Influence of the capillarity on a creeping film flow down an inclined plane with an edge

Summary In creeping flows of thin films, the capillarity can play a dominant role. In this paper, the creeping film flow down an inclined plane with an edge is considered. The influence of the capillarity on the velocity and the film surface is studied analytically, numerically and experimentally. Received 12 April 1999; accepted for publication 9 May 1999     

The Physical Origin of Interfacial Coupling in Two-Phase Flow through Porous Media

Recently developed transport equations for two-phase flow through porous media usually have a second term that has been included to account properly for interfacial coupling between the two flowing phases. The source and magnitude of such coupling is not well understood. In this study, a partition concept has been introduced into Kalaydjian's transport equations to construct modified transport equations that enable a better understanding of the role of interfacial coupling in two-phase flow through natural porous media. Using these equations, it is demonstrated that, in natural porous media, the physical origin of interfacial coupling is the capillarity of the porous medium, and not interfacial momentum transfer, as is usually assumed. The new equations are also used to show that, under conditions of steady-state flow, the magnitude of mobilities measured in a countercurrent flow experiment is the same as that measured in a cocurrent flow experiment, contrary to what has been reported previously. Moreover, the new equations are used to explicate the mechanism by which a saturation front steepens in an unstabilized displacement, and to show that the rate at which a wetting fluid is imbibed into a porous medium is controlled by the capillary coupling parameter, . Finally, it is argued that the capillary coupling parameter, , is dependent, at least in part, on porosity. Because a clear understanding of the role played by interfacial coupling is important to an improved understanding of two-phase flow through porous media, the new transport equations should prove to be effective tools for the study of such flow.     

Two-Phase Flow and the Capillarity Phenomenon in Porous Solids – A Continuum Thermomechanical Approach

Two-phase flow and capillarity phenomenon in porous solids, well known in physics and engineering, are treated from a rigorous continuum thermomechanical point of view for the first time. A ternary model, consisting of a porous solid phase, a liquid phase, and a gas phase, is investigated within the framework of thermodynamics. The main result of the evaluation of the entropy principle turns out to be that the interaction forces between the solid, gas, and liquid phases are dependent on the free Helmholtz energy functions of the corresponding phases and on the gradient of the liquid density. The classical result for the driving volume force for raising a water column in a narrow tube against the force of gravity is contained in the general investigation.     

Simulation and transport phenomena of a ternary two-phase flow

A chemical flood model for a three-component (petroleum, water, injected chemical) two-phase (aqueous, oleic) system is presented. It is ruled by a system of nonlinear partial differential equations: the continuity equation for the transport of each of its components and Darcy's equation for the two-phase flow. The transport mechanisms considered are ultralow interfacial tension, capillary pressure, dispersion, adsorption, and partition of the components between the fluid phases (including solubilization and swelling).The mathematical model is numerically solved in the one-dimensional case by finite differences using an explicit and direct iterative procedure for the discretization of the conservation equations. Numerical results are compared with Yortsos and Fokas' exact solution for the linear waterflood case including capillary pressure effects and with Larson's model for surfactant flooding. The effects of the above-mentioned transport mechanisms on concentration profiles and on oil recovery are also analyzed.     

Internal gravity–capillary solitary waves in finite depth

We consider a two‐dimensional inviscid irrotational flow in a two layer fluid under the effects of gravity and interfacial tension. The upper fluid is bounded above by a rigid lid, and the lower fluid is bounded below by a rigid bottom. We use a spatial dynamics approach and formulate the steady Euler equations as a Hamiltonian system, where we consider the unbounded horizontal coordinate x as a time‐like coordinate. The linearization of the Hamiltonian system is studied, and bifurcation curves in the (β,α)‐plane are obtained, where α and β are two parameters. The curves depend on two additional parameters ρ and h, where ρ is the ratio of the densities and h is the ratio of the fluid depths. However, the bifurcation diagram is found to be qualitatively the same as for surface waves. In particular, we find that a Hamiltonian‐Hopf bifurcation, Hamiltonian real 1:1 resonance, and a Hamiltonian 0²‐resonance occur for certain values of (β,α). Of particular interest are solitary wave solutions of the Euler equations. Such solutions correspond to homoclinic solutions of the Hamiltonian system. We investigate the parameter regimes where the Hamiltonian‐Hopf bifurcation and the Hamiltonian real 1:1 resonance occur. In both these cases, we perform a center manifold reduction of the Hamiltonian system and show that homoclinic solutions of the reduced system exist. In contrast to the case of surface waves, we find parameter values ρ and h for which the leading order nonlinear term in the reduced system vanishes. We make a detailed analysis of this phenomenon in the case of the real 1:1 resonance. We also briefly consider the Hamiltonian 0²‐resonance and recover the results found by Kirrmann. Copyright © 2016 John Wiley & Sons, Ltd.     

Nonequilibrium interface equations: An application to thermocapillary motion in binary systems

Interface equations are derived for both binary diffusive and binary fluid systems subjected to nonequilibrium conditions, starting from coarse-grained (mesoscopic) models. The equations are used to describe thermocapillary motion of a droplet in both purely diffusive and fluid cases, and the results are compared with numerical simulations. A mesoscopic chemical potential shift owing to the temperature gradient, and associated mesoscopic corrections involved in droplet motion, are elucidated.     

对树液上升动力的探讨和比较

提出树液上升有三种驱动力:毛细现象、渗透压和负压.对这三种驱动力的大小进行计算和比较,指出树液上升的主要驱动力是分子距离增大处于拉伸状态后形成的负压.     

低速下润滑接触区补充供油机制的研究

在滚动轴承运行的过程中,滚道上的润滑剂在滚动体的反复碾压下,厚度不断减小,轴承最终进入乏油润滑状态.为了解释长期工作在乏油条件下的轴承依旧能够保持较长时间的良好工作状态,有必要研究在轴承中是否存在某种自发的补充供油机制.本文作者基于球盘接触模型,分别考虑毛细力和分离压力在润滑油迁移过程中的作用,建立赫兹接触区附近油层分布模型,并以此修正弹流计算中的入口供油条件,采用统一Reynolds方程法计算在静止或低速条件下的润滑油膜厚度和压力分布,研究毛细力和分离压力的补充供油机制对润滑条件的改善作用.     

关于"毛细现象的能量来源"的表面热力学讨论

对《大学物理》１９９４年第１２期所刊登的“毛细现象的能量来源”一从表面热力角度进行详细讨论。     

Numerical simulation of bubble and droplet deformation by a level set approach with surface tension in three dimensions

In this paper we present a three‐dimensional Navier–Stokes solver for incompressible two‐phase flow problems with surface tension and apply the proposed scheme to the simulation of bubble and droplet deformation. One of the main concerns of this study is the impact of surface tension and its discretization on the overall convergence behavior and conservation properties. Our approach employs a standard finite difference/finite volume discretization on uniform Cartesian staggered grids and uses Chorin's projection approach. The free surface between the two fluid phases is tracked with a level set (LS) technique. Here, the interface conditions are implicitly incorporated into the momentum equations by the continuum surface force method. Surface tension is evaluated using a smoothed delta function and a third‐order interpolation. The problem of mass conservation for the two phases is treated by a reinitialization of the LS function employing a regularized signum function and a global fixed point iteration. All convective terms are discretized by a WENO scheme of fifth order. Altogether, our approach exhibits a second‐order convergence away from the free surface. The discretization of surface tension requires a smoothing scheme near the free surface, which leads to a first‐order convergence in the smoothing region. We discuss the details of the proposed numerical scheme and present the results of several numerical experiments concerning mass conservation, convergence of curvature, and the application of our solver to the simulation of two rising bubble problems, one with small and one with large jumps in material parameters, and the simulation of a droplet deformation due to a shear flow in three space dimensions. Furthermore, we compare our three‐dimensional results with those of quasi‐two‐dimensional and two‐dimensional simulations. This comparison clearly shows the need for full three‐dimensional simulations of droplet and bubble deformation to capture the correct physical behavior. Copyright © 2009 John Wiley & Sons, Ltd.