linearity of the stochastic fluid equations of motion, we show that there can be an inhomogeneous average stress set up throughout the fluid. The average stress corresponds to a force density on the fluid which is expressed in terms of the Green's function for the fluid in the linearized theory. For simple geometries we obtain the average stress explicitly as a long range pressure field. The effect can be interpreted as a long range effective force acting between the fluid boundaries. In this sense it might have observable consequences in thin films or in suspensions of hard colloid particles. The effect is strongest in incompressible fluids. It is greatly weakened by compressibility but relaxation of the fluid viscosity prevents the effect vanishing.     

Linear and non-linear theories of solvation forces in fluids

From an exact expression for the free energy of a non-uniform classical fluid, due to Saam and Ebner, a closure is used to develop a non-linear theory for the density and solvation force between two planar walls. In the linear limit these expressions reduce to ones used successfully elsewhere. Numerical solution of the equations for a hard sphere fluid shows that while the density profiles predicted by the two theories are markedly different, the solvation forces are similar.     

Frequency dependence of the acoustic radiation force acting on absorbing cylindrical shells

The frequency dependence of the radiation force function Y(p) for absorbing cylindrical shells suspended in an inviscid fluid in a plane incident sound field is analysed, in relation to the thickness and the content of their interior hollow region. The theory is modified to include the effect of hysteresis type absorption of compressional and shear waves in the material. The results of numerical calculations are presented for two viscoelastic (lucite and phenolic polymer) materials, with the hollow region filled with water or air indicating how damping and change of the interior fluid inside the shell's hollow region affect the acoustic radiation force. The acoustic radiation force acting on cylindrical lucite shells immersed in a high density fluid (in this case mercury) and filled with water in their hollow region, is also studied.     

Implicit velocity correction-based immersed boundary-lattice Boltzmann method and its applications

A version of immersed boundary-lattice Boltzmann method (IB-LBM) is proposed in this work. It is based on the lattice Boltzmann equation with external forcing term proposed by Guo et al. [Z. Guo, C. Zheng, B. Shi, Discrete lattice effects on the forcing term in the lattice Boltzmann method, Phys. Rev. E 65 (2002) 046308], which can well consider the effect of external force to the momentum and momentum flux as well as the discrete lattice effect. In this model, the velocity is contributed by two parts. One is from the density distribution function and can be termed as intermediate velocity, and the other is from the external force and can be considered as velocity correction. In the conventional IB-LBM, the force density (external force) is explicitly computed in advance. As a result, we cannot manipulate the velocity correction to enforce the non-slip boundary condition at the boundary point. In the present work, the velocity corrections (force density) at all boundary points are considered as unknowns which are computed in such a way that the non-slip boundary condition at the boundary points is enforced. The solution procedure of present IB-LBM is exactly the same as the conventional IB-LBM except that the non-slip boundary condition can be satisfied in the present model while it is only approximately satisfied in the conventional model. Numerical experiments for the flows around a circular cylinder and an airfoil show that there is no any penetration of streamlines to the solid body in the present results. This is not the case for the results obtained by the conventional IB-LBM. Another advantage of the present method is its simple calculation of force on the boundary. The force can be directly calculated from the relationship between the velocity correction and the force density.     

非保守力与自然对流

为研究自然对流流动和换热的实质,对重力场中自然对流的驱动力进行了进一步分析,提出了自然对流产生的充分必要条件。以二维封闭方腔内空气自然对流为对象,分别对三种不同的自然对流形式进行了数值模拟。结果表明:只要流体所受体积力为非保守力,即可产生自然对流。这为自然对流的控制提供了一定的理论依据。     

N阶闪耀光栅衍射理论分析

首先用标量衍射理论导出一般周期物射效率的推论，然后求出了Ｎ阶二元闪耀光栅衍射效率公式；最后分别对理想情形和有误差情形进行了讨论。     

Propagation of electron cyclotron waves in a weakly relativistic plasma with steep density and temperature profiles

Summary A detailed analysis is made of the deduction of systems of differential equations describing the propagation of both ordinary and extraordinary waves in the electron cyclotron frequency range in a stratified plasma, perpendicularly to the magnetic field and across the electroncyclotron fundamental resonance layer. The equations are derived under conditions of not too large electron temperature (the so-called weakly relativistic condition) and of very weak nonuniformities of the confining magnetic field. The effects of the nonhomogeneities of the equilibrium plasma density and temperature are carefully examined. It is shown that the propagation equations derived previously in the literature can be extended with only a moderately larger effort in computations to take account also of very strong density and temperature gradients.