Modeling of Neutron Diffraction Patterns from Sheared Silica Gels

1994 ◽  
Vol 376 ◽  
Author(s):  
B.D. Butler ◽  
H.J.M. Hanley ◽  
C.D. Muzny ◽  
G.C. Straty
Keyword(s):  
Power Law ◽  
Colloidal Silica ◽  
Volume Fraction ◽  
Silica Particles ◽  
Silica Gels ◽  
Diffraction Maximum ◽  
Gel Structure ◽  
Contact Distance ◽  
Diffraction Patterns ◽  
Equivalent Conditions

ABSTRACTDense silica gels, prepared from suspensions of 24 nm colloidal silica particles, have been studied by small angle neutron scattering. Provided the volume fraction, φ, of the silica is less than about 0.18, the scattered intensity increases at low wavevector, q, as the gelation proceeds and the structure factor, S(q), of the final gel exhibits apparent power law behavior, usually interpreted as a signature of fractal growth. The power law behavior, however, was observed for all measured φ (≤0.30) when the gelation occurred in the presence of an applied shear. Furthermore, the first diffraction maximum, corresponding to the inter-particle contact distance, was more sharply peaked in the high density sheared gels, indicating that the structural arrangement of the silica particles under shear is more densely packed than in gels produced without shear under equivalent conditions. Although it is clear that shear has a marked influence on the gel structure at higher densities, a quantitative interpretation of the diffraction results is difficult because cluster-cluster interference might be present. Such difficulties encountered when trying to interpret the scattering from these dense systems are outlined, and a computer simulation that includes cluster-cluster interference is presented.

Moire Fringes on Precipitates in Quenched and Aged Beryllium

1968 ◽  
Vol 26 ◽  
pp. 426-427
Author(s):  
F. J. Fraikor ◽  
A. W. Brewer
Keyword(s):  
Ternary Phase ◽  
Volume Fraction ◽  
Age Hardening ◽  
Orientation Relationships ◽  
Solute Content ◽  
Moiré Fringes ◽  
Moire Patterns ◽  
Total Volume Fraction ◽  
Diffraction Patterns ◽  
Moiré Patterns

A number of investigators have examined moire patterns on precipitate particles in various age-hardening alloys. For example, Phillips has analyzed moire fringes at cobalt precipitates in copper and Von Heimendahl has reported on moire fringes in the system Al-Au. Recently, we have observed moire patterns on impurity precipitates in beryllium quenched in brine from 1000°C and aged at various temperatures in the range of 500-800°C. This heat treatment of beryllium rolled from vacuum cast ingots produces the precipitation of both an fee ternary phase, AlFeBe4, and an hcp binary phase, FeBe11. However, unlike a typical age-hardening alloy, the solute content of this material is low (less than 1000 ppm of Fe and 600 ppm of Al) and hence the total volume fraction of precipitates is small. Therefore there is some difficulty in distinguishing the precipitates and their orientation relationships with the beryllium matrix since the weak precipitate spots generally do not appear on the diffraction patterns.

Direct imaging of order-disorder and antiphase domain structures in Ti3Al intermetallic compound

1990 ◽  
Vol 48 (4) ◽  
pp. 480-481
Author(s):  
H. Q. Ye ◽  
T.S. Xie ◽  
D. Li
Keyword(s):  
Intermetallic Compound ◽  
Volume Fraction ◽  
Fundamental Problem ◽  
Antiphase Domain ◽  
Atomic Scale ◽  
Orientation Relationships ◽  
Domain Structures ◽  
Α Phase ◽  
Diffraction Patterns ◽  
Two Phases

The Ti3Al intermetallic compound has long been recognized as potentially useful structural materials. It offers attractive strength to weight and elastic modulus to weight ratios. Recent work has established that the addition of Nb to Ti3Al ductilized this compound. In this work the fundamental problem of this alloy, i.e. order-disorder and antiphase domain structures was investigated at the atomic scale.The Ti3Al+10at%Nb alloys used in this study were treated at 1060°C and then aged at 700°C for 2 hours. The specimens suitable for TEM were prepared by standard jet electrolytic-polishing technique. A JEM-200CX electron microscope with an interpretable resolution of about 0.25 nm was used for HREM.The [100] and [001] projections of the α2 phase were shown in Fig.l.The alloy obtained consist of at least two phases-α2(Ti3Al) and β0 structures. Moreover, a disorder α phase with small volume fraction was also observed. Fig.2 gives [100] and [001] diffraction patterns of the α2 phase. Since lattice parameters of the ordered α2 (a=0.579, c=0.466 nm) and disorder α phase (a0=0.294≈a/2, c0=0.468 nm) are almost the same, their diffraction patterns are difficult to be distinguished when they are overlapped with epitaxial orientation relationships.

scholarly journals Jet Impingement Heat Transfer of Confined Single and Double Jets with Non-Newtonian Power Law Nanofluid under the Inclined Magnetic Field Effects for a Partly Curved Heated Wall

2021 ◽  
Vol 13 (9) ◽  
pp. 5086
Author(s):  
Fatih Selimefendigil ◽  
Hakan F. Oztop ◽  
Ali J. Chamkha
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Particle Size ◽  
Aspect Ratio ◽  
Power Law ◽  
Volume Fraction ◽  
Inclined Magnetic Field ◽  
Magnetic Field Effects ◽  
Power Law Nanofluid ◽  
Power Law Index

Single and double impinging jets heat transfer of non-Newtonian power law nanofluid on a partly curved surface under the inclined magnetic field effects is analyzed with finite element method. The numerical work is performed for various values of Reynolds number (Re, between 100 and 300), Hartmann number (Ha, between 0 and 10), magnetic field inclination (γ, between 0 and 90), curved wall aspect ratio (AR, between 01. and 1.2), power law index (n, between 0.8 and 1.2), nanoparticle volume fraction (ϕ, between 0 and 0.04) and particle size in nm (dp, between 20 and 80). The amount of rise in average Nusselt (Nu) number with Re number depends upon the power law index while the discrepancy between the Newtonian fluid case becomes higher with higher values of power law indices. As compared to case with n = 1, discrepancy in the average Nu number are obtained as −38% and 71.5% for cases with n = 0.8 and n = 1.2. The magnetic field strength and inclination can be used to control the size and number or vortices. As magnetic field is imposed at the higher strength, the average Nu reduces by about 26.6% and 7.5% for single and double jets with n greater than 1 while it increases by about 4.78% and 12.58% with n less than 1. The inclination of magnetic field also plays an important role on the amount of enhancement in the average Nu number for different n values. The aspect ratio of the curved wall affects the flow field slightly while the average Nu variation becomes 5%. Average Nu number increases with higher solid particle volume fraction and with smaller particle size. At the highest particle size, it is increased by about 14%. There is 7% variation in the average Nu number when cases with lowest and highest particle size are compared. Finally, convective heat transfer performance modeling with four inputs and one output is successfully obtained by using Adaptive Neuro-Fuzzy Interface System (ANFIS) which provides fast and accurate prediction results.

scholarly journals Non-Newtonian effect on heat transfer and entropy generation of natural convection nanofluid flow inside a vertical wavy porous cavity

2021 ◽  
Vol 3 (3) ◽  
Author(s):  
Mahbuba Tasmin ◽  
Preetom Nag ◽  
Zarin T. Hoque ◽  
Md. Mamun Molla
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Entropy Generation ◽  
Power Law ◽  
Volume Fraction ◽  
Local Entropy ◽  
Nanofluid Flow ◽  
Porosity Level ◽  
Power Law Index ◽  
Local Entropy Generation

AbstractA numerical study on heat transfer and entropy generation in natural convection of non-Newtonian nanofluid flow has been explored within a differentially heated two-dimensional wavy porous cavity. In the present study, copper (Cu)–water nanofluid is considered for the investigation where the specific behavior of Cu nanoparticles in water is considered to behave as non-Newtonian based on previously established experimental results. The power-law model and the Brinkman-extended Darcy model has been used to characterize the non-Newtonian porous medium. The governing equations of the flow are solved using the finite volume method with the collocated grid arrangement. Numerical results are presented through streamlines, isotherms, local Nusselt number and entropy generation rate to study the effects of a range of Darcy number (Da), volume fractions (ϕ) of nanofluids, Rayleigh numbers (Ra), and the power-law index (n). Results show that the rate of heat transfer from the wavy wall to the medium becomes enhanced by decreasing the power-law index but increasing the volume fraction of nanoparticles. Increase of porosity level and buoyancy forces of the medium augments flow strength and results in a thinner boundary layer within the cavity. At negligible porosity level of the enclosure, effect of volume fraction of nanoparticles over thermal conductivity of the nanofluids is imperceptible. Interestingly, when the Darcy–Rayleigh number $$Ra^*\gg 10$$ R a ∗ ≫ 10 , the power-law effect becomes more significant than the volume fraction effect in the augmentation of the convective heat transfer process. The local entropy generation is highly dominated by heat transfer irreversibility within the porous enclosure for all conditions of the flow medium. The particular wavy shape of the cavity strongly influences the heat transfer flow pattern and local entropy generation. Interestingly, contour graphs of local entropy generation and local Bejan number show a rotationally symmetric pattern of order two about the center of the wavy cavity.

Constitutive Equations of Power-Law Composites and Failure of Materials Having Multiple Cracks

1994 ◽  
Vol 116 (3) ◽  
pp. 359-366 ◽  
Author(s):  
S. C. Lin ◽  
Y. Hirose ◽  
T. Mura
Keyword(s):  
Power Law ◽  
Constitutive Equations ◽  
Fracture Criterion ◽  
Volume Fraction ◽  
Piecewise Linear ◽  
Pure Shear ◽  
Failure Criteria ◽  
Multiple Cracks ◽  
Critical Volume Fraction ◽  
The Matrix

Based upon the Mori-Tanaka method, the constitutive equations of power-law materials and the failure criteria of multiple cracks materials are investigated. The piecewise linear incremental approach is also employed to analyze the effective stress and strain of the power-law materials. Results are presented for the case of pure shear where the matrix is a power-law material with rigid or void inhomogeneities. For the multiple cracked materials, the Griffith fracture criterion is applied to determine the critical volume fraction which causes the catastrophic failure of a material. The failure criteria of penny shaped, flat ellipsoidal, and slit-like cracked materials are examined and it is found that the volume fraction of cracks and critical applied stress are in linear relation.

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