Effect of tangential electric field on the evolution of the Rayleigh-Taylor instability of a dielectric liquid film

The effect of surface ponderomotive forces produced by a uniform tangential electric field on the evolution of the Rayleigh-Taylor instability of an isothermal film of a homogeneous incompressible dielectric liquid coating the lower surface of a horizontal insulating plate is studied in the long-wavelength approximation for the hydrodynamic equations and a simplified system of electrostatics equations. The lower boundary of the liquid is the interface with a stationary gas. It is shown in the framework of the linear theory that during the disruption of the continuous film, ponderomotive forces induce the formation of liquid billows extended along the applied field lines.     

Incorporation of smooth spherical bodies in the Lattice Boltzmann method

A method to simulate bodies suspended in a Lattice Boltzmann solvent is proposed. It is based on a generalized reaction force that enforces no-slip boundary conditions at the fluid–body interface as the limiting case of an iterative procedure. A smooth version of the Heaviside function allows to treat spherical particles of arbitrary size and produces smooth hydrodynamic forces as particles move in the continuum. Numerical tests demonstrate the accuracy of the method in reproducing the hydrodynamic field around a single particle and the fluid-mediated forces between pairs of particles. The drag force experienced by a particle moving in a straight channel and at various Reynolds numbers is studied as a non-trivial testcase.     

Acoustic flows in a fluid layer on a vibrating substrate

The field of radiation forces in a fluid layer on a solid substrate is calculated. This field is formed during propagation of surface capillary wave along a free surface. The wave is excited by substrate vibrations as a result of instability development. The structure of acoustic flows is studied. Their effect on small-size particles and the possibilities of generating ordered structures from these particles are discussed.     

A nonlinear theory for the motion of hydrodynamic discontinuity surfaces

The complete system of hydrodynamic equations that describe the free surface of an inviscid fluid, a tangential discontinuity, and the development of the hydrodynamic instability of a reaction front is reduced to a closed system of surface equations using Lagrangian variables, special integrals of motion, and their analogues. The vorticity is shown to play a fundamental role in the pattern of motion of hydrodynamic discontinuities, imparting a differential form to the equations. In the isentropic approximation, it is demonstrated how to take into account the fluid density oscillations caused by this motion. The derived system of equations is consistent with the previously known analytical solutions obtained in special cases.     

Theoretical investigation of hydrodynamic surface mode in a lined duct with sheared flow and comparison with experiment

A spectral collocation method is used to solve the linearized Euler equations in a duct with shear flow and lined walls in order to identify a possible hydrodynamic instability observed in published experiments. This method is first checked against a reference test case in a cylindrical duct. Then a theoretical test case in a plane bi-dimensional duct with no-slip flow is considered: the Briggs-Bers stability criterion is proved to be valid and it shows that the hydrodynamic instability does correspond to a right-running amplified wave. Eigenmode analyses are then performed on the experimental configuration. An unstable hydrodynamic surface mode is found, with an axial wavenumber and velocity eigenfunctions which are in good agreement with the experimental ones. Acoustic energy calculations show that the hydrodynamic instability paradoxically carries noticeable levels of acoustic energy in the upstream direction. Finally, the influence of Mach number and frequency is investigated.     

Numerical investigation of hydrodynamics behaviour of melt layer during laser cutting of steel

Understanding of the melt layer hydrodynamic behaviour during laser-cutting process under gas jet assistance is of high importance for cut quality control. In the present work, a numerical model is developed to calculate the three-dimensional behaviour of the melt flow on the kerf front, while an inert gas jet interacts with the melt film. Fluent CFD code is used to solve the governing hydrodynamic equations by finite volume method. The results show that the melt flow on the kerf front reveals a strong instability, which depends on the cutting speed and on the gas jet velocity. Global flow behaviour (gas and molten metal flows) computed using a laminar model, reveals oscillations of the gas–metal liquid interface, which is assimilated to Kelvin–Helmholtz instability. The origin of this instability is discussed in terms of instabilities in thermal dynamics and hydrodynamics. Instability in thermal dynamics is related to the localized melting, while the instability in hydrodynamics is governed by forces balance between gas and resistant surface tension.     

Pressure induced breather overturning on deep water: Exact solution

A vortical model of breather overturning on deep water is proposed. The action of wind is simulated by nonuniform pressure on the free surface. The fluid motion is described by an exact solution of 2D hydrodynamic equations for an inviscid fluid in Lagrangian variables. Fluid particles rotate in circles of different radii. Formation of contraflexure points on the breather profile is studied. The mechanism of wave breaking and the role of flow vorticity are discussed.     

Effect of longitudinal electric field on capillary instability of a thin axisymmetric layer of liquid dielectric coating a dielectric fiber

The flow of a viscous dielectric liquid surrounded with a gas is investigated in the process of capillary disintegration of a thin axisymmetric liquid layer on an undeformable cylindrical dielectric fiber in a uniform electric field is investigated. An asymptotic analysis of the system of equations and hydrodynamic boundary conditions written with allowance for surface ponderomotive forces is carried out for the case when the average thickness of the layer is much smaller than the radius of the fiber cross section. The problem of the transition of the liquid configuration from the state of a stationary cylindrical layer to the hydrodynamic state in the form of a regular sequence of drops is formulated. In this formulation, a nonlinear parabolic equation that describes the evolution of the local thickness of the layer on the time interval to the instant of drop formation is derived. The effect of the key parameters on the capillary instability is analyzed based on the linearized version of the resultant equation and the linearized electrostatic problem of calculating the field perturbations.     

Scaling limit for a mechanical system of interacting particles

A system of a large number of classical particles moving on a onedimensional segment with virtually reflecting boundaries is studied. The particles interact with one another through repulsive pair-potential forces and are subjected to resistance proportional to their velocities. Because of the latter it is only the number of particles that is conserved under the evolution of the system. It is proved that in the hydrodynamic limit of diffusion type scaling the normalized counting measure of particle locations converges and its limiting density is governed by a non-linear diffusion equation which in typical cases is of porous media equation type.     

Formation of singularities on the charged surface of a liquid-helium layer with a finite depth

The dynamics of the development of an instability of a charged surface of a liquid-helium layer with a finite depth is investigated. The equations describing the evolution of the free surface are derived with the use of conformal variables for the case in which the charge completely screens the electric field above the liquid. A model of the evolution of a spatially localized perturbation of a liquid-helium surface is proposed for the strong-field limit where the dynamics of the liquid is predominantly determined by the effect of electrostatic forces. This model describes the development of an instability of the initially planar boundary to the point of the formation of cuspidal dimples. The limit of an infinitely deep liquid is considered. The stability of the previously revealed liquid flow regime described by the Laplacian growth equations is proved without significant constraints on the surface geometry.     

Capillary disintegration of a ferrofluid cylindrical film magnetized to saturation by an axial magnetic field

The subject of consideration is a film of a magnetic fluid applied on the surface of a thin magnetically soft cylinder. Quantities figuring in equations and boundary conditions describing the axisymmetric flow due to capillary and magnetic forces at capillary disintegration of the film are estimated in order of magnitude. The effect of magnetization on the capillary disintegration of the film is studied using simplified equations of ferrohydrodynamics. It is shown that magnetization shifts the range of Rayleigh capillary instability toward longer wave modes. As a result, drops arising at the final stage are larger than in the case of the nonmagnetic liquid.     

Convection in thick and in thin fluid layers with a free surface – The influence of evaporation

Convective systems are examined by stability analysis as well as numerical solutions of the hydrodynamic basic equations in three spatial dimensions. Instabilities caused by surface tension gradients (Marangoni effect) are analyzed. The effect of evaporation of a volatile oil is studied by a two-layer system as well as by means of an effective Biot number. In thin fluid layers (a few 100 nm), an instability caused by the interaction between free surface and solid substrate manifests itself in form of surface deformation. We discuss this situation using the lubrication approximation. Special emphasis is layed on the influence of evaporation which may stabilize the system and which may lead to interesting new periodic structures.     

Submicron particle removal in post-oxide chemical–mechanical planarization (CMP) cleaning

Particle removal models for soft-pad buffing (the second-step polishing with DI water) and mechanical brush-cleaning processes are proposed and the removal forces are evaluated and compared with the average particle adhesion force to the oxide wafer surface resulting from the primary polishing (the first-step polishing with slurry). The hydrodynamic force due to the fluid flow is too small to remove slurry particles by itself and particles are most likely removed from the surfaces by the pad or brush asperity contact forces and the hydrodynamic drag force together. This conclusion is consistent with the experimental observations. Received: 25 January 1999 / Accepted: 18 May 1999 / Published online: 8 September 1999     

Screening and attraction of dust particles in plasmas

The potential around a dust particle in a plasma is found using the collisional hydrodynamic equations of dusty plasmas, taking into account ion-dust and ion-neutral collisions and considering the plasma source proportional to the dust density. The linear screening is strongly influenced by the collisions and can substantially differ from Debye screening. Attraction of negatively charged dust particles can occur due to overscreening by the ion fluxes in the presence of friction forces.     

Nonthermodynamic fluctuations in two-dimensional hydrodynamic systems

The problem of fluctuations in two-dimensional hydrodynamic systems under nonequilibrium conditions due to external forces is studied on the example of a simple model. The effective action is given; this action makes it possible to construct a perturbation series to calculate fluctuation effects in such systems. Renormalizability of this action with an infinite number of vertices is proved; renormalization group equations are derived. A number of solutions of these equations are found; the asymptotic behaviour of the solution is considered in the limit of large logarithms.     

Clustering and combustion of dilute aluminum particle clouds in a post-detonation flow field

A hybrid two-phase numerical methodology is used to investigate the flow-field subsequent to the detonation of a spherical charge of TNT with an ambient distribution of a dilute cloud of aluminum particles. The interaction of the particle cloud with the contact surface results in Rayleigh–Taylor instability, which grows in time and gives rise to a mixing layer where the detonation products mix with the air and afterburn. At early times, the ambient particles get engulfed into the detonation products and ignite. Subsequently, they catch up with the Rayleigh–Taylor structures, and the vortex rings around the hydrodynamic structures cause transverse dispersion that results in the clustering of particles. Then, the particles leave the mixing layer and quench, yet preserve their hydrodynamic foot print. Preferential heating and combustion of particles occurs due to clustering. A higher initial mass loading in the ambient cloud results in larger clusters due to stronger/larger vortex rings around the hydrodynamic structures. A larger particle size results in the formation of fewer and degenerate clusters when the initial width of the cloud is larger. A theoretical model is used to predict the bubble amplitudes, and are in good accordance with the simulation results. Overall, this study has provided some useful insights on the explosive dispersal of dilute aluminum particle clouds and the gas dynamics of the flow field in the mixing layer.     

溶解与热对流对固体颗粒运动影响的直接数值模拟

对牛顿流体内溶解与热对流对单颗粒在垂直管道中的沉降运动进行了直接数值模拟.流体运动由守恒方程计算,密度和黏性的变化考虑流场温度变化的影响,通过积分黏性应力和压力获得颗粒的受力跟踪颗粒运动,溶解引起的相变及其形状的变化由溶解潜热、溶解质量与分散相边界处的温度梯度的关系建立的方程决定.通过颗粒和流体间相互的作用力和力矩及边界条件的施加实现相间耦合.分别模拟了颗粒在等温流体、热流体、冷流体及颗粒溶解四种情况下的沉降过程.结果表明,在一定雷诺数内,热对流产生的颗粒尾迹处涡的脱落以及溶解引起的颗粒表面形态的变化引起了颗粒的横向摆动,并使颗粒沉降速度发生了变化. 关键词： 溶解 热对流 颗粒两相流 直接数值模拟     

The field of radiative forces and the acoustic streaming in a liquid layer on a solid half-space

The acoustic field and the field of radiative forces that are formed in a liquid layer on a solid substrate are calculated for the case of wave propagation along the interface. The calculations take into account the effects produced by surface tension, viscous stresses at the boundary, and attenuation in the liquid volume on the field characteristics. The dispersion equations and the velocities of wave propagation are determined. The radiative forces acting on a liquid volume element in a standing wave are calculated. The structure of streaming is studied. The effect of streaming on small-size particles is considered, and the possibilities of ordered structure formation from them are discussed.