Open capillary siphons

2021 ◽  
Vol 932 ◽  
Author(s):  
Kaizhe Wang ◽  
Pejman Sanaei ◽  
Jun Zhang ◽  
Leif Ristroph
Keyword(s):  
Surface Tension ◽  
Fluid Transport ◽  
Numerical Solutions ◽  
Strong Dependence ◽  
Viscous Friction ◽  
Geometrical Parameters ◽  
Controlled System ◽  
Free Surfaces ◽  
Biological Phenomena ◽  
Shaped Tube

Flow in the inverted U-shaped tube of a conventional siphon can be established and maintained only if the tube is filled and closed, so that air does not enter. We report on siphons that operate entirely open to the atmosphere by exploiting surface tension effects. Such capillary siphoning is demonstrated by paper tissue that bridges two containers and conveys water from the upper to the lower. We introduce a more controlled system consisting of grooves in a wetting solid, formed here by pressing together hook-shaped metallic rods. The dependence of flux on siphon geometry is systematically measured, revealing behaviour different from the conventional siphon. The flux saturates when the height difference between the two container's free surfaces is large; it also has a strong dependence on the climbing height from the source container's free surface to the apex. A one-dimensional theoretical model is developed, taking into account the capillary pressure due to surface tension, pressure loss due to viscous friction, and driving by gravity. Numerical solutions are in good agreement with experiments, and the model suggests hydraulic interpretations for the observed flux dependence on geometrical parameters. The operating principle and characteristics of capillary siphoning revealed here can inform biological phenomena and engineering applications related to directional fluid transport.

scholarly journals The surface-tension-driven evolution of a two-dimensional annular viscous tube

2007 ◽  
Vol 593 ◽  
pp. 181-208 ◽  
Author(s):  
I. M. GRIFFITHS ◽  
P. D. HOWELL
Keyword(s):  
Surface Tension ◽  
Numerical Solutions ◽  
Applied Pressure ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Free Surfaces ◽  
Final Shape ◽  
Capillary Tubing ◽  
Well Posed

We consider the evolution of an annular two-dimensional region occupied by viscous fluid driven by surface tension and applied pressure at the free surfaces. We assume that the thickness of the domain is small compared with its circumference, so that it may be described as a thin viscous sheet whose ends are joined to form a closed loop. Analytical and numerical solutions of the resulting model are obtained and we show that it is well posed whether run forwards or backwards in time. This enables us to determine, in many cases explicitly, which initial shapes will evolve into a desired final shape. We also show how the application of an internal pressure may be used to control the evolution.This work is motivated by the production of non-axisymmetric capillary tubing via the Vello process. Molten glass is fed through a die and drawn off vertically, while the shape of the cross-section evolves under surface tension and any applied pressure as it flows downstream. Here the goal is to determine the die shape required to achieve a given desired final shape, typically square or rectangular. We conclude by discussing the role of our two-dimensional model in describing the three-dimensional tube-drawing process.

Numerical Solutions to Free Boundary Problems

Acta Numerica ◽  
1995 ◽  
Vol 4 ◽  
pp. 335-415 ◽  
Author(s):  
Thomas Y. Hou
Keyword(s):  
Surface Tension ◽  
Crystal Growth ◽  
Free Boundary ◽  
Water Waves ◽  
Numerical Solutions ◽  
Boundary Integral ◽  
Stability And Convergence ◽  
Instability Wave ◽  
Free Surfaces ◽  
Free Boundary Value Problems

Many physically interesting problems involve propagation of free surfaces. Vortex-sheet roll-up in hydrodynamic instability, wave interactions on the ocean's free surface, the solidification problem for crystal growth and Hele-Shaw cells for pattern formation are some of the significant examples. These problems present a great challenge to physicists and applied mathematicians because the underlying problem is very singular. The physical solution is sensitive to small perturbations. Naïve discretisations may lead to numerical instabilities. Other numerical difficulties include singularity formation and possible change of topology in the moving free surfaces, and the severe time-stepping stability constraint due to the stiffness of high-order regularisation effects, such as surface tension.This paper reviews some of the recent advances in developing stable and efficient numerical algorithms for solving free boundary-value problems arising from fluid dynamics and materials science. In particular, we will consider boundary integral methods and the level-set approach for water waves, general multi-fluid interfaces, Hele–Shaw cells, crystal growth and solidification. We will also consider the stabilising effect of surface tension and curvature regularisation. The issue of numerical stability and convergence will be discussed, and the related theoretical results for the continuum equations will be addressed. This paper is not intended to be a detailed survey and the discussion is limited by both the taste and expertise of the author.

Electrohydrodynamic stability: Taylor–Melcher theory for a liquid bridge suspended in a dielectric gas

2002 ◽  
Vol 452 ◽  
pp. 163-187 ◽  
Author(s):  
C. L. BURCHAM ◽  
D. A. SAVILLE
Keyword(s):  
Surface Tension ◽  
Dielectric Constant ◽  
Electric Fields ◽  
Liquid Bridge ◽  
Numerical Solutions ◽  
Specific Conductivity ◽  
Axisymmetric Deformation ◽  
Aspect Ratios ◽  
The Stability ◽  
Theory And Experiment

A liquid bridge is a column of liquid, pinned at each end. Here we analyse the stability of a bridge pinned between planar electrodes held at different potentials and surrounded by a non-conducting, dielectric gas. In the absence of electric fields, surface tension destabilizes bridges with aspect ratios (length/diameter) greater than π. Here we describe how electrical forces counteract surface tension, using a linearized model. When the liquid is treated as an Ohmic conductor, the specific conductivity level is irrelevant and only the dielectric properties of the bridge and the surrounding gas are involved. Fourier series and a biharmonic, biorthogonal set of Papkovich–Fadle functions are used to formulate an eigenvalue problem. Numerical solutions disclose that the most unstable axisymmetric deformation is antisymmetric with respect to the bridge’s midplane. It is shown that whilst a bridge whose length exceeds its circumference may be unstable, a sufficiently strong axial field provides stability if the dielectric constant of the bridge exceeds that of the surrounding fluid. Conversely, a field destabilizes a bridge whose dielectric constant is lower than that of its surroundings, even when its aspect ratio is less than π. Bridge behaviour is sensitive to the presence of conduction along the surface and much higher fields are required for stability when surface transport is present. The theoretical results are compared with experimental work (Burcham & Saville 2000) that demonstrated how a field stabilizes an otherwise unstable configuration. According to the experiments, the bridge undergoes two asymmetric transitions (cylinder-to-amphora and pinch-off) as the field is reduced. Agreement between theory and experiment for the field strength at the pinch-off transition is excellent, but less so for the change from cylinder to amphora. Using surface conductivity as an adjustable parameter brings theory and experiment into agreement.

scholarly journals The effect of surface tension on steadily translating bubbles in an unbounded Hele-Shaw cell

2017 ◽  
Vol 473 (2201) ◽  
pp. 20170050 ◽  
Author(s):  
Christopher C. Green ◽  
Christopher J. Lustri ◽  
Scott W. McCue
Keyword(s):  
Surface Tension ◽  
Numerical Solutions ◽  
Bubble Velocity ◽  
Number Of Solutions ◽  
Branch Number ◽  
Single Solution ◽  
Countably Infinite ◽  
Prime Function ◽  
Hele Shaw Cell ◽  
Effect Of Surface

New numerical solutions to the so-called selection problem for one and two steadily translating bubbles in an unbounded Hele-Shaw cell are presented. Our approach relies on conformal mapping which, for the two-bubble problem, involves the Schottky-Klein prime function associated with an annulus. We show that a countably infinite number of solutions exist for each fixed value of dimensionless surface tension, with the bubble shapes becoming more exotic as the solution branch number increases. Our numerical results suggest that a single solution is selected in the limit that surface tension vanishes, with the scaling between the bubble velocity and surface tension being different to the well-studied problems for a bubble or a finger propagating in a channel geometry.

Effects of Geometrical Parameters on Improving the Transversal Mass Transport in PEM Fuel Cells

2006 ◽  
Author(s):  
Yanxia Zhao ◽  
Renwei Mei ◽  
James F. Klausner
Keyword(s):  
Fuel Cells ◽  
Flow Rate ◽  
Fluid Transport ◽  
Polymer Electrolyte Membrane ◽  
Pem Fuel Cells ◽  
Gas Diffusion ◽  
Flow Channel ◽  
Geometrical Parameters ◽  
Electrolyte Membrane ◽  
Transversal Flow

A computational model using Lattice Boltzmann Equation (LBE) method is employed to investigate the fluid transport on the anode side of Polymer Electrolyte Membrane (PEM) fuel cells, with an emphasis on mass transfer enhancement. A 3-dimensional LBE code is developed to solve the flows in the channel and the porous media in the gas diffusion layer (GDL) simultaneously. Multiple flow enhancers (obstructions in the flow channel) are placed in the channel to enhance the transversal flow across the GDL. The mass flow rate, the velocity field and the pressure distribution are analyzed. The effects of flow enhancers are assessed. The results show that the transversal flow across the GDL is enhanced by placing flow enhancers in the channel. Increasing flow enhancer size can significantly increase the transversal flow rate, with high pressure-loss through the flow channel. The results also demonstrate that the location of flow enhancers in the flow channel have a remarkable impact on the transversal flow rate. The transversal flow rate increases as the GDL porosity increases.

Estimation of Nusselt Number in Microchannels of Arbitrary Cross-Section With Constant Axial Heat Flux

2008 ◽  
Author(s):  
Ehsan Sadeghi ◽  
Majid Bahrami ◽  
Ned Djilali
Keyword(s):  
Heat Flux ◽  
Nusselt Number ◽  
Cross Section ◽  
Cross Sections ◽  
Numerical Solutions ◽  
Arbitrary Cross Section ◽  
Geometrical Parameters ◽  
Thermal Systems ◽  
Cross Sectional ◽  
Axial Heat

In many practical instances such as basic design, parametric study, and optimization analysis of thermal systems, it is often very convenient to have closed form relations to obtain the trends and a reasonable estimate of the Nusselt number. However, finding exact solutions for many practical singly-connected cross-sections, such as trapezoidal microchannels, is complex. In the present study, the square root of cross-sectional area is proposed as the characteristic length scale for Nusselt number. Using analytical solutions of rectangular, elliptical, and triangular ducts, a compact model for estimation of Nusselt number of fully-developed, laminar flow in microchannels of arbitrary cross-sections with “H1” boundary condition (constant axial wall heat flux with constant peripheral wall temperature) is developed. The proposed model is only a function of geometrical parameters of the cross-section, i.e., area, perimeter, and polar moment of inertia. The present model is verified against analytical and numerical solutions for a wide variety of cross-sections with a maximum difference on the order of 9%.

Tracking of Capillary Interface in Microfluidic Channels

2011 ◽  
Author(s):  
Prashant R. Waghmare ◽  
Farhan Ahmad ◽  
David S. Nobes ◽  
Sushanta K. Mitra
Keyword(s):  
Surface Tension ◽  
Flow Regime ◽  
Fluid Transport ◽  
Capillary Flow ◽  
Laser Source ◽  
Working Fluid ◽  
Microfluidic Channels ◽  
Experimental Setup ◽  
Imaging Device ◽  
Air Interface

Capillarity is commonly used for fluid transport in microfluidic devices. The capillary flow can be divided into three different flow regimes: entry regime, Poiseuille regime, and surface tension regime as shown in Fig. 1[1]. Generally, it is anticipated that at the entrance of any narrow confinement, the flow goes through entrance flow regime. For capillary flow, this entrance regime has generally been neglected in the literature. Beyond this entrance regime, the flow attains the fully developed velocity profile across the channel, which is termed as a Poiseuille flow. Moreover, in the capillary flow, the interface is always under traction — due to the capillary forces and hence, a third flow regime needs to be considered behind the interface which is referred as the surface tension regime. These regimes are yet to be experimentally explored and analyzed. An “in-house” developed μ-PIV system is used to quantify the flow field at the liquid/air interface (surface tension regime) in a rectangular glass microchannel of dimension 1.5 mm (width) × 500 μm (depth). The magnitude of velocity and the flow front evolution along the microchannel is calculated utilizing commercially available image processing software. Figure 2 shows the μ-PIV experimental setup used here. The main components of the experimental setup include an imaging device, magnification optics, and a continuous laser source (473 nm) in back illumination mode. The fluorescent particle of 1.9 m in diameter with DI water is used as a working fluid. The concentration of the microparticles is very less which is approximately 1%, therefore the effect of microbead concentration on the wetting properties is considered to be negligible for the present study. Moreover, it is assumed that the surface properties of the particles also do not affect the fluid flow. The capillary flow interface is captured and the corresponding processed images are presented to depict the velocity field at the liquid/air interface. The enlarged view of the microchannel cross section is shown in Fig. 2. The section A-A is the location at which the images are captured for the analysis.

scholarly journals Dynamical properties of vortical structures on the beta-plane

1994 ◽  
Vol 268 ◽  
pp. 103-131 ◽  
Author(s):  
G. G. Sutyrin ◽  
J. S. Hesthaven ◽  
J. P. Lynov ◽  
J. Juul Rasmussen
Keyword(s):  
Rossby Wave ◽  
Potential Vorticity ◽  
Fluid Transport ◽  
Numerical Solutions ◽  
Critical Value ◽  
Wave Radiation ◽  
Approximate Theory ◽  
Initial Direction ◽  
Vortical Structures ◽  
Long Time

The long-time evolution of monopolar and dipolar vortices influenced by the largescale gradient of the ambient potential vorticity (the β-effect) is studied by direct numerical solutions of the equivalent barotropic quasi-geostrophic equation. Translation and reorganization of vortical structures are shown to depend strongly on their intensity. Transport of trapped fluid by vortical structures is illustrated by calculating particle trajectories and by considering closed isolines of potential vorticity and the streamfunction in a co-moving reference frame.The initial behaviour of strong monopoles is found to be well described by a recent approximate theory for the evolution of azimuthal mode one, even for times longer than the linear Rossby wave period. In the long-time limit, strong monopoles transport particles mainly westward, although the meridional displacement is several times larger than the initial vortex size. The appearance of an annulus with opposite radial gradient of the potential vorticity around the vortex core is demonstrated. This annulus forms owing to the meridional vortex drift on the β-plane and results in reorganization of a strong monopolar vortex into a rotating tripole. A critical value of the vortex intensity is found, below which the tripolar structure does not appear even in the case of an initially shielded vortex. Weak monopolar vortices are able to trap particles and provide some west-meridional fluid transport, even in the case when they decay like a linear Rossby wave packet.The evolution of initial f-plane dipoles on the β-plane is strongly dependent on the initial direction of propagation. Strong dipoles adjust to steadily propagating modon solutions either accelerating (westward case), decelerating (eastward case) or oscillating with a decaying amplitude (meridional case), thereby carrying trapped particles predominantly eastward. A steady state is not reached if the dipole intensity is below a critical value which depends on the initial direction of propagation. Weak dipoles either decay and shrink owing to Rossby wave radiation (westward case), gradually separate and split (eastward case), or disintegrate (meridional case) without longdistance fluid transport. Thus, on the β-plane monopoles provide mainly westward transport of trapped fluid, whereas dipoles provide mainly eastward transport. Only strong monopoles are found to provide significant meridional fluid transport.

Cavitation Bubble Collapse in Viscous, Compressible Liquids—Numerical Analysis

1965 ◽  
Vol 87 (4) ◽  
pp. 977-985 ◽  
Author(s):  
R. D. Ivany ◽  
F. G. Hammitt
Keyword(s):  
Surface Tension ◽  
High Pressures ◽  
Numerical Solutions ◽  
Compressible Liquid ◽  
Navier Stokes ◽  
Bubble Collapse ◽  
Navier Stokes Equation ◽  
Scaling Parameters ◽  
Collapse Behavior ◽  
Normalized Solution

Collapse of a spherical bubble in a compressible liquid, including the effects of surface tension, viscosity, and an adiabatic compression of gas within the bubble is investigated by numerical solutions of the hydrodynamic equations. A limiting value of shear viscosity causes the bubble collapse to slow down markedly, for both compressible and incompressible liquids, whereas moderate viscosities have very little effect on the rate of collapse. The inclusion of surface tension and viscosity introduces two scaling parameters into the solution, so that a single normalized solution is no longer sufficient to describe collapse behavior. The magnitude of the density changes calculated for the compressible liquid and the extremely rapid changes with time suggest that the usual Navier-Stokes equation of motion may not be appropriate. The possibility of liquid relaxational phenomenon and its contribution to sonoluminescence is considered. Shock waves or damagingly high pressures are not generated during collapse at a distance in the liquid equal to the initial radius from the center of collapse, although they will appear at such a distance if the bubble rebounds.

Spreading and instability of a viscous fluid sheet

1990 ◽  
Vol 211 ◽  
pp. 373-392 ◽  
Author(s):  
L. M. Hocking
Keyword(s):  
Surface Tension ◽  
Free Surface ◽  
Related Problem ◽  
Numerical Solutions ◽  
Thin Sheet ◽  
Leading Edge ◽  
Small Disturbance ◽  
Inclined Plane ◽  
Moving Contact Line ◽  
Moving Contact

Experiments by Huppert (1982) have demonstrated that a finite volume of fluid placed on an inclined plane will elongate into a thin sheet of fluid as it slides down the plane. If the fluid is initially placed uniformly across the plane, the sheet retains its two-dimensionality for some time, but when it has become sufficiently long and thin, the leading edge develops a spanwise instability. A similarity solution for this motion was derived by Huppert, without taking account of the edge regions where surface tension is important. When these regions are examined, it is found that the conditions at the edges can be satisfied, but only when the singularity associated with the moving contact line is removed. When the sheet is sufficiently elongated, the profile of the free surface shows an upward bulge near the leading edge. It is suggested that the observed instability of the shape of the leading edge is a result of the dynamics of the fluid in this bulge. The related problem of a ridge of fluid sliding down the plane is examined and found to be linearly unstable. The spanwise lengthscale of this instability is, however, dependent on the width of the channel occupied by the fluid, which is at variance with the observed nature of the instability. Preliminary numerical solutions for the nonlinear development of a small disturbance to the position of a straight leading edge show the incipient development of a finger of fluid with a width that does not depend on the channel size, in accordance with the observations.

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