The Stretching of a Viscoplastic Thread of Liquid

2003 ◽  
Vol 125 (6) ◽  
pp. 946-951 ◽  
Author(s):  
M. A. M. Al Khatib
Keyword(s):  
Coordinate System ◽  
Yield Stress ◽  
Special Interest ◽  
Inertial Effects ◽  
Viscoplastic Fluids ◽  
Lagrangian Coordinate ◽  
Lagrangian Coordinate System

The problem of stretching a viscoplastic (yield-stress) thread of a liquid hanging vertically is considered. The length of the thread at later times and the time at which it ruptures is determined. A Lagrangian coordinate system is used to analyze the extension of the thread as it sags under its own weight, with negligible inertial effects. The biviscosity model has been used to characterize viscoplastic fluids; the Newtonian and Bingham models can be recovered as limiting cases. The Bingham limit is of special interest.

Slow Dripping of Yield-Stress Fluids

2005 ◽  
Vol 127 (4) ◽  
pp. 687-690 ◽  
Author(s):  
M. A. M. Al Khatib ◽  
S. D. R. Wilson
Keyword(s):  
Coordinate System ◽  
Yield Stress ◽  
Special Interest ◽  
Vertical Tube ◽  
Viscoplastic Fluids ◽  
Yield Stress Fluids ◽  
Lagrangian Coordinate ◽  
Lagrangian Coordinate System

The dripping problem of a viscoplastic (yield-stress) liquid running slowly out of a narrow vertical tube is considered. The volume of the drops which break away is determined. A Lagrangian coordinate system is used to analyze the extension of the thread as it sags under its own weight, neglecting inertia and capillarity. The biviscosity model has been used to characterize viscoplastic fluids; the Newtonian and Bingham models can be recovered as limiting cases. The Bingham limit is of special interest.

scholarly journals A quasi-Lagrangian coordinate system based on high resolution tracer observations: implementation for the Antarctic polar vortex

2008 ◽  
Vol 8 (4) ◽  
pp. 16123-16173 ◽  
Author(s):  
E. V. Ivanova ◽  
C. M. Volk ◽  
O. Riediger ◽  
H. Klein ◽  
N. M. Sitnikov ◽  
...  
Keyword(s):  
High Resolution ◽  
Coordinate System ◽  
Vortex Core ◽  
Polar Vortex ◽  
Mixing Ratio ◽  
Lagrangian Coordinate ◽  
Antarctic Polar Vortex ◽  
The Antarctic ◽  
Lagrangian Coordinate System

Abstract. In order to quantitatively analyse the chemical and dynamical evolution of the polar vortex it has proven extremely useful to work with coordinate systems that follow the vortex flow. We propose here a two-dimensional quasi-Lagrangian coordinate system {χi, Δχi}, based on the mixing ratio of a long-lived stratospheric trace gas i, and its systematic use with i = N2O, in order to describe the structure of a well-developed Antarctic polar vortex. In the coordinate system {χi, Δχi} the mixing ratio χi is the vertical coordinate and Δχi = χi(Θ)−χivort(Θ) is the meridional coordinate (χivort(Θ) being a vertical reference profile in the vortex core). The quasi-Lagrangian coordinates {χi, Δχi} persist for much longer time than standard isentropic coordinates, potential temperature Θ and equivalent latitude φe, do not require explicit reference to geographic space, and can be derived directly from high-resolution in situ measurements. They are therefore well-suited for studying the evolution of the Antarctic polar vortex throughout the polar winter with respect to the relevant chemical and microphysical processes. By using the introduced coordinate system {χN2O, ΔχN2O} we analyze the well-developed Antarctic vortex investigated during the APE-GAIA (Airborne Polar Experiment – Geophysica Aircraft in Antarctica – 1999) campaign (Carli et al., 2000). A criterion, which uses the local in-situ measurements of χi=χi(Θ) and attributes the inner vortex edge to a rapid change (δ-step) in the meridional profile of the mixing ratio χi, is developed to determine the (Antarctic) inner vortex edge. In turn, we suggest that the outer vortex edge of a well-developed Antarctic vortex can be attributed to the position of a local minimum of the χH2O gradient in the polar vortex area. For a well-developed Antarctic vortex, the ΔχN2O-parametrization of tracer-tracer relationships allows to distinguish the tracer inter-relationships in the vortex core, vortex boundary region and surf zone and to examine their meridional variation throughout these regions. This is illustrated by analyzing the tracer-tracer relationships χi : χN2O obtained from the in-situ data of the APE-GAIA campaign for i = CFC-11, CFC-12, H-1211 and SF6. A number of solitary anomalous points in the CFC-11 : N2O correlation, observed in the Antarctic vortex core, are interpreted in terms of small-scale cross-isentropic dispersion.

scholarly journals The Lagrangian coordinate system and what it means for two-dimensional crowd flow models

2016 ◽  
Vol 443 ◽  
pp. 272-285 ◽  
Author(s):  
Femke van Wageningen-Kessels ◽  
Ludovic Leclercq ◽  
Winnie Daamen ◽  
Serge P. Hoogendoorn
Keyword(s):  
Coordinate System ◽  
Two Dimensional ◽  
Flow Models ◽  
Lagrangian Coordinate ◽  
Lagrangian Coordinate System

scholarly journals An Alternative Algorithm for Simulating Flash Flood

2021 ◽  
Vol 930 (1) ◽  
pp. 012076
Author(s):  
M F Khaldirian ◽  
A P Rahardjo ◽  
D Luknanto ◽  
R D R Sondi
Keyword(s):  
Numerical Modeling ◽  
Debris Flow ◽  
Coordinate System ◽  
Flash Flood ◽  
Front Propagation ◽  
Bed Elevation ◽  
Forward Difference ◽  
Lagrangian Coordinate ◽  
The Galerkin Method ◽  
Sediment Mixture

Abstract Most of the approaches in numerical modeling techniques are based on the Eulerian coordinate system. This approach faces difficulty in simulating flash flood front propagation. This paper shows an alternative method that implements a numerical modeling technique based on the Lagrangian coordinate system to simulate the water of debris flow. As for the interaction with the riverbed, the simulation uses an Eulerian coordinate system. The method uses the conservative and momentum equations of water and sediment mixture in the Lagrangian form. Source terms represent deposition and erosion. The riverbed in the Eulerian coordinate system interacts with the flow of the mixture. At every step, the algorithm evaluates the relative position of moving nodes of the flow part to the fixed nodes of the riverbed. Computation of advancing velocity and depth uses the riverbed elevation, slope data, and the bed elevation change computation uses the erosion or deposition data of the flow on the moving nodes. Spatial discretization is implementing the Galerkin method. Furthermore, temporal discretization is implementing the forward difference scheme. Test runs show that the algorithm can simulate downward, upward, and reflected backward 1-D flow cases. Two-D model tests and comparisons with SIMLAR software show that the algorithm works in simulating debris flow.

FLOW OF VISCOPLASTIC FLUIDS ON AN INCLINED PLANE: EVALUATION OF YIELD STRESS

1990 ◽  
Vol 96 (1) ◽  
pp. 229-239 ◽  
Author(s):  
D. DE KEE ◽  
R.P. CHHABRA ◽  
M.B. POWLEY ◽  
S. ROY
Keyword(s):  
Yield Stress ◽  
Inclined Plane ◽  
Viscoplastic Fluids

Drift velocity of spatially decaying waves in a two-layer viscous system

1995 ◽  
Vol 299 ◽  
pp. 217-239 ◽  
Author(s):  
Ismael Piedra-Cueva
Keyword(s):  
Mass Transport ◽  
Lower Layer ◽  
Mass Conservation ◽  
Layer System ◽  
Transport Velocity ◽  
Mass Transport Velocity ◽  
Lagrangian Coordinate ◽  
Progressive Waves ◽  
Lagrangian Coordinate System ◽  
Good Agreement

This paper analyses the mass transport velocity in a two-layer system induced by the action of progressive waves. First the movement inside the two layers is obtained. Next the mass transport of spatially decaying waves is calculated by solving the momentum and mass conservation equations in the Lagrangian coordinate system. Two different physical situations are analysed: the first is waves in a closed channel and the second is waves in an unbounded domain, where the steady-state mass flux may be non-zero. The influence of the viscous properties of the lower layer on the mass transport in both layers is studied. Comparison with the experiments of Sakakiyama & Bijker (1989) in a water-mud system shows good agreement. The results show that the mass transport velocity can be quite different from the velocity given by the rigid bed theory, depending on the physical properties of the lower layer.

Tangential flow and advective mixing of viscoplastic fluids between eccentric cylinders

2001 ◽  
Vol 431 ◽  
pp. 65-89 ◽  
Author(s):  
YURUN FAN ◽  
NHAN PHAN-THIEN ◽  
ROGER I. TANNER
Keyword(s):  
Yield Stress ◽  
Outer Cylinder ◽  
Creeping Flow ◽  
Mixing Efficiency ◽  
Steady Flows ◽  
Major Barrier ◽  
Tangential Flow ◽  
Viscoplastic Fluids ◽  
Initial Location ◽  
Advective Mixing

This is a study on the tangential flow and advective mixing of viscoplastic fluids (Bingham plastics) between two eccentric, alternately rotating cylinders. Two geometrical configurations and various rotation modes are considered for a relatively large range of the yield stress. The hp-type finite element method with the mixed formulation is used to solve for the steady velocity and pressure fields. The bi-viscosity and the Papanastasiou models agree quantitatively with each other in predicting the velocity fields and the practically unyielded zones. However, the Papanastasiou model is more robust and economic than the bi-viscosity model in the computation using Newton iteration. In the steady flows, in addition to the motionless zones, we have discovered some plugs with rigid rotation, including rotating plugs stuck onto the outer cylinder and rotating, even counter-rotating, plugs disconnected from both cylinders. The unsteady, periodic flow is composed of a sequence of the steady flows, which is valid in the creeping flow regime. The characteristics of advective mixing in these flows have been studied by analysing the asymptotic coverages of a passive tracer, the distributions of the lineal stretching in the flow and the variations of the mean stretching of the flow with time. The tracer coverage is intuitive but qualitative and, occasionally, it depends on the initial location of the tracer. On the other hand, the distribution of stretching is quantitative and more reliable in reflecting the mixing characteristics. Interestingly, the zones of the lowest stretching in the distribution graphs are remarkably well matched with the regular zones in the tracer-coverage graphs. Furthermore, the mixing efficiency proposed by Ottino (1989) is used to characterize the advective mixing in the two geometrical configurations with various rotation modes. It is important to realize that, for plastic fluids, a major barrier to effective mixing is the unyielded fluid plugs which are controlled by the yield stress and geometrical configurations. Therefore, when designing an eccentric helical annular mixer it is important to pay attention first to the geometric issues then to the operating issues.

scholarly journals A Theory of Elastic/Plastic Plane Strain Pure Bending of FGM Sheets at Large Strain

Materials ◽  
2019 ◽  
Vol 12 (3) ◽  
pp. 456 ◽  
Author(s):  
Sergey Alexandrov ◽  
Yun-Che Wang ◽  
Lihui Lang
Keyword(s):  
Residual Stresses ◽  
Plane Strain ◽  
Material Properties ◽  
Large Strain ◽  
Thickness Distribution ◽  
Functionally Graded ◽  
Pure Bending ◽  
Lagrangian Coordinate ◽  
Lagrangian Coordinate System ◽  
General Method

An efficient analytical/numerical method has been developed and programmed to predict the distribution of residual stresses and springback in plane strain pure bending of functionally graded sheets at large strain, followed by unloading. The solution is facilitated by using a Lagrangian coordinate system. The study is concentrated on a power law through thickness distribution of material properties. However, the general method can be used in conjunction with any other through thickness distributions assuming that plastic yielding initiates at one of the surfaces of the sheet. Effects of material properties on the distribution of residual stresses are investigated.

Flow Between Eccentric Rotating Cylinders

1972 ◽  
Vol 94 (3) ◽  
pp. 266-274 ◽  
Author(s):  
R. C. DiPrima ◽  
J. T. Stuart
Keyword(s):  
Coordinate System ◽  
Journal Bearing ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Inertial Effects ◽  
Rotating Cylinders ◽  
Clearance Ratio ◽  
Navier Stokes Equations ◽  
First Order ◽  
Systematic Expansion

The flow between eccentric rotating cylinders is studied using a modified bipolar coordinate system. The Sommerfeld pressure distribution and associated flow in a journal bearing are derived from the Navier-Stokes equations by a straightforward and systematic expansion in the clearance ratio (assumed small). First order corrections for curvature and inertial effects are given. There is no restriction on the eccentricity.

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