Archimedes Revisited

Archimedes’ beautiful principle may be used to determine how an object floats in a vessel of liquid. This, in turn may be used to determine the global configuration associated with a floating object under the assumption that the surface of the liquid is planar. There are instances, however, in which capillary effects conspire to produce significantly nonplanar liquid interfaces and phenomena which is strikingly at odds with the predictions of the Archimedean principle. A most notable instance involves floatation of convex objects with density greater than that of the liquid. The effects of capillarity on liquid interface configurations invariably manifest themselves globally over the entire system, though the magnitude of such effects is often so small as to be overlooked. This phenomenon presents a major difficulty in obtaining an appropriate generalization of Archimedes’ principle which incorporates capillarity.     

Stratified laminar flows in a circular pipe: New analytical solutions in terms of elementary functions

Laminar stratified two-phase flows in circular pipes are studied. Under the assumption that the wall-liquid wettability properties of the phases are identical, new exact analytical solutions in terms of elementary functions are constructed. The solutions satisfy the Navier–Stokes equations exactly in fluids and the boundary conditions on the pipe walls and the interface for the two cases: the pipe is horizontal and the capillarity forces dominate the gravity ones, the pipe is inclined and the volumetric quantities of liquids in the pipe are the same. For the second case, the capillarity and gravity forces can be arbitrary, but if the gravity forces dominate the capillarity ones, the assumption about the equal wall-liquid tensions of the phases can be withdrawn.     

考虑毛管形状的幂律流体等效渗透率计算方法(英文)

While studying the flow of oil and gas in the reservoir, it is not realistic that capillary with circular section is only used to express the pores. It is more representative to simulate porous media pore with kinds of capillary with triangle or rectangle section etc. In the condition of the same diameter, when polymer for oil displacement flows in the porous medium, there only exists shear flow which can be expressed with power law model. Based on fluid flow-pressure drop equation in single capillary, this paper gives a calculation method of equivalent permeability of power law fluid of single capillary and capillary bundles with different sections.     

Extended scaling invariance of one‐dimensional models of liquid dynamics in a horizontal capillary

In this paper, we consider the adaptive numerical solution of one‐dimensional models of liquid dynamics in a horizontal capillary. The bulk liquid is assumed to be initially at rest and is put into motion by capillarity: the smaller is the capillary radius, the steeper becomes the initial transitory of the meniscus location derivative, and as a consequence, the numerical solution to a prescribed accuracy becomes harder to achieve. Therefore, in order to solve a capillary problem effectively, it would be advisable to apply an adaptive numerical method. Here, we show how an extended scaling invariance that can be used to define a family of solutions from a computed one. In the viscous case, the similarity transformation involves solutions of liquids with different density, surface tension, viscosity, and capillary radii, whereas in the inviscid case, we can generate a family of solutions for the same liquid and capillaries with different radii. With our study, we are able to prove that the monitor function, used in the adaptive algorithm, is invariant with respect to the considered scaling group. It follows, from this particular results, that all the solutions within the generated family verify the adaptive criteria used for the computed one. Moreover, all the solutions have the same order of accuracy even if the maximum value of the step size varies under the action of the scaling group. Copyright © 2012 John Wiley & Sons, Ltd.     

Reorientation of Cryogenic Fluids Upon Step Reduction of Gravity

Experiments to observe the surface oscillation of cryogenic liquids have been performed with liquid nitrogen inside a 50 mm diameter right circular cylinder. The surface oscillation is driven by the capillary force that becomes dominant after a sudden reduction of the gravity acceleration acting on the liquid. The experiments show differences from the speculated behavior and enables one to observe new features. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the thermal runaway of combustible fluids in lagging material

This paper presents the mathematical foundations for a simpletheory for investigating the phenomenon of ignition of flammablefluids in lagging material that are used for insulation of hotpipework, for transport of heat transfer fluids, or other similarsituations. Experiments with porous material impregnated witha flammable fluid have simulated the self-heating known to occurwhen combustible liquids leak from a hot pipe into lagging surroundingthe pipe or are split from another source on to the lagging.A theory to explain these findings is presented which showsthat there is a watershed temperature beyond which substantialself-heating will take place. Although the theory does not takeaccount of diffusion, it simulates the main physics of the phenomenon–thatis, combustible fluid, which normally in the open air wouldevaporate and not be a hazard, can, within a porous medium,remain dispersed within the porous structure long enough forthe exothermic oxidation to develop into ignition.     

Homogenization of compressible two-phase two-component flow in porous media

The paper is devoted to the homogenization of immiscible compressible two-phase two-component flow in heterogeneous porous media. We consider liquid and gas phases, two-component (water and hydrogen) flow in a porous reservoir with periodic microstructure, modeling the hydrogen migration through engineered and geological barriers for a deep repository for radioactive waste. Phase exchange, capillary effects included by the Darcy–Muskat law and Fickian diffusion are taken into account. The hydrogen in the gas phase is supposed compressible and could be dissolved into the water obeying the Henry law. The flow is then described by the conservation of the mass for each component. The microscopic model is written in terms of the phase formulation, i.e. the liquid saturation phase and the gas pressure phase are primary unknowns. This formulation leads to a coupled system consisting of a nonlinear parabolic equation for the gas pressure and a nonlinear degenerate parabolic diffusion–convection equation for the liquid saturation, subject to appropriate boundary and initial conditions. The major difficulties related to this model are in the nonlinear degenerate structure of the equations, as well as in the coupling in the system. Under some realistic assumptions on the data, we obtain a nonlinear homogenized problem with effective coefficients which are computed via a cell problem. We rigorously justify this homogenization process for the problem by using the two-scale convergence.     

A representation of the equations of multicomponent multiphase seepage

A mathematical model of non-isothermal multicomponent flows in a porous medium is investigated. A general case is considered when the model can be used to describe processes with an arbitrary number of components and phases. A general form of the system of mixed-type equations describing the flow, which is similar to the Godunov form for hyperbolic systems is proposed. The equations obtained are applicable to flows with gas, liquid and solid phases. The thermodynamic properties of the medium are determined solely by a single multivalued function, by changing which one can obtain models of different flows in a porous medium. A clear geometrical interpretation of the solutions of the equations is proposed. An equation for the entropy is obtained, and it is shown that in order that the model should not contradict the second law of thermodynamics, it is necessary to take into account, in the energy equation, the work of the gravity force, which is often neglected when investigating seepage.     

基于格子Boltzmann方法的液滴撞击具有不同润湿性孔板的研究

基于格子Boltzmann方法,对液滴撞击不同湿润性节流孔板表面进行了数值模拟.主要研究了在液滴撞击过程中,Weber数(We)、孔板表面湿润性和孔板尺寸对液滴通过孔板时不同状态的影响.数值模拟结果表明:孔板为亲水特性时,在较低We下,液滴不会与孔板表面脱离,而是附着在孔板下表面,并且在毛细作用下液滴会在孔道中上升一段...     

Numerical investigation of a liquid displacing a gas in thin porous layers

This article deals with a liquid displacing a gas in a thin heterogeneous porous material, which occurs e.g. during the filling process of a lithium-ion battery with an electrolyte. The investigation is based upon the local volume-averaged Navier-Stokes equations, using a Volume-of-Fluid method to treat the interface. For the flow the wall effect and capillary forces have to be considered. Capillary rise experiments are used to determine the permeability. Since the layers are thin and the characteristic size of the particles is comparatively large, friction with the electrode is taken into account with respect to the mobility of the contact line. The implemented models are validated against analytical results, showing a good agreement. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A multiphase single relaxation time lattice Boltzmann model for heterogeneous porous media

The lattice Boltzmann (LB) method has been shown to be a highly efficient numerical method for solving fluid flow in confined domains such as pipes, irregularly shaped channels or porous media. Traditionally the LB method has been applied to flow in void regions (pores) and no flow in solid regions. However, in a number of scenarios, this may not suffice. That is partial flow may occur in semi-porous regions. Recently gray-scale LB methods have been applied to model single phase flow in such semi-porous materials. Voxels are no longer completely void or completely solid but somewhere in between. We extend the single relaxation time LB method to model multiphase, immiscible flow (e.g., gas and liquid or water and oil) in a semi-porous medium. We compare the solution to test cases and find good agreement of the model as compared to analytical solutions. We then apply the model to real porous media and recover both capillary and viscous flow regimes. However, some deficiencies in the single relaxation time LB method applied to multiphase flow are uncovered and we describe methods to overcome these limitations.     

Numerical investigation into a liquid displacing a gas in thin porous layers

To examine the filling process in a lithium-ion battery, a numerical model to characterize the displacing flow of a liquid in air-filled pores of thin heterogeneous porous materials is elaborated. The investigation is based on the volume-averaged Navier-Stokes equations for small Reynolds numbers, using a volume-of-fluid method to cover the multiphase flow. The flow is investigated with respect to the wall effect and to capillary action within the porous matrix. On the one hand, model experiments with similar particle-size distributions as in the battery layers are conducted to extract the porosity as function of the wall distance. On the other hand, experiments with the three different porous layers of the battery are performed to receive mean values for the most important properties related to the two-phase flow. Results for the displacement flow in parts of the battery are presented and discussed, showing a considerable influence of the modeled effects onto the flow characteristics. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Pressure of an elastic half space on a rigid base with rectangular hole in the case of a liquid bridge between them

A model of contact between an elastic half space and a rigid base with a shallow surface rectangular hole is proposed. The hole contains an incompressible liquid and gas. The liquid occupies the middle part of the hole and forms a capillary bridge between the opposite surfaces. The remaining volume of the hole is filled with gas under a constant pressure. The liquid completely wets the surfaces of the bodies. The pressure drop at the liquid–gas interface caused by the surface tension is defined by the Laplace formula. The corresponding plane contact problem for the elastic half space is essentially nonlinear because the pressure of the liquid and the length of the capillary in the contact-boundary conditions are not known in advance and depend on the external load. The problem is reduced to a system of three equations (a singular integral equation for the function of height of the hole and two transcendental equations for the length of the capillary and the height of the meniscus). An analytic-numerical procedure for the solution of these equations is proposed. Dependences of the length of the capillary and the pressure drop at the liquid–gas interface on the external load, volume of liquid, and its surface tension are analyzed. Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 51, No. 1, pp. 150–156, January–March, 2008.     

An Enriched Biphasic Model for Solute Driven Degradation

Transport of solutes in porous materials plays an important role in many kinds of materials such as biological tissues, porous implants or even soils. In most of the cases the liquid phase in the pores acts as a solvent for one or more solutions. The motion of the solutions is driven by both, the advective and convective transport. The former is related to the fluid phase velocity whereas the letter follows the concentration gradient. The interactions between the solutes and the solid and liquid phase may influence the overall material behavior. Although the solutes often carry electrical charges this paper is focused on neutrally charged solutions. In this contribution the model to describe the solute transport in a fluid saturated porous material is based on the well founded Theory of Porous Media. We will present the basic framework and the governing equations. Finally, we will show a three dimensional numerical example of the solute driven degradation of a skull implant. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The role of cross terms in the flow law fora gas condensate mixture in a porous medium near a well

The problem of the steady flow of a gas condensate mixture in a porous medium near a well is considered. Capillary forces and cross terms are taken into account in the flow law. It is shown that the problem splits into the purely physicochemical problem of capillary condensation and the problem of determining of the pressure field in the phases. The latter problem can have infinitely many solutions; the solution which is of the greatest interest in practice is separated out. An approximate solution in analytical form is found in the case of a small ratio of the gas and condensate viscosities.     

Capillary breakup of liquid threads: a singularity-free solution

The process of capillary breakup of a thread of Newtonian liquidis considered theoretically in the simplest case where the threadis surrounded by an inviscid, dynamically passive gas. The goalis to remove the singularities inherent in the known solutionsto the problem obtained in the framework of the standard modeland explain some puzzling qualitative features of the processobserved in experiments. The analysis is based on the idea that,since the known solutions indicate that the rate at which freshfree-surface area is created tends to infinity as breakup isapproached, one has that the surface tension, whose relaxationto equilibrium is always associated with a small but finiterelaxation time, is bound to deviate from its equilibrium valuein the process of breakup. This gives rise to a surface-tensiongradient which starts to pull the liquid thread apart (the flow-inducedMarangoni effect), whilst the role of the capillary pressure-drivensqueezing of the liquid out of the neck diminishes as the surfacetension in the minimal cross-section decreases. An earlier developedtheory incorporating the interface formation process is appliedwithout any ad hoc alterations and analysed in the frameworkof the slender-jet approximation. The resulting solution issingularity-free and allows one to describe some previouslyunexplained features of experiment by Kowalewski (1996, FluidDyn. Res., 17, 121).     

原子力显微镜中液桥生成机理探讨

液桥是引起大气环境下原子力显微镜（AFM）图像失真的重要原因,同时也是大气环境下黏着力的主要成分.研究液桥对于成像机理和样品特性的理解有重要意义.提出了AFM液桥生成的物理机理,由3个不同的物理过程组成,即:挤出过程、毛细凝聚和液膜流动.这3种过程的特征平衡时间对认识液桥生成的动力学过程非常重要,挤出过程的平衡时间与接触方式有关,毛细凝聚的平衡时间在微秒量级,而液膜流动的平衡时间随液膜黏度不同变化较大.在此基础上分析了这3种形成机理在AFM不同的操作模式下对液桥体积、毛细力和耗散能的贡献.     

On the Description of Partially Saturated Soils by the Theory of Porous Media

In this contribution, a multi‐phase soil model based on the Theory of Porous Media (TPM) is presented. The model is fully coupled in the following constitutive phases: An elasto‐plastic or elasto‐viscoplastic solid skeleton, a materially incompressible pore‐liquid (water) and a materially compressible pore‐gas (air). The interaction of the solid skeleton and the pore‐fluids is specified by a capillary pressure‐saturation relation, whereas the mobilities of the fluid phases in the pore‐space of the solid skeleton are described by the so‐called relative permeabilities. Finally, a gravity governed initial‐boundary‐value problem solved by the FE method is presented.