Filaments instability

Note that ( )jj = 1 - ( )2j and (l), is the volume fraction of liquid 1 and 2, respectively, at the phase inversion. Equation 7.6 is empirical, proposed by Paul and Barlow [1980] as a generalization of the experimental observations reported by Avgeropoulos et al. [1976]. Equation 7.7 was derived from the filament instability equation by Metelkin and Blekht [1984]. These relations are applicable to systems prepared at low stresses, thus in these equations the viscosity ratio, X, should correspond not to the ratio of the zero-shear viscosities, but to its value at the shear stress used to prepare the blends. The relations were found to describe the phase inversion for systems with nearly equal polymer viscosities, where > 1. 

Continuous Myocardium with Fiber Rotation Filament Instability and Fribrillation. 

Deliberately oriented polystyrene is available in two forms filament (mono-axially oriented) and film (biaxially oriented). In both cases the increase in tensile strength in the direction of stretching is offset by a reduction in softening point because of the inherent instability of oriented molecules. 

Breakup due to capillary instabilities dominates when the length of the filament is more than 15 times the initial radius of the drop. 

Since for liquids ry is of the order of 2 x 109 dyn/cm3, Sps must be of the order of 7,000 V/micron by this mechanism. Schultz and Wiech suggest that filaments of liquid may first be formed by Rayleigh instability from which are torn finer drops by local electrostatic stresses exceeding the tensile strength. 

In order to understand the logic of dynamic instability, we need to keep in mind that cytoskeletal filaments are unstable only when their ends are not attached to particular molecules that have the ability to anchor them. Every microtubule, for example, starts from an organising centre (the centrosome), and the extremity which is attached to this structure is perfectly stable, whereas the other extremity can grow longer or shorter, and becomes stable only when it encounters an anchoring molecule in the cytoplasm. If such an anchor is not found, the whole microtubule is rapidly dismantled and another is launched in another direction, thus allowing the cytoskeleton to explore all the cytoplasm s space in a short time. 

According to the data in Table 25.5 and to Eq. (25.6) the compressive strength of filaments of refractory materials such as carbon and silicon carbide have compressive strengths about 10 times as large as those of organic fibres. This would seem to be a serious restriction to the use of organic polymers such as aramids in their application in composites. For most of the applications this restriction is of minor importance, however, since long before ac max is reached, instability in the construction will occur. The resistance of a column or a panel under pressure is proportional to the product of a load coefficient and a material efficiency criterion ... 

At steady state, a pool of free heterodimers (representing the critical concentration) coexists with filaments. For these filaments, the critical concentration is lower at the plus end than at the minus end. Thus, treadmilling can occur with a net loss of protomers from the minus end and net addition at the plus end. However, for microtubules, treadmilling is generally overshadowed by a related and much more dramatic phenomenon known as dynamic instability. If a filament loses its GTP cap at either end, depolymerization at that end occurs extremely rapidly. Thus, even at steady state, some filaments can be rapidly shortening at one or both ends while other filaments are rapidly growing at one or both ends. Dynamic instability also occurs in vivo and is an essential factor in the proper functioning of many microtubule-based networks. 

Centrifugal discs produce sheets of liquid that perforate, forming filaments that break up by Rayleigh instabilities. See Figure 8.4. 

Kale SP, Bennett JW Strain instability in filamentous fiingi in Handbook of Applied Mycology in Bhatnagar D, Lillehoj EB, Arora DK (eds) Mycotoxins in Ecological Systems. New York, Dekker, 1992, pp 311-332. 

PSP is the second most common cause of Parkinsonism typified by early gait instability and difficulty with vertical eye movement. PSP is characterized by neurofibrillary tangles composed almost entirely of sdaight filaments of four repeats of Tau protein. Although most cases of PSP appear to be sporadic, genetic diatheses have been implicated. De Yebenes described a pattern of inheritance consistent with a Mende-lian autosomal dominant disorder (De Yebenes et al., 1995). Difficulty recognizing the variable phenotypic expression of PSP may be one reason fewer familial cases have been identified than expected (Rojo et al., 1999). The HI haplotype of the Tau gene has also been found to have association with increased risk for PSP, as it has been for PD (Conrad et al.. 

This formula is crude, and it does not account for differences in shear rates between the droplet and the medium (which are large when the viscosity ratio differs greatly from unity). Nevertheless, because of the shear-rate-dependence of, Eq. (9-22) can predict a.minimum in droplet size as a function of shear rate that is observed in some cases (Sundararaj and Macosko 1995 Plochocki et al. 1990 Favis and Chalifoux 1987). Viscoelastic forces have indeed been shown to suppress the breakup of thin liquid filaments that would otherwise rapidly occur via Rayleigh s instability (Goldin et al. 1969 Hoyt and Taylor 1977 Bousfield et al. 1986). Elongated filaments, for example, are observed in polymer blends (Sondergaard... 

---