Mullins number

A more pronounced increase of the hysteresis number [69, 175] with increasing the strain amplitude was found in the case of the materials derived from DBDI as compared to materials based on MDI. The hysteresis number ranged between 0.56-0.75 (for the MDI type polymer), and between 0.93-0.99 (for the DBDI based materials) as seen in Eig. 4.16. Similar observations were made by us, with regard to the Mullins number, which increased with increasing the strain amplitude [69,175]. Examples are shown in Fig. 4.17-4.19. As seen the Mulllins number increased with increasing the strain amplitude, irrespective of the type of chain extender (DEG or BG), or type of diisocyanate (MDI or DBDI). 

Table 4.6 Mullins number (M) data at 300% maximum strain tests conducted at variable strain rate for PUll (DBD1 BG PTHF)...

The ratio of t/t, which is characteristic of the possibility of vortices, does not depend on the micro-channel diameter and is fully determined by the Reynolds number and L/d. The lower value of Re at which f/fh > 1 can be treated as a threshold. As was shown by Darbyshire and Mullin (1995), under conditions of an artificial disturbance of pipe flow, a transition from laminar to turbulent flow is not possible for Re < 1,700, even with a very large amplitude of disturbances. 

The importance of the flow pattern on the experimental data is clearly apparent, and the reasons for discrepancies between the results of different workers are largely attributable to the rather different characters of the fluidised systems. It is of particular interest to note that, at high values of the Reynolds number when the effects of back-mixing are unimportant, similar results are obtained in fixed and fluidised beds. This conclusion was also reached by Mullin and Treleaven 116 1 in their tests with models. 

A number of fractional crystallisation schemes have been devised by Mullin(3) and Gordon etalSn5 and the use of such schemes has been discussed by Joy and Payne(116) and Salutsky and Sm s(l l7). 

Current particle sizing technology limits the smallest particle measurable to around 1 pm. A number of extrapolation methods have been suggested by Misra and White (5). Workers like Jones, Budz and Mullin (6) cautioned extrapolating to zero size and recommended the use of effective nucleation rate instead. It was thus decided not to extrapolate back to zero size but to find the effective nucleation rate basing on the smallest particle measurable. In contrast, the... 

Detailed information about crystal growth is available in the books by Sunagawa (1987) and Mullin (1993). A very brief summary of the topic is provided here. Crystal growth from solution involves a number of steps. They are ... 

Ellison and Mullin (1997) estimated that the threat of Clinton health care reform reduced the market value of pharmaceutical firms by about 44% during the period from September 1992 to October 1993. Lichtenberg (2004a) estimated that the elasticity of R D investment with respect to market value is 0.225, that is, that a 10% decline in market value is associated with a 2.25% decline in R D investment. Combining these two estimates implies that the threat of Clinton health care reform reduced R D investment by about 9.9% (0.225 0.44). During the period 1986-2000, the average annual number of new molecular entities approved by the FDA was 28.1. Hence, the temporary reduction in R D investment attributable to the threat of Clinton health care reform may, with a lag of 12-15 years, temporarily reduce the number of new molecular entities approved by about 2.8 (9.9% 28.1) per year. 

The discrepancy was explained by Scanlan (755) as well as by Mullins and Thomas (129). Because of the chain ends the network contains elastically effective four- and threefunctional units (in addition to ineffective two- and unifunctional units), which can be equally effective in constraints on four and three chains so that the number of elastically effective chains is given by... 

The origin of this concept is that the fraction of the total area under a normal distribution curve between the 16 and 84% points is twice the standard deviation. The smaller CV, the more nearly uniform the crystal sizes. Products of DTB crystallizers, for instance, often have CVs of 30-50%. The number is useful as a measure of consistency of operation of a crystallizer. Some details are given by Mullin (1972, pp. 349, 389). 

Normally, it is not possible to obtain analytical solutions for this transport problem and so we cannot a priori calculate the reaction path. Kirkaldy [J. S. Kirkaldy, D. J. Young (1985)] did pioneering work on metal systems, based on investigations by C. Wagner and the later work of Mullins and Sekerka. They used the diffusion path concept to formulate a number of stability rules. These rules can explain the facts and are predictive within certain limits if applied properly. One of Kirkaldy s results is this. The moving interface in a ternary system is morphologically stable if... 

So far the micro-mechanical origin of the Mullins effect is not totally understood [26, 36, 61]. Beside the action of the entropy elastic polymer network that is quite well understood on a molecular-statistical basis [24, 62], the impact of filler particles on stress-strain properties is of high importance. On the one hand the addition of hard filler particles leads to a stiffening of the rubber matrix that can be described by a hydrodynamic strain amplification factor [22, 63-65]. On the other, the constraints introduced into the system by filler-polymer bonds result in a decreased network entropy. Accordingly, the free energy that equals the negative entropy times the temperature increases linear with the effective number of network junctions [64-67]. A further effect is obtained from the formation of filler clusters or a... 

Second, the new surface can be created without increasing the number of surface atoms by purely elastic strain of the solid (Figure 1.1.b). The extra stress due to the surface, called by Gibbs surface tension or by other authors surface stress (Mullins 1963, Cahn 1989), is denoted as ysv and expressed as a force per unit length. 

In the same period, researchers at the University of Kiel devised a method using multidimensional gas chromatography-ECD for direct measurement of non-ortho CBs in commercial mixtures [81]. This method utilized the high resolution separation power of two capillary columns in series and permitted a selected portion of a mixture to be moved from the first column to the second without loss using a pneumatically controlled live-T piece (heart-cut). Using this method, they [13] resolved the 11 pairs of unresolved congeners from the study of Mullin et al. [78] and corrected minor errors in the Ballschmiter and Zell [76] scheme of PCB numbering. 

Structure, or in the case of polymorphs, with a limited number of well-defined structures. Those structures are invariant across a wide variety of conditions, in some cases almost under any conditions for which crystals form. Two of the principal questions to be asked for such a process is how it begins and how it proceeds, especially in the context of polymorphic systems. A great deal of work has been devoted to attempts to answer these questions, and in spite of considerable progress especially on experimental and empirical fronts, there is still much to be learnt in developing current models. Historical treatments of the classic notions of crystallization and recrystallization, including many important references, have been given by Tipson (1956) and van Hook (1961). A more recent thorough account may be found in Mullin s book (1993). 

Secondary nucleation deals with the situation in which nuclei are generated in the vicinity of crystals of the solute already present in a supersaturated solution. The solute crystals may have resulted from primary nucleation or may be deliberately added. This subject has also been covered by Mullin, as well as in a number of reviews (Strickland-Constable 1968 Botsaris 1976 DeJong 1979 Garside and Davey 1980 Garside 1985 Nyvlt etal. 1985). 

Mullin has argued that the minimum number of molecules in a stable crystal nucleus can vary from about ten to several thousand. A model based on the simultaneous collision of this number of molecules with the degree of order required for it to be recognized by additional molecules as a crystal is highly unlikely. A more likely scenario is that the nucleus would be generated by a sequence of bimolecular additions in which the so-called critical cluster would be built up stepwise ... 

Hooli BV, Kovacs-Vajna ZM, Mullin K, Blumenthal MA, Mattheisen M, Zhang C et al (2014) Rare autosomal copy number variations in early-onset familial Alzheimer s disease. Mol Psychiatry. 19 676-681... 

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