THE INFLUENCE OF DEBORAH NUMBER ON SOME COUETTE FLOWS OF A MAXWELL FLUID

2013 ◽  
Vol 05 (01) ◽  
pp. 1350010 ◽  
Author(s):  
NAZISH SHAHID ◽  
MEHWISH RANA
Keyword(s):  
Shear Stress ◽  
Shear Rate ◽  
Laplace Transform ◽  
Fluid Motion ◽  
Maxwell Fluid ◽  
Deborah Number ◽  
Wall Shear Rate ◽  
Bottom Plate ◽  
Sinusoidal Oscillations ◽  
Constant Shear Rate

Some Couette flows of a Maxwell fluid caused by the bottom plate applying shear rate on the fluid, are studied. Exact expressions for velocity and shear stress corresponding to the fluid motion are determined using Laplace transform. Two particular cases of constant shear rate on the bottom plate and sinusoidal oscillations of the wall shear rate are discussed. Some important characteristics of fluid motion are highlighted through graphs.

Exact Solutions for the Flow of Fractional Maxwell Fluid in Pipe-Like Domains

2016 ◽  
Vol 8 (5) ◽  
pp. 784-794 ◽  
Author(s):  
Vatsala Mathur ◽  
Kavita Khandelwal
Keyword(s):  
Shear Stress ◽  
Velocity Field ◽  
Newtonian Fluid ◽  
Outer Cylinder ◽  
Fluid Motion ◽  
Maxwell Fluid ◽  
Circular Cylinders ◽  
Generalized Solutions ◽  
Special Cases ◽  
Graphical Illustration

AbstractThis paper presents an analysis of unsteady flow of incompressible fractional Maxwell fluid filled in the annular region between two infinite coaxial circular cylinders. The fluid motion is created by the inner cylinder that applies a longitudinal time-dependent shear stress and the outer cylinder that is moving at a constant velocity. The velocity field and shear stress are determined using the Laplace and finite Hankel transforms. Obtained solutions are presented in terms of the generalized G and R functions. We also obtain the solutions for ordinary Maxwell fluid and Newtonian fluid as special cases of generalized solutions. The influence of different parameters on the velocity field and shear stress are also presented using graphical illustration. Finally, a comparison is drawn between motions of fractional Maxwell fluid, ordinary Maxwell fluid and Newtonian fluid.

Plastic Deformation Kinetics of 95.5Sn4Cu0.5Ag Solder Joints

1995 ◽  
Vol 117 (2) ◽  
pp. 100-104 ◽  
Author(s):  
Z. Guo ◽  
Yi-Hsin Pao ◽  
H. Conrad
Keyword(s):  
Plastic Deformation ◽  
Shear Stress ◽  
Shear Rate ◽  
Solder Joints ◽  
Deformation Kinetics ◽  
Constant Shear ◽  
Controlling Mechanism ◽  
Deformation Equation ◽  
Kinetics Of ◽  
Constant Shear Rate

The plastic deformation kinetics of 95.5Sn4Cu0.5Ag solder joints were determined in monotonic loading shear over the temperature range of 25°–150°C using three types of tests: (a) constant shear rate, (b) constant shear stress (creep), and (c) differential tests (changes in shear rate or temperature during an otherwise isothermal constant shear rate test). The deformation kinetics were evaluated in terms of the Dorn high temperature plastic deformation equation γ˙p=A(μb/kT)D(b/d)P(τ/μ)n where γ˙p is the shear rate, μ the shear modulus, b the Burgers vector, D the appropriate diffusion coefficient, d the grain size and τ the shear stress. A, p, and n are constants whose values depend on the rate controlling mechanism. It was found that n increased with stress from ~4 at 2 MPa to ~20 at 25 MPa, relatively independent of temperature. The activation ΔH was determined to be 21.1 ± 2 kcal/mole. The constant A, however, decreased with temperature from a value of ~1018 at 25°C to ~1010 at 150°C. The values of n and ΔH suggest that dislocation glide and climb is the rate controlling mechanism and hence that p ≈ 0. It is speculated that the large decrease in A with temperature may be the result of an effect on the microstructure.

scholarly journals Twice Order Slip on the Flows of Fractionalized MHD Viscoelastic Fluid

2019 ◽  
Vol 12 (3) ◽  
pp. 1018-1051 ◽  
Author(s):  
Muhammad Jamil ◽  
Israr Ahmed
Keyword(s):  
Shear Stress ◽  
Velocity Field ◽  
Magnetic Force ◽  
Mhd Flow ◽  
Maxwell Fluid ◽  
Slip Condition ◽  
Bottom Plate ◽  
Oscillatory Movement ◽  
The Impact ◽  
Slip Coefficients

The objective of this article is to investigate the effect of twice order slip on the MHD flow of fractionalized Maxwell fluid through a permeable medium produced by oscillatory movement of an infinite bottom plate. The governing equations are developed by fractional calculus approach. The exact analytical results for velocity field and related shear stress are calculated using Laplace transforms and presented in terms of generalized M-function satisfying all imposed initial and boundary conditions. The flow results for fractionalized Maxwell, traditional Maxwell and Newtonian fluid with and without slips, in the presence and absence of magnetic and porous effects are derived as the limiting cases. The impact of fractional parameter, slip coefficients, magnetic force and porosity parameter over the velocity field and shear stress are discussed and analyzed through graphical illustrations. The outcomes demonstrate that the speed comparing to streams with slip condition is lower than that for stream with non-slip conditions, and the speed with second-slip condition is lower than that with first-order slip condition.

scholarly journals Aging, Rejuvenation and Thixotropy in Complex Fluids: Time-dependence of the Viscosity at Rest and under Constant Shear Rate or Shear Stress

2008 ◽  
Vol 18 (5) ◽  
pp. 53298-1-53298-13
Author(s):  
Daniel Quemada
Keyword(s):  
Shear Stress ◽  
Shear Rate ◽  
Volume Fraction ◽  
Complex Fluids ◽  
Transient Behaviour ◽  
Volume Fractions ◽  
Constant Shear ◽  
Constant Shear Stress ◽  
Constant Shear Rate ◽  
Viscosity Changes

Abstract Complex fluids exhibit time-dependent changes in viscosity that have been ascribed to both thixotropy and aging. However, there is no consensus for which phenomenon is the origin of which changes. A novel thixotropic model is defined that incorporates aging. Conditions under which viscosity changes are due to thixotropy and aging are unambiguously defined. Viscosity changes in a complex fluid during a period of rest after destructuring exhibit a bifurcation at a critical volume fraction ϕc2. For volume fractions less than ϕc2 the viscosity remains finite in the limit t →∞. For volume fractions above critical the viscosity grows without limit, so aging occurs at rest. At constant shear rate there is no bifurcation, whereas under constant shear stress the model predicts a new bifurcation in the viscosity at a critical stress σB, identical to the yield stress σy observed under steady conditions. The divergence of the viscosity for σ≤σB is best defined as aging. However, for σ > σB, where the viscosity remains finite, it seems preferable to use the concepts of restructuring and destructuring, rather than aging and rejuvenation. Nevertheless, when a stress σA(≤σB) is applied during aging, slower aging is predicted and discussed as true rejuvenation. Plastic behaviour is predicted under steady conditions when σ > σB. The Herschel-Bulkley model fits the flow curve for stresses close to σB, whereas the Bingham model gives a better fit for σ >> σB. Finally, the model’s predictions are shown to be consistent with experimental data from the literature for the transient behaviour of laponite gels.

Shear Flow and Large Amplitude Oscillation Shear Study of Solutions of Aggregating Micellar Casein Particles

2008 ◽  
Vol 18 (2) ◽  
pp. 23050-1-23050-7 ◽  
Author(s):  
Anne Pitkowski ◽  
Taco Nicolai ◽  
Dominique Durand
Keyword(s):  
Shear Stress ◽  
Shear Rate ◽  
Shear Flow ◽  
Heating Temperature ◽  
Constant Shear ◽  
Micellar Casein ◽  
Large Amplitude Oscillation ◽  
Increasing Temperature ◽  
Small Shear ◽  
Constant Shear Rate

Abstract Small micellar casein particles were formed in aqueous solutions of native casein after addition of polyphosphate. These so-called submicelles aggregated and gelled with a rate that increased with increasing temperature. The evolution of the viscosity during this process was determined at constant shear rate or shear stress. When applying a small shear stress the viscosity increased strongly until the shear rate became immeasurably slow, but when the applied shear stress exceeded a critical value (σc) the aggregates broke up and the viscosity reached a maximum. At longer times the viscosity decreased rapidly at first, followed by a very slow decrease. σc was independent of the shear rate and heating temperature, but increased strongly with increasing casein concentration. At constant shear rate the stress remained close to σc, but fluctuated irregularly. After cessation of shear flow, gels were formed rapidly. Oscillation shear measurements for σ > σc showed a strongly non-linear response at the time of maximum viscosity.

ELECTRORHEOLOGY OF DISPERSIONS OF BaxSr(1-x)TiO3 IN SILICONE OIL UNDER AC OR DC ELECTRIC FIELD

2012 ◽  
Vol 26 (14) ◽  
pp. 1250081 ◽  
Author(s):  
GLAUBER M. S. LUZ ◽  
ANTONIO J. F. BOMBARD ◽  
SILVIO L. M. BRITO ◽  
DOUGLAS GOUVÊA ◽  
SHEILA L. VIEIRA
Keyword(s):  
Shear Stress ◽  
Shear Rate ◽  
Electric Field ◽  
Silicone Oil ◽  
Ferroelectric Materials ◽  
Dc Electric Field ◽  
Ac Fields ◽  
Er Fluid ◽  
Constant Shear Rate

Electrorheology (ER) of ferroelectric materials such as nanometric BaTiO 3 is still not fully understood. In this paper, nanoparticles of Ba x Sr (1-x) TiO 3 (where x = 0.8, 0.9 or 1.0) were synthesized using the method of Pechini, calcinated at 950°C, and after, lixiviated under pH 1 or pH 5. A controlled stress rheometer (MCR-301) was used to make the ER characterization of dispersions made of Ba x Ti 1-x O 3 in silicone oil (30% w/w), where (a) shear stress as a function of DC electric field (under constant shear rate) or (b) shear stress as a function of shear rate (under constant AC or DC electric field) were measured. We observed that electrophoresis occurred under electric field DC, creating a concentration gradient which induced phase separation in ER fluid. On the other hand, under AC fields above 1 kV/mm, the ER effect is stronger than for DC field, and almost without electrophoresis. Furthermore, there is an AC frequency, dependent on the disperse phase, where the ER effect has a maximum.

EXACT SOLUTIONS FOR THE POISEUILLE FLOW OF A GENERALIZED MAXWELL FLUID INDUCED BY TIME-DEPENDENT SHEAR STRESS

2010 ◽  
Vol 51 (4) ◽  
pp. 416-429 ◽  
Author(s):  
W. AKHTAR ◽  
CORINA FETECAU ◽  
A. U. AWAN
Keyword(s):  
Shear Stress ◽  
Velocity Field ◽  
Circular Cylinder ◽  
Poiseuille Flow ◽  
Fluid Motion ◽  
Maxwell Fluid ◽  
Time Dependent ◽  
Infinite Cylinder ◽  
Similar Solutions ◽  
Generalized Maxwell Fluid

AbstractThe Poiseuille flow of a generalized Maxwell fluid is discussed. The velocity field and shear stress corresponding to the flow in an infinite circular cylinder are obtained by means of the Laplace and Hankel transforms. The motion is caused by the infinite cylinder which is under the action of a longitudinal time-dependent shear stress. Both solutions are obtained in the form of infinite series. Similar solutions for ordinary Maxwell and Newtonian fluids are obtained as limiting cases. Finally, the influence of the material and fractional parameters on the fluid motion is brought to light.

Thixotropic Strength and Thixotropic Criteria in Semi-Solid Processing

2008 ◽  
Vol 141-143 ◽  
pp. 319-323 ◽  
Author(s):  
W.C. Keung ◽  
Y.F. Lee ◽  
Wei Wei Shan ◽  
Shou Jing Luo
Keyword(s):  
Shear Stress ◽  
Shear Rate ◽  
Shape Factor ◽  
Shear Thickening ◽  
Solid Material ◽  
Solid Content ◽  
Solid Particles ◽  
Thixotropic Behavior ◽  
Semi Solid ◽  
Constant Shear Rate

Thixotropy is essential to semi-solid processing, and because of it the semi-solid material is characterized by ‘shear shinning’. Here, thixotropic strength and thixotropic criteria in semi-solid processing are put forward based on related theories and experiments, and thixotropic mechanism and its influencing factors are also investigated. The results are as follows: 1) the term of thixotropic strength means that with constant shear rate at semi-solid temperature, the semi-solid body begins to flow when the shear stress reach a certain value. This value of shear stress is defined as the thixotropic strength; 2) Thixotropic behavior happens with ‘shear thinning’ because of the deagglomeration of solid particles, while ‘shear thickening’ happens because of the agglomeration at the same time. With increasing shear time, the shear stress increases first and then decreases rapidly to reach a stable value. 3) There are three important factors that influence ‘thixotropic strength’: temperature (hence solid content), initial microstructure (including size, shape factor and uniformity of solid particles) and shear rate.

Effects of slip on oscillating fractionalized Maxwell fluid

2016 ◽  
Vol 5 (1) ◽  
Author(s):  
Muhammad Jamil
Keyword(s):  
Shear Stress ◽  
Velocity Field ◽  
Boundary Conditions ◽  
Laplace Transform ◽  
Maxwell Fluid ◽  
Slip Parameter ◽  
General Solutions ◽  
Initial And Boundary Conditions ◽  
Oscillating Plate

AbstractThe flow of an incompressible fractionalized Maxwell fluid induced by an oscillating plate has been studied, where the no-slip assumption between the wall and the fluid is no longer valid. The solutions obtained for the velocity field and the associated shear stress, written in terms of H-functions, using discrete Laplace transform, satisfy all imposed initial and boundary conditions. The no-slip contributions, that appeared in the general solutions, as expected, tend to zero when slip parameter

ELECTRO-MAGNETORHEOLOGICAL FLUIDS DISPERSING ZEOLITE PARTICLES CONTAINING IRON

2002 ◽  
Vol 16 (17n18) ◽  
pp. 2405-2411 ◽  
Author(s):  
A. SHIBAYAMA ◽  
T. MIYAZAKI ◽  
K. YAMAGUCHI ◽  
K. MURAKAMI ◽  
T. FUJITA
Keyword(s):  
Magnetic Field ◽  
Shear Stress ◽  
Shear Rate ◽  
Electric Field ◽  
Electric Fields ◽  
Fluid Viscosity ◽  
Magnetic Field Direction ◽  
Constant Shear ◽  
Stress Curve ◽  
Constant Shear Rate

Some functional fluids that respond to both magnetic and electric fields have been prepared and their characteristics are described. In this study, an electro-magnetorheological fluid (EMRF) dispersing zeolite particles containing metallic iron by reducing precipitated magnetite has been investigated. When the viscosity is measured by cone plate viscometer and cylindrical viscometer, electric and magnetic fields are applied both between cone and plate or two cylinders. In case of cone plate, the shear stress at constant shear rate increased with the increase of both magnetic field and electric field. On the other hand when the viscosity is measured by cylindrical viscometer, the shear stress at constant shear rate increased with the increase of electric field, however, the increase rate of shear stress by magnetic field is very small. In this case the magnetic field direction is perpendicular to electric field. The EMRF has typical characteristics to respond with magnetic and electric field. The shear stress of EMRF in electric field is stronger than that of magnetic field. Additionally, the inflection and peak point in the shear rate-shear stress curve are appeared and the behaviors of the clusters in the electric field are observed. The experimental results suggested that the fluid viscosity (shear stress/shear rate) is affected by the arrangement of clusters parallel or perpendicular to the direction of the EMRF flow.

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