scholarly journals Solution selection of axisymmetric Taylor bubbles

2018 ◽  
Vol 843 ◽  
pp. 518-535 ◽  
Author(s):  
A. Doak ◽  
J.-M. Vanden-Broeck
Keyword(s):  
Surface Tension ◽  
Constant Velocity ◽  
Numerical Scheme ◽  
Solution Space ◽  
Selection Mechanism ◽  
Small Surface ◽  
Taylor Bubble ◽  
Solution Selection ◽  
Selection Of ◽  
Taylor Bubbles

A finite difference scheme is proposed to solve the problem of axisymmetric Taylor bubbles rising at a constant velocity in a tube. A method to remove singularities from the numerical scheme is presented, allowing accurate computation of the bubbles with the inclusion of both gravity and surface tension. This paper confirms the long-held belief that the solution space of the axisymmetric Taylor bubble for small surface tension is qualitatively similar to that of the plane Taylor bubble. Furthermore, evidence suggesting that the solution selection mechanism associated with plane bubbles also occurs in the axisymmetric case is presented.

scholarly journals The singular perturbation of surface tension in Hele-Shaw flows

2000 ◽  
Vol 409 ◽  
pp. 251-272 ◽  
Author(s):  
HECTOR D. CENICEROS ◽  
THOMAS Y. HOU
Keyword(s):  
Surface Tension ◽  
Numerical Method ◽  
Complex Singularity ◽  
Small Perturbations ◽  
Interface Evolution ◽  
Small Surface ◽  
The Impact ◽  
Equilibrium Growth ◽  
Dynamic Formation ◽  
Selection Of

Morphological instabilities are common to pattern formation problems such as the non-equilibrium growth of crystals and directional solidification. Very small perturbations caused by noise originate convoluted interfacial patterns when surface tension is small. The generic mechanisms in the formation of these complex patterns are present in the simpler problem of a Hele-Shaw interface. Amid this extreme noise sensitivity, what is then the role played by small surface tension in the dynamic formation and selection of these patterns? What is the asymptotic behaviour of the interface in the limit as surface tension tends to zero? The ill-posedness of the zero-surface-tension problem and the singular nature of surface tension pose challenging difficulties in the investigation of these questions. Here, we design a novel numerical method that greatly reduces the impact of noise, and allows us to accurately capture and identify the singular contributions of extremely small surface tensions. The numerical method combines the use of a compact interface parametrization, a rescaling of the governing equations, and very high precision. Our numerical results demonstrate clearly that the zero-surface-tension limit is indeed singular. The impact of a surface-tension-induced complex singularity is revealed in detail. The singular effects of surface tension are first felt at the tip of the interface and subsequently spread around it. The numerical simulations also indicate that surface tension defines a length scale in the fingers developing in a later stage of the interface evolution.

Harmony as licensing

2018 ◽  
Author(s):  
Harry van der Hulst
Keyword(s):  
Vowel Harmony ◽  
Selection Mechanism ◽  
Phonological Structure ◽  
Explicit Theory ◽  
Selection Of

This chapter develops an explicit theory of vowel harmony based on unary elements and lateral and positional licensing which is embedded in a general dependency-based theory of phonological structure (called ‘Radical CV Phonology’). Harmony is analyzed in terms of a licensing requirement, which results in ‘agreement’, both intra-morphemically and inter-morphemically, that is, within the domain of the word In essence, the view put forward is that lexical vowel harmony involves the selection of lexically listed allomorphs. Licensing will be the selection mechanism for the proper allomorph. The chapter discusses the treatment of morpheme-internal harmony, trigger and targets in harmony, and the notion of cyclicity.

Application of a Genetic Algorithm to Concept Variant Selection

2006 ◽  
Author(s):  
Ryan S. Hutcheson ◽  
Robert L. Jordan ◽  
Robert B. Stone ◽  
Janis P. Terpenny ◽  
Xiaomeng Chang
Keyword(s):  
Genetic Algorithm ◽  
Product Development ◽  
Solution Space ◽  
Variant Selection ◽  
Functional Modeling ◽  
Detailed Design ◽  
Modeling Techniques ◽  
Break Even Point ◽  
Future Work ◽  
Selection Of

This paper outlines a framework for applying a genetic algorithm to the selection of component variants between the conceptual and detailed design stages of product development. A genetic algorithm (GA) is defined for the problem and an example is presented that demonstrates its application and usefulness. Functional modeling techniques are used to formulate the design problem and generate the chromosomes that are evaluated with the algorithm. In the presented example, suitable GA parameters and the break-even point where the GA surpassed an enumerated search of the same solution space were found. Recommend uses of the GA along with limitations of the method and future work are presented as well.

On the drag-out problem in liquid film theory

2008 ◽  
Vol 617 ◽  
pp. 283-299 ◽  
Author(s):  
E. S. BENILOV ◽  
V. S. ZUBKOV
Keyword(s):  
Surface Tension ◽  
Liquid Film ◽  
Constant Velocity ◽  
Stokes Equations ◽  
Film Theory ◽  
Infinite Plate ◽  
Self Similar Solution ◽  
Self Similar ◽  
The Mean ◽  
Steady Solutions

We consider an infinite plate being withdrawn (at an angle α to the horizontal, with a constant velocity U) from an infinite pool of viscous liquid. Assuming that the effects of inertia and surface tension are weak, Derjaguin (C. R. Dokl. Acad. Sci. URSS, vol. 39, 1943, p. 13.) conjectured that the ‘load’ l, i.e. the thickness of the liquid film clinging to the plate, is l=(μU/ρgsinα)1/2, where ρ and μ are the liquid's density and viscosity, and g is the acceleration due to gravity.In the present work, the above formula is derived from the Stokes equations in the limit of small slopes of the plate (without this assumption, the formula is invalid). It is shown that the problem has infinitely many steady solutions, all of which are stable – but only one of these corresponds to Derjaguin's formula. This particular steady solution can only be singled out by matching it to a self-similar solution describing the non-steady part of the film between the pool and the film's ‘tip’.Even though the near-pool region where the steady state has been established expands with time, the upper, non-steady part of the film (with its thickness decreasing towards the tip) expands faster and, thus, occupies a larger portion of the plate. As a result, the mean thickness of the film is 1.5 times smaller than the load.

Liquid Taylor Bubbles Rising in a Vertical Column of a Heavier Liquid: An Approximate Analysis

2008 ◽  
Vol 131 (1) ◽  
Author(s):  
T. K. Mandal ◽  
G. Das ◽  
P. K. Das
Keyword(s):  
Empirical Equation ◽  
Flow Analysis ◽  
Rise Velocity ◽  
Vertical Column ◽  
Taylor Bubble ◽  
Two Fluids ◽  
Viscosity Effects ◽  
Semi Empirical ◽  
Theoretical Analyses ◽  
Taylor Bubbles

It has been noted that a volume of lighter liquid when injected into a stationary column of a heavier liquid, it rises up as a simple elongated Taylor bubble. In the present study, experimental and theoretical analyses have been performed to understand the rise of liquid Taylor bubbles. The experiments have been performed with different liquid pairs with their viscosities ranging from 0.71mPas to 1.75mPas and conduit sizes ranging from 0.012 m to 0.0461 m. The bubble shape has been predicted using a potential flow analysis and validated from photographic measurements. This analysis has been further modified to predict the rise velocity. The modified analysis accounts for the density difference between the two liquids, viscosity effects of the primary liquid, and interfacial tension of two fluids. A semi-empirical equation has been developed, which gives satisfactory results for most of the cases.

scholarly journals Why, sometimes, primaries? Intraparty democratization as a default selection mechanism in German and Spanish mainstream parties

2018 ◽  
Vol 26 (5) ◽  
pp. 594-604 ◽  
Author(s):  
Javier Astudillo ◽  
Klaus Detterbeck
Keyword(s):  
Political Parties ◽  
Selection Method ◽  
Regional Level ◽  
Selection Mechanism ◽  
Leadership Selection ◽  
Limited Knowledge ◽  
Western Democracies ◽  
Selection Of

In many Western democracies, political parties have started to open to members the selection of their leaders. While most studies focus on the introduction of this new selection method, its subsequent practice is still understudied. The article contributes to our still limited knowledge of this process by looking at two multilevel countries, Germany and Spain, where the mainstream parties have sometimes organized membership ballots, especially at the regional level, for leadership selection. Thanks to two original databases on party conferences and membership ballots, the article analyzes the background of this process and reviews the most common explanations offered by the literature. It shows that they are not held when parties want to regain power, or party chairs seek their nomination, as commonly believed, but when there are intraparty leadership disputes.

scholarly journals On the deflection of a liquid jet by an air-cushioning layer

2018 ◽  
Vol 846 ◽  
pp. 711-751 ◽  
Author(s):  
M. R. Moore ◽  
J. P. Whiteley ◽  
J. M. Oliver
Keyword(s):  
Surface Tension ◽  
Equations Of Motion ◽  
Constant Thickness ◽  
Liquid Jet ◽  
Pressure Jump ◽  
Length Scales ◽  
Small Surface ◽  
Numerical Studies ◽  
Impact Problems ◽  
Systematic Derivation

A hierarchy of models is formulated for the deflection of a thin two-dimensional liquid jet as it passes over a thin air-cushioning layer above a rigid flat impermeable substrate. We perform a systematic derivation of the leading-order equations of motion for the jet in the distinguished limit in which the air pressure jump, surface tension and gravity affect the displacement of the centreline of the jet, but not its thickness or velocity. We identify thereby the axial length scales for centreline deflection in regimes in which the air layer is dominated by viscous or inertial effects. The derived length scales and reduced equations aim to expand the suite of tools available for future analyses of the evolution of lamellae and ejecta in impact problems. Assuming that the jet is sufficiently long that tip and entry effects can be neglected, we demonstrate that the centreline of a constant-thickness jet moving with constant axial speed is destabilised by the air layer for sufficiently small surface tension. Expressions for the fastest-growing modes are obtained in both the viscous-dominated air and inertia-dominated air regimes. For a finite-length jet emanating from a nozzle, we show that, in one particular asymptotic limit, the evolution of the jet centreline is akin to the flapping of an unfurling flag above a thin air layer. We discuss the distinguished limit in which tip retraction can be neglected and perform numerical investigations into the resulting model. We show that the cushioning layer causes the jet centreline to bend, leading to rupture of the air layer. We discuss how our toolbox of models can be adapted and utilised in the context of recent experimental and numerical studies of splash dynamics.

scholarly journals Rigorous results in existence and selection of Saffman–Taylor fingers by kinetic undercooling

2018 ◽  
Vol 30 (1) ◽  
pp. 63-116
Author(s):  
XUMING XIE
Keyword(s):  
Surface Tension ◽  
Rigorous Results ◽  
Engineering Mathematics ◽  
Stokes Lines ◽  
Kinetic Undercooling ◽  
Finger Width ◽  
Linear Differential ◽  
Finger Tip ◽  
Selection Of ◽  
Hele Shaw Cell

The selection of Saffman–Taylor fingers by surface tension has been extensively investigated. In this paper, we are concerned with the existence and selection of steadily translating symmetric finger solutions in a Hele–Shaw cell by small but non-zero kinetic undercooling (ε2). We rigorously conclude that for relative finger width λ near one half, symmetric finger solutions exist in the asymptotic limit of undercooling ε2 → 0 if the Stokes multiplier for a relatively simple non-linear differential equation is zero. This Stokes multiplier S depends on the parameter $\alpha \equiv \frac{2 \lambda -1}{(1-\lambda)}\epsilon^{-\frac{4}{3}}$ and earlier calculations have shown this to be zero for a discrete set of values of α. While this result is similar to that obtained previously for Saffman–Taylor fingers by surface tension, the analysis for the problem with kinetic undercooling exhibits a number of subtleties as pointed out by Chapman and King (2003, The selection of Saffman–Taylor fingers by kinetic undercooling, Journal of Engineering Mathematics, 46, 1–32). The main subtlety is the behaviour of the Stokes lines at the finger tip, where the analysis is complicated by non-analyticity of coefficients in the governing equation.

scholarly journals Selection of Multimode Resource-Constrained Project Scheduling Scheme Based on DEA Method

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Song Zhang
Keyword(s):  
Project Scheduling ◽  
Data Envelopment ◽  
Resource Constrained ◽  
Resource Constrained Project Scheduling ◽  
Scheduling Scheme ◽  
Solution Selection ◽  
Project Scheduling Problem ◽  
Dea Method ◽  
Multiobjective Algorithms ◽  
Selection Of

A multimode resource-constrained project scheduling problem (MRCPSP) may have multifeasible solutions, due to its nature of targeting multiobjectives. Given the NP-hard MRCPSP and intricate multiobjective algorithms, finding the optimized result among those solutions seems impossible. This paper adopts data envelopment analysis (DEA) to evaluate a series of solutions of an MRCPSP and to find an appropriate choice in an objective way. Our approach is applied to a typical MRCPSP in practice, and the results validate that DEA is an effective and objective method for MRCPSP solution selection.

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