Compressive Collapse

Gibson and Ashby (a. 13) propose separate models for elastic collapse by cell edge buckling and plastic collapse by stretching of cell faces. The latter model gave a scaling relationship between the (initial) collapse stress a pi and the relative densities  

In reality, the microstmcture of LDPE foams remains very similar as the density inaeases from 18 to 100 kg m, the main changes being in the cell face thickness. The fraction of polymer in the cell faces is greater than 70%, and the initial compressive yield stress of LDPE varies approximately with the 1.5th power of the density (a.15). This does not mean that the model behind Equation (7) is appropriate. 

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The limiting compression (or maximum v value) is, theoretically, the one that places the film in equilibrium with the bulk material. Compression beyond this point should force film material into patches of bulk solid or liquid, but in practice one may sometimes compress past this point. Thus in the case of stearic acid, with slow compression collapse occurred at about 15 dyn/cm [81] that is, film material began to go over to a three-dimensional state. With faster rates of compression, the v-a isotherm could be followed up to 50 dyn/cm, or well into a metastable region. The mechanism of collapse may involve folding of the film into a bilayer (note Fig. IV-18). 

The difference between the static or equilibrium and dynamic surface tension is often observed in the compression/expansion hysteresis present in most monolayer Yl/A isotherms (Fig. 8). In such cases, the compression isotherm is not coincident with the expansion one. For an insoluble monolayer, hysteresis may result from very rapid compression, collapse of the film to a surfactant bulk phase during compression, or compression of the film through a first or second order monolayer phase transition. In addition, any combination of these effects may be responsible for the observed hysteresis. Perhaps understandably, there has been no firm quantitative model for time-dependent relaxation effects in monolayers. However, if the basic monolayer properties such as ESP, stability limit, and composition are known, a qualitative description of the dynamic surface tension, or hysteresis, may be obtained. 

The samples which are swollen under the action of tensile forces exhibit the characteristic shape shown in Fig. 24. In the places where the parts of the gels were compressed, collapsed gels were observed. The regions which were elongated became strongly swollen. The boundary between completely collapsed and swollen gel is rather sharp. 

Neumann has adapted the pendant drop experiment (see Section II-7) to measure the surface pressure of insoluble monolayers [70]. By varying the droplet volume with a motor-driven syringe, they measure the surface pressure as a function of area in both expansion and compression. In tests with octadecanol monolayers, they found excellent agreement between axisymmetric drop shape analysis and a conventional film balance. Unlike the Wilhelmy plate and film balance, the pendant drop experiment can be readily adapted to studies in a pressure cell [70]. In studies of the rate dependence of the molecular area at collapse, Neumann and co-workers found more consistent and reproducible results with the actual area at collapse rather than that determined by conventional extrapolation to zero surface pressure [71]. The collapse pressure and shape of the pressure-area isotherm change with the compression rate [72]. 

There appear to be two stages in the collapse of emulsions flocculation, in which some clustering of emulsion droplets takes place, and coalescence, in which the number of distinct droplets decreases (see Refs. 31-33). Coalescence rates very likely depend primarily on the film-film surface chemical repulsion and on the degree of irreversibility of film desorption, as discussed. However, if emulsions are centrifuged, a compressed polyhedral structure similar to that of foams results [32-34]—see Section XIV-8—and coalescence may now take on mechanisms more related to those operative in the thinning of foams. 

Fouling Industrial streams may contain condensable or reactive components which may coat, solvate, fill the free volume, or react with the membrane. Gases compressed by an oil-lubricated compressor may contain oil, or may be at the water dew point. Materials that will coat or harm the membrane must be removed before the gas is treated. Most membranes require removal of compressor oil. The extremely permeable poly(trimethylsilylpropyne) may not become a practical membrane because it loses its permeability rapidly. Part of the problem is pore collapse, but it seems extremely sensitive to contamination even by diffusion pump oil and gaskets [Robeson, op. cit., (1994)]. 

Zusammenbruch, m. breakdown, collapse, zusammendrdngen, v.i. press together, compress, condense. 

In general, the following loads must be considered i.e., tension, collapse, burst and compression, and the reasonably worst working conditions ought to be assumed. 

Material Density (g/cm 1 Coating weight (kg/m ) 0-025 mm thickness Brinell hardness Ratio of contraction stresses in sprayed deposits 0-51 mm thick Compressive strength (stress to collapse) (MN/m )... 

Initially, the compression does not result in surface pressure variations. Molecnles at the air/water interface are rather far from each other and do not interact. This state is referred to as a two-dimensional gas. Farther compression results in an increase in snrface pressure. Molecules begin to interact. This state of the monolayer is referred as two-dimensional liquid. For some compounds it is also possible to distingnish liqnid-expanded and liquid-condensed phases. Continnation of the compression resnlts in the appearance of a two-dimensional solid-state phase, characterized by a sharp increase in snrface pressure, even with small decreases in area per molecule. Dense packing of molecnles in the mono-layer is reached. Further compression results in the collapse of the monolayer. Two-dimensional structure does not exist anymore, and the mnltilayers form themselves in a non-con trollable way. 

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