Damping Behavior of the Free Liquid Interface Oscillation upon Step Reduction in Gravity

Experiments were carried out to investigate the damping behavior of the reorientation of a free liquid interface in a right circular cylinder, partly filled with a liquid and suddenly exposed to a step reduction in gravity. The damping behavior basically depends on the Ohnesorge number and the static contact angle. This study shows the strong influence of the contact point for low static contact angles.     

Capillary driven Oscillations of a Free Liquid Interface under Non‐Isothermal Conditions

In this study the reorientation behavior of a free liquid interface in a partly filled right circular cylinder upon a step reduction in gravity is investigated experimentally. The experiments focus on the investigation of non‐isothermal boundary conditions on the liquid reorientation. The situation is similar to a spacecraft which enters a ballistic flight after the end of thrust. Heat flux between the liquid propellant and the tank wall occurs and influences the behavior of the liquid reorientation. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

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)     

Thin liquid droplet on top of a rotating non-isothermal liquid layer

Wafers are usually coated by using spin-coating, where centrifugal forces are used to spread a droplet on the rotating wafer. This flow is unstable to the fingering instability, where several segments of the wetting front spread faster than the average, resulting in several fingers. The liquid flows via the existing fingers while the area in between does not get coated. A precise experimental investigation is problematic, as the droplet has to be placed quite exactly in the center of the rotation. Replacing the wafer by a second liquid should lead to a parabolic-shaped free interface and the droplet should center itself due to gravity. Here, we derive a model for the free interfaces of a thin droplet on top of a rotating liquid by taking gravity, centrifugal forces, friction, (thermo-)capillary and line forces into account. Additionally, this setup is the simplest example of multiple coating, where several free interfaces and contact lines influence each other. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Coupled wetting meniscus model for the mechanism of spontaneous capillary action

Capillarity plays a significant role in many natural and artificial processes, but the mechanism responsible for its dynamics is not completely understood. In this study, we consider capillary flow characteristics and propose a coupled wetting meniscus model for the mechanism of spontaneous capillary action. In this model, capillary action is considered as the dynamic coupling of two interfacial forces, i.e., the wall wetting force at the contact line and the meniscus restoring force on the free interface. The wetting force promotes the motion of the contact line directed toward an equilibrium contact angle, whereas the meniscus restoring force promotes a reduction in the interface curvature, which is more consistent with a 90° contact angle. The competing interaction between these two forces is coupled together via the evolution of the interface shape. The model is then incorporated into a finite volume method for a two-fluid flow with an interface. Capillary flow experiments were performed, including vertical and horizontal flows. Phenomena analysis and data comparisons were conducted to verify the proposed model. According to the results of our study, the model can explain the capillary flow process well and it can be also used to accurately guide capillary flow calculations.     

Stability of a thin liquid layer,spreading on a quasi–rotating disk

In many industrial processes solids are coated to obtain specific surface properties, as e.g. corrosion resistance, mechanical (wear) resistance, optical, or electrical properties. Even today many coating processes are not fully understood and the choice of parameters is largely based on experience. Hence, a prediction of the complete hydrodynamic process and the appearance of instabilities in its dependency on the parameters appears highly desirable. This would serve to optimize the quality of the coating. A common coating technique is the so-called spin coating. The coating agent is dissolved or suspended in a liquid, brought onto the solid, spread by rotation, and the carrier liquid is finally removed by evaporation or by chemical reactions. In this article an evolution equation is derived from lubrication theory, valid for thin liquid layers. The model involves a dynamic contact angle, centrifugal, capillary, and gravitational forces. The evolution equation can be solved analytically, provided the capillary number is small. Then a coupled linear stability analysis of the contact line and the free interface is performed. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

An Applicable Boundary Condition at the Moving Contact Line in Case of a Free Surface Reorientation after Step Reduction in Gravity

In this study the sudden change in the acceleration level on a free surface in a right circular cylinder is investigated numerically. The intention to describe the .uid motion encounters the difficulty modelling the moving contact‐line problem. In the numerical simulations the Navier slip boundary condition and a model for the dynamic contact angle are used. The model for the dynamic contact angle γ_d includes the dependence on the Capillary number as well as the contact angle hysteresis. We achieved very good agreement with experimental data.     

Spreading of thin liquid droplets on rotating disks

In many industrial processes solids are coated to obtain specific surface properties, as e.g. corrosion resistance, mechanical, optical, or electrical properties. Even today many of such coating processes are not fully understood and the choice of parameters is mainly based on experience. Hence, a prediction of the complete hydrodynamic process in its dependency on the parameters appears highly desirable. This would e.g. allow for a precise prediction of the (liquid) layer thickness and shape and help to optimize the quality of the coating. A common coating technique is the so–called spin coating. The coating agent is dissolved or suspended in a liquid, brought onto the solid, spread by rotation, and the carrier liquid is finally removed by evaporation or by chemical reactions. In this article an evolution equation is derived from lubrication theory, valid for thin liquid layers. The model involves a dynamic contact angle, centrifugal, capillary, gravitational, and molecular (London–van–der–Waals) forces. The evolution equation without molecular forces can even be solved analytically, provided the capillary number is small. Otherwise a numerical integration of the governing equations is engaged. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Minimal surfaces,corners, and wires

Weierstrass representations are given for minimal surfaces that have free boundaries on two planes that meet at an arbitrary dihedral angle. The contact angles of a surface on the planes may be different. These surfaces illustrate the behavior of soapfilms in convex and nonconvex comers. They can also be used to show how a boundary wire can penetrate a soapfilm with a free end, as in the overhand knot surface. They should also cast light on the behavior of capillary surfaces.     

The equations of the perturbed motion of a rocket as a thin-walled structure with a liquid

The perturbed motion of a rocket as an elastic thin-walled structure with compartments partially filled with liquid propellant is considered. It is assumed that the normal modes of the hydroelastic oscillations of the rocket are determined under the condition that the velocity potential on the free surface of the liquid is equal to zero and with standard remaining conditions. Certain features of these modes with zero fundamental frequencies are pointed out and the “loss” of mass effect associated with this is explained. Equations are derived for the perturbed motion of a rocket taking account of the hydroelastic oscillations of its structure and the oscillations of the liquid with deviations of the free surface from the equilibrium position under the action of mass forces. The coefficients of these equations, characterizing the relation between the different type of oscillations, are expressed in terms of known hydrodynamic parameters and the values of the oscillation modes at certain points.     

Capillary oscillations at a circular orifice

We compute the normal frequencies and normal modes for the oscillation of the free surface of a perfect incompressible fluid inside a semi-infinite container with a circular orifice. In doing that, a dual integral equation system involving the Bessel functions must be solved. We discuss the cases where the contact line between the free surface and the container is pinned as well as the case where it moves with a constant contact angle.     

Transport of fluids in capillary porous solids

Capillarity is a well known phenomenon in physics and engineering. The term denotes the transport of liquids and gas, against the force of gravity in narrow tubes, cracks and pores, caused by the intermolecular forces of cohesion and adhesion of the constituents involved. We will exclusively investigate the rise of liquids in porous bodies due to the capillarity phenomenon. Well‐known examples are the capillary rise in drying processes in soils with small pores and the moisture motion in walls consisting of bricks or concrete. The treatment of the capillary problem, based on thermomechanical investigations, yields the result that the capillarity force is a volume interaction force and depends on the free Helmholz energy functions of the solid phases and the density gradient of the liquid. The aim of this investigation is the numerical simulation of the behavior of liquid and gas phases in a rigid porous body at rest. An example will demonstrate the usefulness of the proposed theory.     

Sur les petites oscillations d'une goutte de liquide caténoïdale entre deux plaques parallèles en apesanteur

Résumé L'article est consacré á l'étude mathématique du probléme des petites oscillations d'une goutte de liquide placée entre deux plaques paralleles qu'elle coupe sous un angle constant, en l'absence de pesanteur, dans le cas oú la surface libre de la goutte est un caténoïde dans la position d'équilibre.Utilisant une méthode fonctionnelle, nous retrouvons d'abord une condition de stabilité et nous obtenons ensuite une formulation variationnelle du probléme á l'aide laquelle nous démontrons l'existence des fréquences propres des petites oscillations du liquide.

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This paper deals with the mathematical study of the problem of the small oscillations of a liquid drop with a free surface held together by surface tension between two parallel plates with free contact line, the contact angle being constant, under zero gravity, in the case of a catenoïdal liquid drop in the equilibrium position.Using a functional method, we find again, at first, a condition of stability and, then, we obtain a variational formulation of the problem by means of which we prove the existence of the eigenfrequencies of the small oscillations of the liquid.

     

Free boundary fluid flow in a trough: A numerical approach

This paper examines the slow flow of a viscous liquid in an open rectangular container, one side (the base) of which moves steadily along its own plane, thereby providing the driving force the liquid needs. Unlike the two vertical sides that are rigid and stationary, the top side is left open so that the upper part of the liquid is in contact with air and is being controlled by surface tension and gravity. A numerical procedure for obtaining solutions for the cases when the capillary numbers are small is provided and the curves of the free boundaries obtained here are presented for some flow parameters. The deviation of the shape of the free boundary is observed to be strongly dependent on the aspect ratio of the boundary (i.e., the ratio of the vertical to horizontal spread of the liquid) with its curvature changing sign in the interval [1, 1.5].     

Non uniqueness and uniqueness of capillary surfaces

It is shown that for any gravity fieldg and contact angle, a containerC can be found which can be partially filled with liquid in a continuum of distinct ways, so as to obtain a one parameter familyF of capillary surface interfaces, no two of which are mutually congruent, and all of which bound the same liquid volume and yield the same mechanical energy. This answers affirmatively a question raised by Gulliver and Hildebrandt, who obtained such a container in the caseg=0,=/2. For a particular configuration inF, the second variation of energy is calculated and it is shown that-at least for small g- it can be made negative. As a consequence, a rotationally symmetric container deviating arbitrarily little from a circular cylinder is characterized, so that an energy minimizing configuration filling half the container exists but cannot be symmetric. Finally, a condition on rotationally symmetric container shapes is given, for the existence of a unique disk-type symmetric stationary surface. In the particular case of a spherical container in zero gravity, this surface is unique and minimizing among all disk-type surfaces with the given contact angle and enclosed volume.The major part of this work was completed while the author was visiting at the Max-Planck-Institut in Bonn. The work was also supported in part by grants from the Fulbright Commission, from the National Science Foundation, and from the National Aeronautics and Space AdministrationI wish to thank K. -S. Chua, P. Concus, M. Grüter, and R. Gulliver for helpful comments and discussions.     

Flows with quasi-equilibrium free boundaries in the dynamics of wetting of solids

Slow flows of a viscous fluid with free boundary over the solid surface when there is the moving three-phase contact line are considered. The second-order asymptotic theory, which describes the regularities of free boundary variations under the action of capillary forces, is developed.     

Floating Drops and Functions of Bounded Variation

A variational problem for three fluids in which gravitational and surface tension forces are in equilibrium is studied using sets of finite perimeter and functions of bounded variation. Existence theorems are proven which imply the existence of an axisymmetric floating drop. This problem has been studied previously as a free boundary problem for axisymmetric capillary surfaces by Elcrat, Neel and Siegel, but the general existence problem for arbitrary drop volumes was left open. The results presented here settle a version of this question.     

A circulating gravity wave in a cylindrical tank

A circular cylindrical vertical tank is partially filled with a liquid (Water) and a gas (air) above it. The top lid of the container rotates around the cylinder axis and induces a flow in the gas and the liquid. Above a critical rotational speed a large amplitude circulating gravity wave forms. The two phase flow problem will be reduced to a free surface single phase flow problem and the critical parameters, when the axis-symmetric flow becomes unstable with respect to the circulating gravity wave will be determined. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Lattice Boltzmann Study on the Motion of Dual Droplets in Microchannels With Contact Angle Hysteresis北大核心CSCD

接触角滞后表现为流体在非理想固体表面上运动时前进接触角和后退接触角不同,是两相流体在润湿表面上流动的重要现象.该文采用改进的伪势格子Boltzmann(LB)多组分模型,并与几何润湿边界条件相结合,研究了两个液滴在具有接触角滞后性微通道表面上的运动行为,主要研究了通道内特征数、通道表面性质以及液滴初始参数的影响.研究结果表明：毛细数的增大有助于液滴的移动,然而并不利于液滴的排出,且毛细数的增加对上游液滴的影响大于其对下游液滴的影响;另一方面,接触角滞后性窗口越大,液滴运动和形变更迟缓,但形变程度更明显,两液滴更早地发生合并,但更晚地排出管道;液滴间距的增加使液滴的运动行为在不同阶段表现为不同的模式,但都导致通道中残留小液滴,使得液滴排出通道的时间增加.研究结果还表明：上游液滴和下游液滴的相对尺寸差距越大,越不利于液滴排出管道.     

Critical Velocities and Flow Rate Limitations in Open Capillary Channel Flows (CCF)

In the present study a forced liquid flow through an open capillary channel is investigated experimentally and numerically under reduced gravity conditions (microgravity). An open capillary channel is a structure that establishes a liquid flow path at low Bond numbers, when the capillary pressure caused by the surface tension force dominates in comparison to the hydrostatic pressure induced by gravitational or residual accelerations. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)