The role of external influences in the formation of waves on the surface of a flowing-down film of a viscous fluid

The example of two non-stationary forces is used to study the impact of external influences leading to the occurrence of additional ponderomotive forces on the wave regimes of the film freely flowing down a vertical surface. The first case describes a ferromagnetic fluid film affected by the magnetic field, and the second case touches upon a dielectric fluid film affected by the electric field. For the given forces, in the case of small flow rates, the problem is reduced to the solution of a model equation for the perturbation of the film thickness. The numerical solutions of the problem are obtained, and several characteristic scenarios of evolution of periodical perturbations are considered. It is shown that changes in the boundaries of the region of linear stability of the unperturbed flow with a flat free surface under the influence of ponderomotive forces have a great impact on the flow.     

Computing the force distribution on the surface of complex,deforming geometries using vortex methods and Brinkman penalization

The distribution of forces on the surface of complex, deforming geometries is an invaluable output of flow simulations. One particular example of such geometries involves self‐propelled swimmers. Surface forces can provide significant information about the flow field sensed by the swimmers and are difficult to obtain experimentally. At the same time, simulations of flow around complex, deforming shapes can be computationally prohibitive when body‐fitted grids are used. Alternatively, such simulations may use penalization techniques. Penalization methods rely on simple Cartesian grids to discretize the governing equations, which are enhanced by a penalty term to account for the boundary conditions. They have been shown to provide a robust estimation of mean quantities, such as drag and propulsion velocity, but the computation of surface force distribution remains a challenge. We present a method for determining flow‐induced forces on the surface of both rigid and deforming bodies, in simulations using remeshed vortex methods and Brinkman penalization. The pressure field is recovered from the velocity by solving a Poisson's equation using the Green's function approach, augmented with a fast multipole expansion and a tree‐code algorithm. The viscous forces are determined by evaluating the strain‐rate tensor on the surface of deforming bodies, and on a “lifted” surface in simulations involving rigid objects. We present results for benchmark flows demonstrating that we can obtain an accurate distribution of flow‐induced surface forces. The capabilities of our method are demonstrated using simulations of self‐propelled swimmers, where we obtain the pressure and shear distribution on their deforming surfaces.     

Effect of Thermocapillary Forces on the Initial Section of a Melt Film

The previous analysis of fields near the upper triple point of the floating–zone melting process is supplemented by the analysis of thermocapillary forces on the melt surface. It is shown that the effect of these forces is large in the general case, and a melt film with a macroscopic radius of curvature may be formed only if the temperature gradient over the melt surface and thermocapillary forces are small; in this case, the angular coordinates of the melt–film cross section are also small.     

Stability of the lateral surface of viscous fingers formed when a fluid is displaced from a Hele-Shaw cell

It is shown that instability develops on the lateral surface of viscous fingers formed when a fluid is displaced from a Hele-Shaw cell. This instability is caused by the inertia forces, whereas the viscous forces acting in the plane of the cell stabilize the surface.     

Numerical modeling of the impact pressure in a compressible liquid medium: application to the slap phase of the locomotion of a basilisk lizard

The forces acting on a solid body just at the time of impact on the surface of a medium with very low compressibility, such as water, can be quantified at acoustic time scales. This is necessary in wide range of applications varying from large-scale ship designs to the walking or running mechanisms of small creatures such as the basilisk lizard. In order to characterize such forces, a numerical model is developed in this study and is validated using analytical expressions of pressure as a function of the speed of sound-wave propagation in water. The computational results not only accurately match the analytical values but are also able to effectively capture the propagation of acoustic waves in water. The model is further applied to a case study wherein the impact impulse required by the basilisk lizard to assist in its walking on the water surface is evaluated. The numerical results are found to be in agreement with the closest available experimental data. The model and approach are thus proposed to evaluate impact forces for wide range of applications.     

The combined effect of electric forces and confinement ratio on the bubble rising

In this work, the combined effect of electrohydrodynamic forces and domain confinement on the formation of a toroidal bubble is numerically studied. The numerical scheme is the Volume of Fluid (VOF) method and the surface tension and electric forces are implemented using the Continuum Surface Force (CSF) and leaky dielectric models, respectively. It is found that both domain confinement and electric forces are influential on the formation of a toroidal bubble. For smaller confinement ratios, larger electric forces are required to pierce the bubble. Moreover, the influence of both electric forces and confinement ratio are presented and discussed for bubble vertical velocity, terminal Reynolds number, velocity streamlines and side-wall shear stress.     

On determining the shape of weld pools

The equations governing heat and fluid flow in weld pools for the TIG fusion welding process are presented and this coupled system is solved numerically using finite differences. Electromagnetic forcing terms, buoyancy forces, shear forces on the pool surface due to the variation in surface tension with temperature and an additional uniform magnetic field applied normal to the workpiece are all included in our model and results are displayed indicating the relative importance of these four mechanisms.     

On the theory of loaded inhomogeneous cylinders

This article is concerned with the relaxed Saint-Venant’s problem in the case when the body forces and surface tractions on the lateral surface are polynomials in the axial coordinate. A new method of solving this problem is presented. The method is applied to study the problem of a uniformly loaded cylinder.     

流体边界层上电磁力的控制效应研究

利用作用于流体边界层上的电磁体积力改变流体边界层的结构，研究电磁力对流场的控制 作用效果. 电极与磁极交替分布的电磁场激活板包覆在圆柱体表面置于流动的电解质溶液 中，产生的电磁力沿圆柱体表面分布，可以改变流体边界层的结构，从而实现对流场的控制. 用电磁屏蔽和时域控制的方法调整电磁力的时空分布参数，圆柱绕流分离点可以在前驻点和 后驻点之间变动，产生不同的控制效果. 流体边界层上的电磁力能连续控制圆柱绕流、尾流 涡街的形态. 正向电磁力具有较好的消涡、减震和减阻控制效应. 反向电磁力具有明显的增 涡控制效应，具有较强的制动控制效应，此时圆柱体表面涡量分布的对称性和稳定性被破坏.     

The role of the configurational force balance in the nonequilibrium epitaxy of films

We discuss the epitaxial growth of an elastic film, allowing for stress and diffusion within the film surface as well as nonequilibrium interactions between the film and the vapor. Our approach, which relies on recent ideas concerning configurational forces, is based on: (i) standard (Newtonian) balance laws for forces and moments together with an independent balance law for configurational forces; (ii) atomic balances, one for each species of mobile atoms; (iii) a mechanical version of the second law that accounts for temporal changes in free energy, energy flows due to atomic transport, and power expended by both standard and configurational forces; (iv) thermodynamically consistent constitutive relations for the film surface and for the interaction between the surface and the vapor environment. The normal component of the configurational force balance at the surface represents a generalization, to a dynamical context involving dissipation, of a condition that would arise in equilibrium by considering variations of the total free energy with respect to the configuration of the film surface. Our final results consist of partial differential equations that govern the evolution of the film surface.     

地震作用下水库坝体与水体相互作用数值模拟

地震作用下水库坝体受迫振动,推动坝后水体波动,造成水体动压作用于坝体,形成坝-水耦合作用,影响坝体安全.为了评估坝体振动引起的水面波动及坝体所受动水荷载作用,建立坝体动边界条件下的不可压水体运动数学模型,模拟了地震波作用下的坝后水体波动和动力荷载.结果 表明,在忽略坝体自身弹性变形的条件下,地震作用下坝体激发的水体表面...     

Effect of small parameters on the structure of the front formed by unstable viscous-fluid displacement from a Hele-Shaw cell

The process of displacement of a viscous fluid from a Hele-Shaw cell consisting of two plates separated by a small gap is investigated. The front formed when the fluid is displaced from the cell by another, lower-viscosity fluid is unstable. The lower-viscosity fluid breaks through the layer of displaced fluid and forms channels called viscous fingers. As a result, a mixing zone occupied by both displaced and displacing fluids is formed. The structure of the unstable displacement front is investigated when the surface tension forces have no effect on the shape of the fingers. This situation is realized when a water-glycerin mixture is rapidly displaced from the cell by water. Equations taking the inertial and viscous forces acting in the plane of the plates into account are obtained by averaging the Navier-Stokes equations over the cell gap. Using the equations obtained the stability of a plane displacement front traveling in the direction of its normal and the stability of the lateral surfaces of the viscous fingers is investigated when the fluid velocities are parallel to the interface. From the solution for stability of the transverse displacement front it follows that the viscous forces acting in the plane of the plates determine the finger width (when there is no surface tension). Instability also develops in the flow on the longitudinal fluid interface. In this case the destabilizing factor is the inertial forces. Under the action of this instability the fingers, in their turn, lose stability and disintegrate into viscous bubbles.     

Modification of the elastic properties of nanostructures with surface charges in applied electric fields

The influences of applied electric fields and surface charges on elastic modulus of nanostructures such as nanowires and nanofilms are investigated within the framework of classic continuum mechanics. Under an applied electric field, the surfaces of structures are subjected to the electrostatic forces (negative pressure) along the direction of the electric field, and the resulting surface charges also change the surface mechanical properties due to the Hellman–Feynman (H–F) forces. Through incorporating the surface energy from the negative pressure and the H–F forces into surface free energy, the exact and analytical expressions of the effective elastic modulus of nanowires and nanofilms are addressed by considering the surface energy effects on the elastic modulus of nanostructures, which involves the contribution of the applied electric field and surface charges. The numerical results indicate that applied electric fields parallel to the axis of the nanowire and nanofilms enhance the transverse Young's modulus while reducing axial modulus of nanostructures. The effective modulus of nanowires and nanofilms with lateral surface charges depends on the surface charges density and the sign of the charges. In addition, the effect of electric field and surface charges on Young's moduli of nanowires and nanofilms has been found to be sensitive to structural geometric dimensions such as the thickness of the film and the diameter of the wire.     

Shape of the free surface of a magnetic fluid containing a cylindrical concentrator of the magnetic field

The shape of the surface of a magnetic fluid containing a cylindrical body made of a well-magnetizable material (magnetic field concentrator) in a uniform applied magnetic field is studied experimentally and theoretically. Various static shapes of the surface are calculated numerically taking into account the gravity forces, the surface tension, and the dependence of the magnetic fluid magnetization on the magnetic field strength. It is found that there exists several equilibrium shapes of the magnetic fluid surface. Abrupt changes in the magnetic fluid surface and its hysteresis are predicted theoretically and observed experimentally. The theoretical and experimental results are compared.     

Full-field strain measurements of the inside of an agricultural tyre using digital image correlation

This paper investigates strain measured on the inside of an agricultural tyre with large tread-blocks during a series of static tests using a novel measuring system. The full field strain measurements may be used in the development of a tyre which is capable of estimating tyre forces from strain measurements. The strain measurement system makes use of a calibrated stereo camera system on a mechanical stabilizing system that keeps the cameras pointed at the inside surface of the tyre in contact with the road while the wheel rotates. A static tyre test rig is used to displace the road surface relative to the tyre in the vertical and longitudinal direction. The large tread-blocks caused strain concentrations on the inner surface as the tyre deforms to comply with the road surface. Vertical and longitudinal tests each produce unique strain patterns in the contact patch region. Relationships between the applied forces and strain measurements were developed and showed that these relationships are near linear with R² values above 0.97. The strain measurements also show that the location where strain gauges, for single point strain measurements, are placed inside the tyre is very important on large lugged tyres.     

Effect of tangential and normal forces on the wave formation in the flow of a liquid film and a gas

The effect of surface forces on nonlinear waves induced by the hydrodynamic instability in the flow of a viscous liquid film along the inner surface of a tube blown with a gas.     

Elastic Displacement in a Half-Space Under the Action of a Tensor Force. General Solution for the Half-Space with Point Forces

The elastic displacement in an isotropic elastic half-space with free surface is calculated for a point tensor force which may arise from the seismic moment of seismic sources concentrated at an inner point of the half-space. The starting point of the calculation is the decomposition of the displacement by means of the Helmholtz potentials and a simplified version of the Grodskii-Neuber-Papkovitch procedure. The calculations are carried out by using generalized Poisson equations and in-plane Fourier transforms, which are convenient for treating boundary conditions. As a general result we compute the displacement in the isotropic elastic half-space with free surface caused by point forces with arbitrary structure and orientation, localized either beneath the surface (generalized Mindlin problem) or on the surface (generalized Boussinesq-Cerruti problems). The inverse Fourier transforms are carried out by means of Sommerfeld-type integrals. For forces buried in the half-space explicit results are given for the surface displacement, which may exhibit finite values at the origin, or at distances on the surface of the order of the depth of the source. The problem presented here may be viewed as an addition to the well-known static problems of elastic equilibrium of a half-space under the action of concentrated loads. The application of the method to similar problems and another approach to the starting point of the general solution are discussed.     

Temperature pulsations and thermocapillary effects on the surface of a wavy heated liquid film

The temperature pulsations and wave characteristics in water film flow along a vertical plate with a heater are investigated. Using an infrared scanner, the temperature field on the film surface is measured for various heat flux densities on the heater. Experimental data on the variation of the temperature with time on a local segment of the liquid film surface during wave transmission are obtained. In the absence of a heat flux the data obtained are in good agreement with the results of other researchers for an isothermal liquid film. When the down-flowing liquid is heated, the thermocapillary forces lead to the formation of rivulets and a thin film between them. It is shown that in the inter-rivulet zone the relative wave amplitude increases due to the action of the thermocapillary forces.     

Finite element method for the stress analysis of isotropic cylindrical helical spring

This paper presents an efficient two nodes finite element with six degrees of freedom per node, capable to model the total behaviour of a helical spring. The formulation, which includes the shear deformation effects, is based on the assumed forces hybrid approach. The resultant forces approximation verifies exactly the resultant equilibrium equations. The developed model proves its accuracy compared with other elements. This element permits to get the distribution of different stresses along the spring and through the wire surface by only one element.     

On the stress state of a piezoceramic medium with a tunneled elliptical recess

An explicit solution of the static problem of electroelasticity for a transversally isotropic piezoceramic medium containing a tunneled elliptical recess, one axis of which coincides with the axis of the medium's anisotropy, is constructed in this study. It is assumed that the surface of the recess is free of mechanical forces, and the normal component of the induction vector on this surface is equal to zero. Tensile forces act at a sufficient distance from the recess along its axis. The solution of the corresponding problem for a medium containing an internal crack is obtained as a special case. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 35, No. 7, pp. 77–84, July, 1999.