Yield stress of structured fluids measured by squeeze flow

Various structured fluids were placed between the parallel circular plates of a squeeze-flow rheometer and squeezed by a force F until the fluid thickness h was stationary. Fluid thickness down to a few microns could be measured. Most fluids showed two kinds of dependence of f on h according to an experimentally-determined thickness h ^*. If h > h ^* then F varied in proportion to h ⁻¹ as predicted by Scott (1931) for a fluid with a shear yield stress τ₀. The magnitude of τ₀ from squeeze-flow data in this region was compared with the yield stress measured by the vane method. For some fluids τ₀ measured by squeeze flow was less than the vane yield stress, suggesting that the yield stress of fluid in contact with the plates was less than the bulk yield stress. If h < h ^* then F varied approximately as h ^−5/2 and the squeeze-flow data in this region analysed with Scott's relationship gave a yield stress which increased as the fluid thickness decreased. This previously unreported effect may result from unconnected regions of large yield stress in the fluid of size similar to h ^* which are not sensed by the vane and which become effective in squeeze flow only when h < h ^*. Received: 13 December 1999/Accepted: 4 January 2000     

Investigation of liquid–liquid drop coalescence using tomographic PIV

High-speed tomographic PIV was used to investigate the coalescence of drops placed on a liquid/liquid interface; the coalescence of a single drop and of a drop in the presence of an adjacent drop (side-by-side drops) was investigated. The viscosity ratio between the drop and surrounding fluids was 0.14, the Ohnesorge number (Oh = μ_d/(ρ_dσD)^1/2) was 0.011, and Bond numbers (Bo = (ρ _d  − ρ _s )gD ²/σ) were 3.1–7.5. Evolving volumetric velocity fields of the full coalescence process allowed for quantification of the velocity scales occurring over different time scales. For both single and side-by-side drops, the coalescence initiates with an off-axis film rupture and film retraction speeds an order of magnitude larger than the collapse speed of the drop fluid. This is followed by the formation and propagation of an outward surface wave along the coalescing interface with wavelength of approximately 2D. For side-by-side drops, the collapse of the first drop is asymmetric due to the presence of the second drop and associated interface deformation. Overall, tomographic PIV provides insight into the flow physics and inherent three-dimensionalities in the coalescence process that would not be achievable with flow visualization or planar PIV only.     

Bifurcation From Stability to Instability for a Free Boundary Problem Arising in a Tumor Model

We consider a time-dependent free boundary problem with radially symmetric initial data: σ_t − Δσ + σ = 0 if and σ(r,0)=σ₀(r) in {r < R(0)} where R(0) is given. This is a model for tumor growth, with nutrient concentration (or tumor cells density) σ(r,t) and proliferation rate then there exists a unique stationary solution (σ_S(r), R_S), where R_S depends only on the number . We prove that there exists a number μ_*, such that if μ < μ_* . . . then the stationary solution is stable with respect to non-radially symmetric perturbations, whereas if μ > μ_* then the stationary solution is unstable.     

Stability of an Initially, Stably Stratified Fluid Subjected to a Step Change in Temperature

The onset of convective instability in an initially quiescent, stably stratified fluid layer between two horizontal plates is analyzed with linear theory. The bottom boundary is heated suddenly from below, subjected to a step change in surface temperature. The critical time t _c to mark the onset of Rayleigh-Bénard convection is predicted by propagation theory. This theory uses the length scaled by , where α denotes thermal diffusivity. Under the normal mode analysis the dimensionless disturbance equations are obtained as a function of τ(=αt/d ²) and ζ(=Z/), where d is the fluid layer depth and Z is the vertical distance. The resulting equations are transformed to self-similar ones by using scaling and finally fixing τ as τ_c under the frame of coordinates τ and ζ. For a given γ, Pr and τ_c, the minimum value of Ra is obtained from the marginal stability curve. Here γ denotes the temperature ratio to represent the degree of stabilizing effect, Pr is the Prandtl number and Ra is the Rayleigh number. With γ=0, the minimum Ra value approaches the well-known value of 1708 as τ_c increases. However, it is inversely proportional to τ_c ^3/2 as τ_c decreases. With increasing γ, the system becomes more stable. It is interesting that in the present system, propagation theory produces the stability criteria to bound the available experimental data over the whole domain of time. Received 5 November 2001 and accepted 29 March 2002 Published online: 2 October 2002 RID="*" ID="*" This work has been supported by both SK Chemicals Co. Ltd. and LG Chemical Ltd., Seoul under the Brain Korea 21 Project of the Ministry of Education. Communicated by H.J.S. Fernando     

Non-linear rheology and flow-induced transition of a lamellar-to-vesicle phase in ternary systems of alkyldimethyl oxide/alcohol/water

 The time-dependent transformation of an ionically charged lamellar phase (L _α-phase) into a vesicle phase under the influence of shear is investigated using rheological and conductivity measurements. The L _α-phase consists of the zwitterionic surfactant tetradecyldimethylaminoxide (C₁₄DMAO), hexanol, oxalic acid and water. The experiments were carried out on the L _α-phase in a well defined state. It was prepared by a special route from the neighbouring L ₃-phase that consists of 100 mM C₁₄DMAO, 250 mM hexanol and 5 mM oxalicdiethylester (OEE). The OEE hydrolyses in the L ₃ -phase to oxalic acid and ethanol. The result is a virgin L _α-phase which consists of stacked bilayers and which has not been exposed to shear. When this low-viscous phase is subjected to shear it is transformed into a highly viscous vesicle phase. The transformation of the L _α-phase into vesicles under constant shear was monitored by recording the viscosity and conductivity with time. It is observed that at least three different time constants can be distinguished in the transformation process. The conductivity passes through a minimum (τ₁) in the direction of shear. The viscosity first passes through a minimum (τ₂) and then over a maximum (τ₃). It is concluded that τ₁ belongs to the complete alignment of the bilayer parallel to the wall, τ₂ to the beginning of the break-up of the bilayers to the vesicles and τ₃ to the complete transformation of the L _α- to the vesicle phase. When the shear rate was varied, it was noted that the product of the time constants and shear is constant. Received: 30 June 1999/Accepted: 30 August 1999     

An experimental—Numerical evaluation of the<Emphasis Type="Italic">T</Emphasis><Stack><Subscript>ε</Subscript><Superscript>*</Superscript></Stack> integral for a three-dimensional crack front

TheT _ε ^* integral was calculated on the surface of single edge notched, three-point bend (SE(B)) specimens using experimentally obtained displacements. Comparison was made withT _ε ^* calculated with the measured surface displacements andT _ε ^* calculated at several points through the thickness of a finite element (FE) model of the SE(B) specimen. Good comparison was found between the surfaceT _ε ^* calculated from displacements extracted from the FE model and the surfaceT _ε ^* calculated from experimentally obtained displacements. The computedT _ε ^* integral was also observed to decrease as the crack front was traversed from the surface to the mid-plane of the specimen. Mid-planeT _ε ^* values tend to be approximately 10% of the surface values.     

Stability of Degenerate Stationary Waves for Viscous Gases

This paper is concerned with the asymptotic stability of degenerate stationary waves for viscous gases in the half space. We discuss the following two cases: (1) viscous conservation laws and (2) damped wave equations with nonlinear convection. In each case, we prove that the solution converges to the corresponding degenerate stationary wave at the rate t ^−α/4 as t → ∞, provided that the initial perturbation is in the weighted space L²_a=L²(\mathbb R₊; (1+x)^a dx){L^2_\alpha=L^2({\mathbb R}_+;\,(1+x)^\alpha dx)} . This convergence rate t ^−α/4 is weaker than the one for the non-degenerate case and requires the restriction α < α_*(q), where α_*(q) is the critical value depending only on the degeneracy exponent q. Such a restriction is reasonable because the corresponding linearized operator for viscous conservation laws cannot be dissipative in L²_a{L^2_\alpha} for α > α^*(q) with another critical value α^*(q). Our stability analysis is based on the space–time weighted energy method in which the spatial weight is chosen as a function of the degenerate stationary wave.     

Finite element solutions for laminar flow and combined convection around a square prism

The finite element solutions of the full Navier-Stokes and energy equations for steady laminar flow and combined convection around square prisms with attack angles of 0° and 45° are obtained for a gas having Pr=0.7. The variations of surface shear stress, local pressure and Nusselt number are obtained over the entire prism surface including the zone beyond the point of the separation. The predicted values of drag coefficients, the location of separation, average Nusselt number and the plots of velocity flow fields and isotherms are also presented. The trend of the present numerical results seems reasonable.

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Finite-Elemente-Verfahren für laminare Strömung und kombinierte Naturkonvektion um ein quadratisches Prisma

Zusammenfassung Es wird über Lösungen der Navier-Stokesund der Energiegleichungen mit Hilfe der Finite-Elemente-Methode für stationäre laminare Strömung, kombiniert mit Naturkonvektion, um ein quadratisches Prisma berichtet, wobei als Anströmwinkel 0° und 45° gewählt wurden und Gasströmung mitPr=0,7 angenommen wurde. Die Rechnung ergibt den Verlauf der Wandschubspannungen, des örtlichen Druckes und der Nusselt-Zahl über die gesamte Oberfläche des Prismas, einschließlich des Bereiches hinter dem Ablösepunkt. Weiterhin werden in dem Aufsatz Angaben gemacht über die Widerstandskoeffizienten, die Lage des Ablösepunktes, der mittleren Nusselt-Zahl sowie der Geschwindigkeits- und Temperaturfelder. Die numerischen Ergebnisse erscheinen im Trend vernünftig zu sein.

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Nomenclature a side length of square - C _f friction drag coefficient - C _p pressure drag coefficient - C _D total drag coefficient - F _f total friction drag force - F _P total pressure drag force - Gr Groshoff number,g (T _w -T )a ³/v ² - g gravitational acceleration - h local heat transfer coefficient - K thermal conductivity - L dimensionless location of surface from the front stagna tion point,L ^*/a - L ^* dimension location of prism surface - Lc location of separation - N _j shape function - Nu, local and average Nusselt numbers - M _l shape function - P dimensionless pressure,p ^*/u ² - P ^* pressure - p _x ^* x-componentP ^* - Pe Peclet number,Re Pr - Pr Prandtl number, c/K - Ra Rayleigh number,Gr Pr - Re Reynolds number,a u /v - s direction along the sides of prism - u dimensionlessX-direction component of velocity,u ^*/u - u ^* X-direction component of velocity - u free stream velocity - dimensionlessY-direction component of velocity,v*/u - ^* Y-direction component of velocity - X X-direction axis - x dimensionlessX-direction coordinate,x ^*/a - x ^* X- direction coordinate - Y Y-direction axis - y ^* dimensionless 7-direction coordinate,y ^*/a - y ^* Y-direction coordinate Greek symbols coefficient of volumetric thermal expansion - attack angle - dynamic viscosity - kinematic viscosity,/ - density of fluid - _w dimensionless surface shear stress, _w ^* /u ² - _w ^* surface shear stress - _wx ^* x-component of _w ^/* - dimensionless temperature,      

An investigation of electromagnetic wave propagation in plasma by shock tube

This paper presents the electromagnetic wave propagation characteristics in plasma and the attenuation coefficients of the microwave in terms of the parameters he, v, w, L, wb. The φ800 mm high temperature shock tube has been used to produce a uniform plasma. In order to get the attenuation of the electromagnetic wave through the plasma behind a shock wave, the microwave transmission has been used to measure the relative change of the wave power. The working frequency is f = (2-35)GHz (ω=2πf, wave length A =15cm-8mm). The electron density in the plasma is ne = (3&#215;10^10-1&#215;10^14) cm^-3. The collision frequency v = (1&#215;10^8-6&#215;10^10) Hz. The thickness of the plasma layer L = (2-80)cm. The electron circular frequency ωb=eBo/me, magnetic flux density B0 = (0-0.84)T. The experimental results show that when the plasma layer is thick (such as L/λ≥10), the correlation between the attenuation coefficients of the electromagnetic waves and the parameters ne,v,ω, L determined from the measurements are in good agreement with the theoretical predictions of electromagnetic wave propagations in the uniform infinite plasma. When the plasma layer is thin (such as when both L and A are of the same order), the theoretical results are only in a qualitative agreement with the experimental observations in the present parameter range, but the formula of the electromagnetic wave propagation theory in an uniform infinite plasma can not be used for quantitative computations of the correlation between the attenuation coefficients and the parameters ne,v,ω, L. In fact, if ω&lt;ωp, v^2&lt;&lt;ω^2, the power attenuations K of the electromagnetic waves obtained from the measurements in the thin-layer plasma are much smaller than those of the theoretical predictions. On the other hand, if ω&gt;ωp, v^2&lt;&lt;ω^2 (just v≈f), the measurements are much larger than the theoretical results. Also, we have measured the electromagnetic wave power attenuation value under the magnetic field and without a magnetic field. The result indicates that the value measured under the magnetic field shows a distinct improvement.     

Free convection from a vertical plate with concentrated and distributed thermal sources

An analysis is developed for the laminar free convection from a vertical plate with uniformly distributed wall heat flux and a concentrated line thermal source embedded at the leading edge. We introduce a parameter=(1 +Q _L/Q_w)^–1=(1 + Ra_L/Ra_w)^–1 to describe the relative strength of the two thermal sources; and propose a unified buoyancy parameter=( Ra_L+ Ra_w)^1/5 with=1/(1 +Pr ^–1) to properly scale the dependent and independent variables. The variables are so defined that the resulting nonsimilar boundary-layer equations can describe exactly the buoyancy-induced flow from the dual sources with any relative strength to fluids of any Prandtl number from very small values to infinity. These nonsimilar equations are readily reducible to the self-similar equations of an adiabatic wall plume for=0, and to those of free convection from uniform flux plate for=1. Rigorous finite-difference solutions for fluids of Pr from 0.001 to are obtained over the entire range of from 0 to 1. The effects of both relative source strength and Prandtl number on the velocity profiles, temperature profiles, and the variations of wall temperature, are clearly illustrated.

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Freie Konvektion an einer vertikalen Platte mit einer konzentrierten und einer gleichmäßig verteilten Wärmequelle

Zusammenfassung Für die freie Konvektion an einer vertikalen Platte mit einer gleichmäßig verteilten Wandwärmestromdichte und einer in der Vorderkante eingebetteten linienförmigen Wärmequelle wird eine Berechnungsmethode entwickelt. Zur Beschreibung der relativen Stärke der beiden Wärmequellen führen wir einen Parameter=(1 + Q_L/Q_w)^–1=(1 + Ra_L/Ra_w)^–1 ein und schlagen einen vereinheitlichten Auftriebsparameter=( Ra _L+ Ra _w)^1/5 mit=1/(1 +Pr ^–1 für die Skalierung der abhängigen und unabhängigen Variablen vor. Die Variablen werden so definiert, daß mit den sich ergebenden unabhängigen Grenzschichtgleichungen die von den beiden Wärmequellen beliebiger Stärke verursachte Auftriebsströmung von Fluiden beliebiger Prandtl-Zahl genau beschrieben werden kann. Diese unabhängigen Gleichungen können ohne weiteres auf die selbstähnlichen Gleichungen für den Fall einer lokalen Wärmezufuhr an einer sonst adiabatischen Wand für=0 und jenen der freien konvektion an einer Platte mit einheitlichem Wärmestrom für=1 zurückgeführt werden. Für Fluide mit der Prandtl-Zahl zwischen 0,001 und Unendlich werden nach der strengen finite Differenzen-Methode Lösungen im Bereich von zwischen 0 und 1 erhalten. Der jeweilige Einfluß der relativen Quellenstärke und der Prandtl-Zahl auf die Geschwindigkeits- und Temperaturprofile sowie die Veränderung der Wandtemperatur werden deutlich dargestellt.

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Nomenclature C _f friction coefficient - C _p specific heat - f reduced stream function - g gravitational acceleration - k thermal conductivity - L width of the plate - Nu local Nusselt number - Pr Prandtl number - q _w wall heat flux - Q _L heat generated by the line source - Q _w heat released by the uniform-flux wall from 0 tox, q _w Lx - Ra _L local Rayleigh number, g T _L ^* x ³/( ) - Ra _w local Rayleigh number,g T _w ^* w ³/( ) - T fluid temperature - T temperature of ambient fluid - T _L ^* characteristic temperature of the line source,Q _{L/(C p} L) - T _w ^* characteristic temperature of the uniform flux wall, =q _w x/k=Q _w /(C _p L) - u velocity component in then-direction - U₀ dimensionless velocity,u/(/x) Ra _L ^2/5 - U ₁ dimensionless velocity,u/(/x) Ra _w ^2/5 - velocity component in they-direction - x coordinate parallel to the plate - y coordinate normal to the plate - thermal diffusivity - thermal expansion coefficient - pseudo-similarity variable,(y/x) - dimensionless temperature, (T–T )/(T _L ^* +T _w ^* ) - ₀ dimensionless temperature, (Ra_l)^1/5 (T–T )/T _L ^* - ₁ dimensionless temperature, (Ra_w)Ra_w)^1/5 (T–T )/T _w ^* - (Ra _L+Ra_w)^1/5 - kinematic viscosity - (1 +Ra _L/Ra_w)^–1=(1 +T _L ^* /T _w ^* )^–1=(1 + Q_L/Q_w)^–1 - density - Pr/(1 +Pr) - _w wall shear stress - stream function     

Experiments on the lift of a spinning sphere in a range of intermediate Reynolds numbers

 The lift force experienced by a spinning sphere moving in a viscous fluid, with constant linear and angular velocities, is measured by means of a trajectographic technique. Measurements are performed in the range of dimensionless angular velocities γ=aω/V lying between 1 and 6, and in the range of Reynolds numbers Re=2aV/ν lying between 10 and 140 (a sphere radius, ω angular velocity, V relative velocity of the sphere centre, ν fluid kinematic viscosity). A notable departure from the theoretical relationship at low Reynolds number, C _L =2γ, is obtained, the ratio C _L /γ being found to significantly decrease with increasing γ and increasing Re. The following correlation is finally proposed to estimate the lift coefficient in the range 10<Re<140: C _L ≅0.45+(2γ−0.45) exp (−0.075γ^0.4 Re ^0.7) Received: 20 May 1996/Accepted: 9 November 1997     

Flow of viscous and viscoelastic fluids through and around porous bodies

The slow flow of a viscous fluid through and around porous spheres is considered. The numerical simulation uses a special mixture of computational techniques: quadratic approximation and expansion in power series. The resulting calculations predict the evolution of the main features of the flow if the boundary conditions are varying, particularly if the tangential velocity is neglected or if a viscous filtration velocity is assumed at the sphere surface. The cases of full and hollow spheres with uniform and non uniform permeabilities are considered, the external impermeable walls of the flow being concentric spheres or cylinders. Some influence of viscoelastic properties of the fluid is also given.Nomenclature AA _n , A_n, B_n, b_n, C_n, c_n, D_n constants of integration - C _n (t) Gegenbauer functions with degree n and order –1/2 - e shell thickness - K, K* permeability - P _n (t) Legendre functions - Q _v volumetric rate of flow - p, p ₀, p _e pressure, far away pressure, average pressure - R* sphere radius - r, spherical coordinates - Re Reynolds' number (see equation 37) - s, t sinus and cosinus - V ₀ ^* uniform velocity - v velocity component - We Weissenberg's number (see equation (37)) - permeability coefficient - thickness coefficient - structural coefficient - diameter ratio sphere-cylinder - * dynamic viscosity of the fluid - stream functions - normal stress ( _rr ) - tangential stress ( ) - ₀ ^* relaxation time of the fluid     

Range-pair-counting fatigue gage

In this paper, the surface roughening phenomenon of an aluminum foil during fatigue process is utilized for monitoring of a variable amplitude stress. It is found that constant mean stress does not affect surface roughness. When the mean stress varies, however, it causes surface roughening. In such a case, the equivalent stress defined by (Σσ _i ^α N _i /ΣN _i )^1/α dominates surface roughness of an aluminum foil, where σ _i andN _i are stress amplitude and the number of cycles counted by the rangepair method, respectively, and α is a gage factor which is peculiar to the foil used. It is concluded that the aluminum foil can be used as the range-pair counting fatigue gage with high accuracy.     

Nonsimilarity solutions for non-Darcy mixed convection from horizontal surfaces in a porous medium

Non-Darcy mixed convection in a porous medium from horizontal surfaces with variable surface heat flux of the power-law distribution is analyzed. The entire mixed convection regime is divided into two regions. The first region covers the forced convection dominated regime where the dimensionless parameter ζ _f =Ra^* _x /Pe² _x is found to characterize the effect of buoyancy forces on the forced convection with K ^′ U _∞/ν characterizing the effect of inertia resistance. The second region covers the natural convection dominated regime where the dimensionless parameter ζ _n =Pe _x /Ra^*1/2 _x is found to characterize the effect of the forced flow on the natural convection, with (K ^′ U _∞/ν)Ra^*1/2 _x /Pe _x characterizing the effect of inertia resistance. To obtain the solution that covers the entire mixed convection regime the solution of the first regime is carried out for ζ _f =0, the pure forced convection limit, to ζ _f =1 and the solution of the second is carried out for ζ _n =0, the pure natural convection limit, to ζ _n =1. The two solutions meet and match at ζ _f =ζ _n =1, and R ^* _h =G ^* _h . Also a non-Darcy model was used to analyze mixed convection in a porous medium from horizontal surfaces with variable wall temperature of the power-law form. The entire mixed convection regime is divided into two regions. The first region covers the forced convection dominated regime where the dimensionless parameter ξ _f =Ra _x /Pe _x ^3/2 is found to measure the buoyancy effects on mixed convection with Da _x Pe _x /ɛ as the wall effects. The second region covers the natural convection dominated region where ξ _n =Pe _x /Ra _x ^2/3 is found to measure the force effects on mixed convection with Da _x Ra _x ^2/3/ɛ as the wall effects. Numerical results for different inertia, wall, variable surface heat flux and variable wall temperature exponents are presented. Received on 8 July 1996     

On the orders of the best approximations of integrals of functions by integrals of rank σ

We study the values e _σ(f) of the best approximation of integrals of functions from the spaces L _p (A, dμ) by integrals of rank σ. We determine the orders of the least upper bounds of these values as σ → ∞ in the case where the function ƒ is the product of two nonnegative functions one of which is fixed and the other varies on the unit ball U _p (A) of the space L _p (A, dμ). We consider applications of the obtained results to approximation problems in the spaces S _p ^ϕ. __________ Translated from Neliniini Kolyvannya, Vol. 10, No. 4, pp. 528–559, October–December, 2007.     

Molecular dynamics studies on the dislocation gliding near a tilt boundary

The gliding behavior of edge dislocation near a grain boundary (GB) in copper under pure shear stresses is simulated by using molecular dynamics(MD) method. Many-body potential incorporating the embedded atom method (EAM) is used. The critical shear stresses for a single disocation to pass across GB surface are obtained at values of σ _c =23MPa ∼ 68 MPa and 137MPa∼274 MPa for Ω=165 small angle tilt GB at 300K and 20K, respectively. The first result agrees with the experimental yield stress σ _y (=42MPa) quite well. It suggests that there might be one of the reasons of initial plastic yielding caused by single dislocation gliding across GB. In addition, there might be possibility to obtain yield strength from microscopic analysis. Moreover, the experimental value of σ _y at low temperature is generally higher than that at room temperature. So, these results are in conformity qualitatively with experimental fact. On the other hand, the Ω=25 GB is too strong an obstacle to the dislocation. In this case, a dislocation is able to pass across GB under relatively low stress only when it is driven by other dislocations. This is taken to mean that dislocation pile-up must be built up in front of this kind of GB, if this GB may take effect on the process of plastic deformation. The project supported by KM85-33 of Academia Sinica and the National Natural Science Foundation of China     

Linear viscoelastic behavior of perfluorooctyl sulfonate micelles: effects of counter-ions

Linear viscoelastic behavior was investigated for aqueous solutions of perfluorooctyl sulfonate (C₈F₁₇SO⁻ ₃; abbreviated as FOS) micelles having a mixture of tetraethylammonium (N⁺(C₂H₅)₄; TEA) and lithium (Li⁺) ions as the counter-ions. The solutions had the same FOS concentration (0.1 mol l⁻¹) and various Li⁺ fractions in the counter-ions, φ_Li = 0−0.6, and the FOS micelles in these solutions formed threads which further organized into dendritic networks. At T ≤ 15 °C, the terminal relaxation time τ and the viscosity η, governed by thermal scission of the networks, increased with increasing φ_Li up to 0.55. A further increase of φ_Li resulted in decreases of τ and η and in broadening of the relaxation mode distribution. These rheological changes are discussed in relation to the role of TEA ions in thermal scission: Previous NMR studies revealed that only a fraction of TEA ions were tightly bound to the FOS micellar surfaces and these bound ions stabilized the thread/network structures. The concentration of non-bound TEA ions, C_TEA ^*, decreased and finally vanished on increasing φ_Li up to φ_Li ^* ≅ 0.6, and the concentration of the bound TEA ions significantly decreased on a further increase of φ_Li. The non-bound TEA ions appeared to catalyze the thermal scission of the FOS threads, and the observed increases of τ and η for φ_Li < 0.55 were attributed to the decrease of C_TEA ^*. On the other hand, the decreases of τ and η as well as the broadening of the mode distribution, found for φ_Li > 0.55 (where C_TEA ^* ≅ 0), were related to destabilization of the FOS threads/networks due to a shortage of the bound TEA ions and to the existence of concentrated Li⁺ ions. Viscoelastic data of pure FOSTEA and FOSTEA/FOSLi/TEACl solutions lent support to these arguments for the role of TEA ions in the relaxation of FOSTEA/FOSLi solutions. Received: 12 October 1999/Accepted: 1 November 1999     

Hybrid stress analysis by digitized photoelastic data and numerical methods

A method is presented that determines photoelastic isochromatic values at the nodal points of a grid mesh which in turn is generated by a computer program that accepts digitized input. Values of σ₁ - σ₂ are computed from the digitized fringe orders. The Laplace equation is solved to separate the principal stresses at each nodal point. The method is extended to digitize isoclinics. Subsequently, σ _x - σ _y and τ _xy are calculated to be used as starting values for the solution of the pertaining partial differential equations to enhance convergence. For further accelerating the rate of convergence, superfluous boundary conditions are added from the digitized data; significant improvement is demonstrated. Estimated values of σ _x - σ _y from the digitized data are further used in conjunction with the solution of the Laplace equation to determine the state of stress without solving the boundary value problems. Paper was presented at the 1988 SEM Spring Conference on Experimental Mechanics held in Portland, OR on June 5–10.     

Pore structures and transport properties of sandstone

To quantitatively analyze the macroscopic properties of the flow in porous media by means of the continuum approach, detailed information (velocity and pressure fields) on the microscopic scale is necessary. In this paper, the numerical solution for incompressible, Newtonian flow in a diverging-converging representative unit cell (RUC) is presented. A new solution procedure for the problem is introduced. A review of the accuracy of the computational method is given.Nomenclature A _ff ^* area of entrance and exit of RUC - A _fs ^* interfacial area between the fluid and solid phases - d throat diameter of RUC (m) - D pore diameter of RUC (m) - i, j unit vector for RUC - L ^* wave length of a unit cell - L _p pore length of RUC (m) - L _t throat length of RUC (m) - n unit outwardly directed vector for the fluid phase - p ^* fluid pressure - ^* cross-sectional mean pressure - _en ^* entrance cross-sectional mean pressure - Re _d Reynolds number - x ^*, r^* cylindrical coordinates - u ^*, v^* velocity - u _cl ^* centerline velocity - _d mean velocity at the throat of RUC (m/s) - _D mean velocity at the large segment of RUC (m/s) Greek viscosity coefficient (Ns/m²) - _p excess momentum loss factor defined in (4.1) - fluid density (kg/m³) - ^* stream function - ^* vorticity - dimensionless circulation defined in (2.7) Symbols - the mean value - * dimensionless quantities     

Non-Darcy mixed convection from a vertical plate in saturated porous media-variable surface heat flux

Nonsimilarity solutions for non-Darcy mixed convection from a vertical impermeable surface embedded in a saturated porous medium are presented for variable surface heat flux (VHF) of the power-law form. The entire mixed convection region is divided into two regimes. One region covers the forced convection dominated regime and the other one covers the natural convection dominated regime. The governing equations are first transformed into a dimensionless form by the nonsimilar transformation and then solved by a finite-difference scheme. Computations are based on Keller Box method and a tolerance of iteration of 10⁻⁵ as a criterion for convergence. Three physical aspects are introduced. One measures the strength of mixed convection where the dimensionless parameter Ra^* _x /Pe^3/2 _x characterizes the effect of buoyancy forces on the forced convection; while the parameter Pe _x /Ra^*2/3 _x characterizes the effect of forced flow on the natural convection. The second aspect represents the effect of the inertial resistance where the parameter K′U _∞/ν is found to characterize the effect of inertial force in the forced convection dominated regime, while the parameter (K′U _∞/ν)(Ra^*2/3 _x /Pe _x ) characterizes the effect of inertial force in the natural convection dominated regime. The third aspect is the effect of the heating condition at the wall on the mixed convection, which is presented by m, the power index of the power-law form heating condition. Numerical results for both heating conditions are carried out. Distributions of dimensionless temperature and velocity profiles for both Darcy and non-Darcy models are presented. Received on 26 May 1997