The rheology of some two-dimensional disperse systems

1957 ◽  
Vol 53 (2) ◽  
pp. 514-524 ◽  
Author(s):  
J. G. Oldroyd
Keyword(s):  
Surface Tension ◽  
Elastic Moduli ◽  
Equations Of State ◽  
Two Dimensional ◽  
Flow Properties ◽  
Disperse Systems ◽  
Continuous Component ◽  
Fluid System ◽  
Interfacial Films ◽  
Small Deformations

ABSTRACTAn investigation is made of the deformation and flow properties of two-dimensional disperse systems consisting of small circular patches of one component widely dispersed in a continuous component with different rheological properties. Attention is restricted to small deformations (or small rates of deformation in the case of a fluid system) so that the equations of state are linear and the properties of each component can be characterized by two elastic moduli, or by two operators involving d/dt which take the place of moduli. Surface tension in each component and boundary tension between the components are taken into account, so that the theory can be applied to interfacial films at liquid-liquid or liquid-gas interfaces as well as to thicker sheets and films. General formulae are derived, expressing the two modulus operators of a disperse system in terms of those of the components, and their use is illustrated by means of examples.

A novel interface method for two-dimensional multiphase SPH: Interface detection and surface tension formulation

2021 ◽  
Vol 431 ◽  
pp. 110119
Author(s):  
B.X. Zheng ◽  
L. Sun ◽  
P. Yu
Keyword(s):  
Surface Tension ◽  
Two Dimensional

scholarly journals Nonlinear two-dimensional free surface solutions of flow exiting a pipe and impacting a wedge

2021 ◽  
Vol 126 (1) ◽  
Author(s):  
Alex Doak ◽  
Jean-Marc Vanden-Broeck
Keyword(s):  
Surface Tension ◽  
Integral Equation ◽  
Free Surface ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Two Dimensional ◽  
Numerical Schemes ◽  
Additional Advantage ◽  
Infinite Wedge ◽  
Good Agreement

AbstractThis paper concerns the flow of fluid exiting a two-dimensional pipe and impacting an infinite wedge. Where the flow leaves the pipe there is a free surface between the fluid and a passive gas. The model is a generalisation of both plane bubbles and flow impacting a flat plate. In the absence of gravity and surface tension, an exact free streamline solution is derived. We also construct two numerical schemes to compute solutions with the inclusion of surface tension and gravity. The first method involves mapping the flow to the lower half-plane, where an integral equation concerning only boundary values is derived. This integral equation is solved numerically. The second method involves conformally mapping the flow domain onto a unit disc in the s-plane. The unknowns are then expressed as a power series in s. The series is truncated, and the coefficients are solved numerically. The boundary integral method has the additional advantage that it allows for solutions with waves in the far-field, as discussed later. Good agreement between the two numerical methods and the exact free streamline solution provides a check on the numerical schemes.

The Elastic Moduli of Silver Thin Films Measured with a New Microtensile Tester

1991 ◽  
Vol 239 ◽  
Author(s):  
J. Ruud ◽  
D. Josell ◽  
A. L. Greer ◽  
F. Spaepen
Keyword(s):  
Thin Film ◽  
Thin Films ◽  
Diffraction Grating ◽  
Strain Measurement ◽  
Elastic Moduli ◽  
Two Dimensional ◽  
Bulk Crystals ◽  
Free Standing ◽  
Tensile Direction ◽  
Silver Thin Films

ABSTRACTA new design for a thin film microtensile tester is presented. The strain is measured directly on the free-standing thin film from the displacement of laser spots diffracted from a thin grating applied to its surface by photolithography. The diffraction grating is two-dimensional, allowing strain measurement both along and transverse to the tensile direction. In principle, both Young's modulus and Poisson's ratio of a thin film can be determined. Ag thin films with strong <111> texture were tested. The measured Young moduli agreed with those measured on bulk crystals, but the measured Poisson ratios were low, most likely due to slight transverse folding of the film that developed during the test.

scholarly journals Elastic Moduli of Collagen Gels Can Be Predicted from Two-Dimensional Confocal Microscopy

2009 ◽  
Vol 97 (7) ◽  
pp. 2051-2060 ◽  
Author(s):  
Ya-li Yang ◽  
Lindsay M. Leone ◽  
Laura J. Kaufman
Keyword(s):  
Confocal Microscopy ◽  
Elastic Moduli ◽  
Two Dimensional ◽  
Collagen Gels

Study on C–S and P–R EOS in pseudo-potential lattice Boltzmann model for two-phase flows

2017 ◽  
Vol 28 (09) ◽  
pp. 1750120 ◽  
Author(s):  
Yong Peng ◽  
Yun Fei Mao ◽  
Bo Wang ◽  
Bo Xie
Keyword(s):  
Surface Tension ◽  
Lattice Boltzmann ◽  
Equations Of State ◽  
Density Ratio ◽  
Maximum Density ◽  
Lattice Boltzmann Model ◽  
Two Phase Flows ◽  
Two Phase ◽  
Spurious Currents ◽  
Pseudo Potential

Equations of State (EOS) is crucial in simulating multiphase flows by the pseudo-potential lattice Boltzmann method (LBM). In the present study, the Peng and Robinson (P–R) and Carnahan and Starling (C–S) EOS in the pseudo-potential LBM with Exact Difference Method (EDM) scheme for two-phase flows have been compared. Both of P–R and C–S EOS have been used to study the two-phase separation, surface tension, the maximum two-phase density ratio and spurious currents. The study shows that both of P–R and C–S EOS agree with the analytical solutions although P–R EOS may perform better. The prediction of liquid phase by P–R EOS is more accurate than that of air phase and the contrary is true for C–S EOS. Predictions by both of EOS conform with the Laplace’s law. Besides, adjustment of surface tension is achieved by adjusting [Formula: see text]. The P–R EOS can achieve larger maximum density ratio than C–S EOS under the same [Formula: see text]. Besides, no matter the C–S EOS or the P–R EOS, if [Formula: see text] tends to 0.5, the computation is prone to numerical instability. The maximum spurious current for P–R is larger than that of C–S. The multiple-relaxation-time LBM still can improve obviously the numerical stability and can achieve larger maximum density ratio.

scholarly journals A remark on the two dimensional water wave problem with surface tension

2019 ◽  
Vol 266 (9) ◽  
pp. 5748-5771
Author(s):  
Shuanglin Shao ◽  
Hsi-Wei Shih
Keyword(s):  
Surface Tension ◽  
Water Wave ◽  
Two Dimensional ◽  
Wave Problem ◽  
Water Wave Problem

scholarly journals Kelvin-Helmholtz discontinuity in two superposed viscous conducting fluids in a horizontal magnetic field

2008 ◽  
Vol 12 (3) ◽  
pp. 103-110 ◽  
Author(s):  
Aiyub Khan ◽  
Neha Sharma ◽  
P.K. Bhatia
Keyword(s):  
Magnetic Field ◽  
Surface Tension ◽  
Growth Rate ◽  
Unstable Mode ◽  
Two Dimensional ◽  
Horizontal Magnetic Field ◽  
Streaming Velocity ◽  
The Stability ◽  
Conducting Fluids ◽  
Streaming Motion

The Kelvin-Helmholtz discontinuity in two superposed viscous conducting fluids has been investigated in the taking account of effects of surface tension, when the whole system is immersed in a uniform horizontal magnetic field. The streaming motion is assumed to be two-dimensional. The stability analysis has been carried out for two highly viscous fluid of uniform densities. The dispersion relation has been derived and solved numerically. It is found that the effect of viscosity, porosity and surface tension have stabilizing influence on the growth rate of the unstable mode, while streaming velocity has a destabilizing influence on the system.

Flow and Chemical Kinetics Simulations of Endothermic Fuels

2003 ◽  
Author(s):  
Thomas A. Ward ◽  
Jamie S. Ervin ◽  
Richard C. Striebich ◽  
Steven Zabarnick
Keyword(s):  
Heat Transfer ◽  
Computational Model ◽  
Chemical Kinetics ◽  
Flow Reactor ◽  
Two Dimensional ◽  
Flow Properties ◽  
Supercritical Regime ◽  
Fuel Flow ◽  
Product Distributions ◽  
Heat Transfer Limit

Advanced aircraft engines are reaching a practical heat transfer limit beyond which the convective heat transfer provided by hydrocarbon fuels is no longer adequate. One solution is to use an endothermic fuel that absorbs heat through chemical reactions. This paper describes the development of a two-dimensional computational model of the heat and mass transport associated with a flowing fuel using a unique global chemical kinetics model. Most past models do not account for changes in the chemical composition of a flowing fuel and also do not adequately predict flow properties in the supercritical regime. The two-dimensional computational model presented here calculates the changing flow properties of a supercritical reacting fuel by use of experimentally derived proportional product distributions. The present calculations are validated by measured experimental data obtained from a flow reactor of mildly cracked n-decane. It is believed that these simulations will assist the fundamental understanding of high temperature fuel flow experiments.

scholarly journals Derivation of Ice Sliding Properties from The Numerical Modelling of Surging Ice Masses

1979 ◽  
Vol 23 (89) ◽  
pp. 420-421 ◽  
Author(s):  
W. F. Budd ◽  
B. J. McInnes ◽  
I. Smith
Keyword(s):  
Shear Stress ◽  
Numerical Modelling ◽  
Sliding Friction ◽  
Two Dimensional ◽  
Dimensional Model ◽  
Flow Properties ◽  
Two Dimensional Model ◽  
Two Parameters ◽  
Basal Shear ◽  
Best Fit

Abstract It is difficult to deduce sliding properties from the numerical modelling of ordinary glaciers because the flow law of ice is still not known well enough to clearly differentiate sliding from internal deformation of the ice. For glaciers undergoing high-speed surges it appears that the majority of the total speed is due to sliding. Furthermore the average basal shear stress of the ice mass is lowered during the surge. This suggests that surging glaciers can be modelled by incorporating a sliding friction law which has the effective friction coefficient decreasing for high velocities. A relation of this type has been found for ice sliding on granite at −0.5°C by Barnes and others (1971) and has also been obtained for rough slabs with ice at the pressure-melting point by Budd and others (1979). A simple two-dimensional model was developed by Budd and McInnes (1974) and Budd (1975), which was found to exhibit the typical periodic surge-like characteristics of real ice masses. Since the sliding-stress relation for the low velocities and stresses was not known, and was not so important for the surges, it was decided to use the condition of gross equilibrium (i.e. that the ice mass as a whole does not accelerate) together with a single-parameter relation for the way in which the friction decreases with stress and velocity to prescribe the basal shear-stress distribution. The low-stress-velocity relation can thus be obtained as a result. This two-dimensional model has now been parameterized to take account of the three-dimensional aspects of real ice masses. A number of ice masses have since been closely matched by the model including three well-known surging ice masses: Lednik Medvezhiy, Variegated Glacier, and Bruarjökull. Since the flow properties of ice are so poorly known—especially for longitudinal stress and strain-rates—the model has been run with two unknown parameters: one a flow-law parameter (η) and the other a sliding parameter (ø). The model is run over a wide range of these two parameters to see if a good match can be made to the real ice masses and if so what the values of the parameters η and ø are for best fit. The matching of the three above ice masses gave very similar values for each of the two parameters η and ø, the value of η being within the range of values expected for the flow properties of temperate ice as determined by laboratory experiments. Using the same values of η and ø it is found that the ordinary glaciers modelled so far do not develop surging but that they could do if the value of ø were increased or if the mass-balance input were sufficiently increased. For Lednik Medvezhiy a detailed analysis of the friction coefficient with velocity was carried out and it was found that the values required for best fit showed a very close agreement to the sliding friction curve of Barnes and others (1971) at −0.5°C. It is concluded that this type of sliding relation can account for the major features of glacier surge phenomena. Finally it is apparent that the numerical modelling technique can be used very effectively to test any large-scale bulk sliding relation by the analysis of real surges of ice masses and in addition can provide further insight into the sliding relation in association with other stresses in the ice mass.

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