Effect of Elasticity

Van Oene. Levitt et al. [25] have observed that polypropylene droplets were elongated perpendicular to the flow direction in a polystyrene matrix that was highly elashc. The extent of particle stretching in the perpendicular direction of flow was found to be proportional to the normal stress differences between the phases. Particle contraction was observed upon cessation of the shearing action, which confirms the role of tire elasticity on deformation. 

The shear stress was reported to have an effect on the shape of the dispersed phase. In a polyamide/polyethylene blend extruded through a slit die, an increase of shear stress from 17 kPa to 29 kPa resulted in a change of the nylon phase from a spherical to a fiber-like particle shape [30]. 

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Tamayo, J. and Garcia, R., Effects of elastic and inelastic interactions on phase contrast images in tapping-mode scanning force microscopy. Appl. Phys. Lett., 71(16), 2394-2396 (1997). 

Phase transitions in two-dimensional (adsorbed) layers have been reviewed. For the multicomponent Widom-Rowlinson model the minimum number of components was found that is necessary to stabilize the non-trivial crystal phase. The effect of elastic interaction on the structures of an alloy during the process of spinodal decomposition is analyzed and results in configurations similar to those found in experiments. Fluids and molecules adsorbed on substrate surfaces often have phase transitions at low temperatures where quantum effects have to be considered. Examples are layers of H2, D2, N2, and CO molecules on graphite substrates. We review the PIMC approach, to such phenomena, clarify certain experimentally observed anomahes in H2 and D2 layers and give predictions for the order of the N2 herringbone transition. Dynamical quantum phenomena in fluids are also analyzed via PIMC. Comparisons with the results of approximate analytical theories demonstrate the importance of the PIMC approach to phase transitions, where quantum effects play a role. 

Another effect of elastic deformation is that it causes a long-range interaction between steps. From the continuum elasticity theory, two steps sepa-rated by a distance have a repulsive interaction proportional to l for homo- and to In i for hetero-epitaxial cases, respectively [84]. This interaction plays an important role, for example, in step fluctuations, terrace width distribution, step bunching, and so forth [7,85-88]. 

Prud HGMMti, R. K. and Shaqfeh. E. A.l.Ch.E. Jl 30 (1984) 485 Effect of elasticity on mixing torque requirements for Rnshton turbine impellers. 

Trinh, X. A., Fukuda, J., Adachi, Y, Nakanishi, H., Norisuye, T. and Tran-Cong-Miyata, Q. (2007) Effects of elastic deformation on phase separation of a polymer blend driven by a reversible photo-cross-linking reaction. Macromolecules, 40, 5566-5574. 

When one measures fluorescence spectra of a microsphere, a complication occurs that is not encountered in the study of bulk samples. That complication is the effect of elastic resonances on the inelastic scattering. Chew et al. (1976) predicted that the high internal electric field associated with morphological resonances leads to enhancement of fluorescence and Raman emissions, and Benner and his coworkers (1980) were among the first to observe morphological resonances associated with fluorescing molecules embedded in a microsphere. 

Nardin, M. and Schultz, J. (1993). Effect of elastic moduli and interfacial adhesion energy on the critical fiber aspect ratio in single fiber composites. J. Mater. Sci. Lett. 12, 1245-1247. 

Table IV. Effect of Elastic Modulus of Binder on Propellant at — 61°C."...

Ogawa K, Kuroda C (1986) Experimental study on the effect of elasticity on drag reduction and turbulent fluctuations in the laminar-turbulent transition region in pipe flow of dilute polymer solutions Can J Chem Eng 64 497... 

Schmerwitz H, Reher EO (1986) Effect of elastic properties on turbulent flow of petroleum and petroleum products in pipelines Wiss Z Tech Hochsch Carl Schorlemmer Leuna-Merseburg 28 235... 

Figure 19.9 Effect of elastic inhomogeneity on elastic strain energy of a coherent...

B. Caroli, C. Caroli, B. Roulet, and P.W. Voorhees. Effect of elastic stresses on the morphological stability of a solid sphere growing from a supersaturated melt. Acta Metall., 37 257-268, 1989. 

The paper of 1939 [1 ], On the Chain Decay of the Main Uranium Isotope, studies the effects of elastic and non-elastic neutron moderation and concludes that chain fission reactions by fast neutrons in pure metallic natural uranium are impossible. The 1940 paper, On the Chain Decay of Uranium under the Influence of Slow Neutrons [2 ], is classic in the best sense of this word its value is difficult to overestimate. The theoretical study performed showed clearly that the effect of resonance absorption of neutrons by nuclei of 238U is a governing factor in the calculation of the coefficient of neutron breeding in an unbounded medium it was concluded that a self-sustained chain reaction in a homogeneous natural uranium-light water system is impossible. 

Stabilization of BP consisting of bent-core N with chiral dopant was also investigated [29-31]. One of the most dramatic results is that BPIII is easily induced by adding a very small amount of chiral dopant such as 1% [29]. The BPIII temperature range was more than 20°. If BSMs show the N phase at room temperature, the BPIII phase over 20° including room temperature is easily realized [30]. Since BSMs have low compared with Kn [25, 32], the effect of elastic constant on the BP stabilization is confirmed [28]. 

In summary it is clear that the effects of coherency stresses are very far from understood, although experiments suggest that in intrinsically strong materials their effect is relatively small. This has led to the consideration of other possibilities, in particular the effects of elastic inhomogeneity. 

The importance of such effects was deduced from the data shown in Fig. 8.2 from the elegant experiments of Barnett and co-workers (Chu and Barnett, 1995). In the TiN/VN multilayers the two layers are both elastically strained with respect to one another and have different elastic moduli, that of TiN being greater than that of VN, which is similar to that of NbN. Shinn and Barnett (1994) have used this to study the effects of elastic modulus mismatch. As shown in Fig. 8.2, systems where there was a difference in elastic modulus showed a substantial increase in hardness. Where there was no difference in elastic modulus little or no hardening was observed, whilst hardening was obtained in a TiN/Vo.6Nb0.4N system where there was a modulus mismatch but no lattice mismatch (Mirkarimi et al., 1990 Hubbard et al., 1992). 

The results of Eq. (104) are plotted in Fig. 1. The agreement with the experimental results is excellent. Again, the effect of elastic deformation in the experimental results should be kept in mind. 

Anderson/ As elastic strain can be calculated by classical elasticity theory in a relatively straightforward way, it was natural to put some effort into such theoretical attempts to understand the microstructures found in, for example, the CS phases. The first paper on this topic was by Stoneham and Durham. This was followed by several reports by Iguchi and Tilley, Iguchi, and Iguchi and Shimizu, while recently Bursill, Netherway, and Grey have used a different approach to evaluate effect of elastic strain on the microstructures of CS phases in rutile-derived oxides. We will not describe these in chronological order, but rather consider the results in terms of isolated faults and then arrays of faults. Unfortunately, the calculations have all been restricted to CS phases with but one exception (Iguchi, unpublished results) and so we can only consider these materials here. 

Typically, finer granules with lower bulk densities can be obtained when a smaller volume of liquid is added during mixing. Moreover, these granules of smaller particle size yield tablets with faster dissolution rates and lower hardness values (75). The mechanical properties of a binder film are important as well and a good tablet binder should be able to offer flexibility and plasticity and yield without rupturing in order to absorb the effects of elastic recovery (62). 

From the beginning of the 1930s, studies on a melt treatment by elastic oscillations were carried out in three main directions (1) the study of an effect of elastic oscillations of various frequencies with the aim to establish a mechanism of nucleation and growth of solidification nuclei in supercooled liquids, i.e. melts and solutions (2) the study of structure and properties of metals and alloys subjected to low-frequency vibration and (3) the study of an ultrasonic oscillation effect on molten metals. Significant research in this area was performed in the 1950s by Danilov, Kapustin, Polotskii, Sirota, and their associates on solidification of organic substances and a number of metals in ultrasonic field. 

Clearly shrinkage anisotropy is a eomplex issue. A number of faetors ean contribute and the relative importance of each will vary between timbers. In some cases a large microfibril angle might be significant, as in corewood and in compression wood. Ray tissue will be important in species such as beech and oak. Contrasting earlywood and latewood densities is a likely cause in Douglas fir, but would be irrelevant for a tropical hardwood. The effects of elastic anisotropy would be more apparent in low density softwoods. 

Tao, J. Feng, J.J. Effects of elastic anisotropy on the flow and orientation of sheared nematic liquid crystals. J. Rheol. 2003, 47 (4), 1051-1070. 

Prud homme R.K., Shaqfeh E., Effect of Elasticity on Mixing Requirements for Rushton Turbine Impellers, AIChE J. 30 (1984) 5, p. 485-486... 

Elastic isotropy considerably simplifies the analyses that we are forced to undertake in our goal of characterizing the deformation fields associated with a dislocation. On the other hand, there are some instances in which it is desirable to make the extra effort to include the effects of elastic anisotropy. On the other hand, because the present work has already grown well beyond original intentions and because the addition of anisotropy is for the most part an elaboration of the physical ideas already set forth above, we refer the reader to the outstanding work of Bacon et al. (1979). 

It should be noted that Eq. 4 is valid only for thin films for which the thickness is much smaller than the wave length of the shear mode oscillations. In this case the frequency shift is determined by the inertial force of the film acting on the quartz surface. Eor thicker films effects of elasticity or viscoelasticity become important and Eq. 4 should be modified essentially [30]. 

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