scholarly journals Capillary bridges between a plane and a cylindrical wall

2015 ◽  
Vol 773 ◽  
Author(s):  
Etienne Reyssat
Keyword(s):  
Numerical Solution ◽  
Quantitative Agreement ◽  
Horizontal Cylinder ◽  
Numerical Results ◽  
Planar Boundary ◽  
Cylindrical Wall ◽  
Good Quantitative Agreement ◽  
Capillary Bridges

We report experimental, theoretical and numerical results on the shapes of liquid menisci connecting a planar boundary and the surface of a horizontal cylinder placed above. The gradient of confinement traps the wetting drops in the most confined regions, which promotes their elongation along the line of smallest gap between the walls. The experimental shapes of these stretched capillary bridges are shown to be in good quantitative agreement with the numerical solution of the equation describing their contour. In particular, we show that the measured shapes are better described when taking into account the correction resulting from the coupling of in-plane and transverse interfacial curvatures calculated by Park & Homsy (J. Fluid Mech., vol. 139, 1984, pp. 291–308) over thirty years ago.

Using the generalized Adams-Bashforth-Moulton method for obtaining the numerical solution of some variable-order fractional dynamical models

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Mohamed M. Khader
Keyword(s):  
Differential Equations ◽  
Fractional Derivative ◽  
Numerical Solution ◽  
Numerical Results ◽  
Convergence Order ◽  
Variable Order ◽  
Numerical Treatment ◽  
Dynamical Models ◽  
Fractional Modeling ◽  
Dynamics Problems

AbstractThis paper is devoted to introduce a numerical treatment using the generalized Adams-Bashforth-Moulton method for some of the variable-order fractional modeling dynamics problems, such as Riccati and Logistic differential equations. The fractional derivative is described in Caputo variable-order fractional sense. The obtained numerical results of the proposed models show the simplicity and efficiency of the proposed method. Moreover, the convergence order of the method is also estimated numerically.

Steady streaming within a periodically rotating sphere

2008 ◽  
Vol 608 ◽  
pp. 71-80 ◽  
Author(s):  
RODOLFO REPETTO ◽  
JENNIFER H. SIGGERS ◽  
ALESSANDRO STOCCHINO
Keyword(s):  
Series Expansion ◽  
Oscillation Frequency ◽  
Small Amplitude ◽  
Quantitative Agreement ◽  
Torsional Oscillations ◽  
Rotating Sphere ◽  
Good Quantitative Agreement ◽  
Steady Streaming ◽  
Theory And Experiments ◽  
Streaming Flow

We consider the flow in a spherical chamber undergoing periodic torsional oscillations about an axis through its centre, and analyse it both theoretically and experimentally. We calculate the flow in the limit of small-amplitude oscillations in the form of a series expansion in powers of the amplitude, finding that at second order, a steady streaming flow develops consisting of two toroidal cells. This streaming behaviour is also observed in our experiments. We find good quantitative agreement between theory and experiments, and we discuss the dependence of the steady streaming behaviour as both the oscillation frequency and amplitude are varied.

Rods falling near a vertical wall

1977 ◽  
Vol 83 (2) ◽  
pp. 273-287 ◽  
Author(s):  
W. B. Russel ◽  
E. J. Hinch ◽  
L. G. Leal ◽  
G. Tieffenbruck
Keyword(s):  
Integral Equation ◽  
Viscous Fluid ◽  
Numerical Solution ◽  
Vertical Wall ◽  
Numerical Results ◽  
Slender Body ◽  
Asymptotic Results ◽  
Slender Body Theory ◽  
Friction Coefficients ◽  
Body Theory

As an inclined rod sediments in an unbounded viscous fluid it will drift horizontally but will not rotate. When it approaches a vertical wall, the rod rotates and so turns away from the wall. Illustrative experiments and a slender-body theory of this phenomenon are presented. In an incidental study the friction coefficients for an isolated rod are found by numerical solution of the slender-body integral equation. These friction coefficients are compared with the asymptotic results of Batchelor (1970) and the numerical results of Youngren ' Acrivos (1975), who did not make a slender-body approximation.

Numerical solution of a source identification problem: Almost coercivity

2019 ◽  
Vol 27 (4) ◽  
pp. 457-468 ◽  
Author(s):  
Allaberen Ashyralyev ◽  
Abdullah Said Erdogan ◽  
Ali Ugur Sazaklioglu
Keyword(s):  
Numerical Solution ◽  
Source Identification ◽  
Identification Problem ◽  
Second Order ◽  
Numerical Results ◽  
Difference Schemes ◽  
Stability Estimates ◽  
Order Of Accuracy ◽  
Accuracy Difference ◽  
Coercive Stability

Abstract The present paper is devoted to the investigation of a source identification problem that describes the flow in capillaries in the case when an unknown pressure acts on the system. First and second order of accuracy difference schemes are presented for the numerical solution of this problem. Almost coercive stability estimates for these difference schemes are established. Additionally, some numerical results are provided by testing the proposed methods on an example.

scholarly journals Numerical solution of an integral equation arising in the problem of cruciform crack using Daubechies scale function

2019 ◽  
Vol 14 (1) ◽  
pp. 21-27
Author(s):  
Jyotirmoy Mouley ◽  
M. M. Panja ◽  
B. N. Mandal
Keyword(s):  
Stress Intensity Factor ◽  
Integral Equation ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Numerical Solution ◽  
Present Method ◽  
Numerical Results ◽  
Scale Function ◽  
Forcing Term ◽  
Classical Integral

Abstract This paper is concerned with obtaining approximate numerical solution of a classical integral equation of some special type arising in the problem of cruciform crack. This integral equation has been solved earlier by various methods in the literature. Here, approximation in terms of Daubechies scale function is employed. The numerical results for stress intensity factor obtained by this method for a specific forcing term are compared to those obtained by various methods available in the literature, and the present method appears to be quite accurate.

scholarly journals Numerical Simulation of the Solar Granulation

1980 ◽  
Vol 58 ◽  
pp. 293-299
Author(s):  
Lawrence D. Cloutman
Keyword(s):  
Numerical Simulation ◽  
Numerical Solution ◽  
Stokes Equations ◽  
Solar Physics ◽  
Quantitative Agreement ◽  
Time Dependent ◽  
Navier Stokes ◽  
Vortex Rings ◽  
Solar Granulation ◽  
Navier Stokes Equations

AbstractThe solar granulation has been simulated by numerical solution of the multidimensional, time-dependent, nonlinear Navier-Stokes equations applied to the solar atmosphere. Granules may be explained as buoyantly rising bubbles created at the level where T = 8000 K, and which have collapsed into vortex rings. The calculation is in quantitative agreement with observations and has a number of implications for solar physics and convection theory.

A Lagrangian Reactive Transport Simulator with Successive Paths and Stationary-States: Concepts, Implementation and Verification

1989 ◽  
Vol 176 ◽  
Author(s):  
R. B. Knapp
Keyword(s):  
Reference Frame ◽  
Peclet Number ◽  
Software Package ◽  
Reactive Transport ◽  
Quantitative Agreement ◽  
Stationary States ◽  
Good Quantitative Agreement ◽  
Analytical Results ◽  
Single Path ◽  
Aqueous Species

ABSTRACTA geochemical software package which models static, single-path kinetic water-rock interactions, EQ3/6, has been modified to incorporate successive-paths and stationary states under high Peclet number transport conditions in a Lagrangian reference frame. These modifications permit calculation of reactive transport with reasonable computational requirements. Results from the new option in EQ3/6 have been compared with analytical results for the simple HC1 - SiO2 system; excellent agreements were achieved. Results have also been compared with published results for a portion of the A12O3 - HCI - K2O - SiO2 system. The results are in good qualitative and, in some cases, good quantitative agreement. However, the values of some variables differ substantially; these differences can be attributed to use of a different set of Al and Si aqueous species.

On two dimensional electrohydrostatic stability

1976 ◽  
Vol 349 (1657) ◽  
pp. 231-243 ◽  
Keyword(s):  
Approximate Solution ◽  
Numerical Solution ◽  
Edge Effects ◽  
Complex Variable ◽  
Equilibrium Configuration ◽  
Quantitative Agreement ◽  
Two Dimensional ◽  
Equilibrium Conditions ◽  
Conducting Membranes ◽  
Special Case

Complex variable techniques are used for the study of the electrohydrostatic stability of two dimensional charged conducting membranes, which are assumed to be fixed along their edges. The formulation of the problem is quite general, but the numerical solution presented refers to the case when the membranes are symmetrical with respect to the plane bisecting their width and carry equal and opposite charges. It is found, as expected, that for a given set of data the equilibrium configuration breaks down if the membranes are sufficiently charged. When the membranes are sufficiently apart the breakdown occurs at their edges and is manifested as inability of the system to satisfy the equilibrium conditions there. When the membranes are sufficiently close together and are charged to a certain level, they touch at their mid-points and the equilibrium breaks down. Our results are compared with an approximate solution of this problem, presented by two other authors. The approximate solution ignores the edge effects of the membranes and overestimates the amount of charge that the membranes can carry before breakdown occurs. In the special case when the gap between the membranes is much less than their width, our results are in quantitative agreement with the approximate solution but as the gap between the membranes increases, the accuracy of the approximate solution decreases.

Evolution of Matt Surface Topography in Aluminium Pack Rolling

2005 ◽  
Author(s):  
Hiroshi Utsunomiya ◽  
Michael P. F. Sutcliffe ◽  
Hugh R. Shercliff ◽  
Pete S. Bate ◽  
Dan B. Miller
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Surface Topography ◽  
Material Properties ◽  
Quantitative Agreement ◽  
Aluminium Foil ◽  
The Finite Element Method ◽  
Good Quantitative Agreement ◽  
Pack Rolling ◽  
Element Method

Roughening of the matt surface of pack rolled aluminium foil has been modelled. The model is based on the finite element method using isotropic plasticity. A distribution in material properties has been used to simulate the distribution of orientations through the material. The predictions of roughness show good quantitative agreement with the experiments.

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