Foam structural coefficient

Typically, large-scale gas filling makes the main characteristics of foam plastics — coefficients of heat and temperature conductivity, dielectric permeability, and the tangent of the dielectric loss angle — totally independent of the chemical structure of the original polymer [1],... 

In the middle of cells and in faces that are perpendicular to the flowing direction, the borders are branched, which means that the effective number of borders, equivalent to that in a real system, is different from five. The number of independent borders with constant by height radius and length L can be determined by the electro-hydrodynamic analogy between current intensity and liquid flow rate through borders, both being directly proportional to the cross-sectional areas [6,35]. This analogy indicates that the proportionality coefficients (structural coefficients B = 3) in the dependences border hydroconductivity vs. foam expansion ratio and foam electrical conductivity vs. foam expansion ratio, are identical [10]. From the electrical conductivity data about foam expansion ratio it follows... 

In a polyhedral foam the liquid is distributed between films and borders and for that reason the structure coefficient B depends not only on foam expansion ratio but also on the liquid distribution between the elements of the liquid phase (borders and films). Manegold [5] has obtained B = 1.5 for a cubic model of foam cells, assuming that from the six films (cube faces) only four contribute to the conductivity. He has also obtained an experimental value for B close to the calculated one, studying a foam from a 2% solution of Nekal BX. Bikerman [7] has discussed another flat cell model in which a raw of cubes (bubbles) is shifted to 1/2 of the edge length and the value obtained was B = 2.25. A more detailed analysis of this model [45,46] gives value for B = 1.5, just as in Manegold s model. 

Analysing the vast experimental data Lemlich [56] has pointed out that the structural coefficient B monotonously changes from 1.5 to 3 with the increase in foam expansion ratio. He proposed an expression that is in good agreement with the experimental data and approximates the B(net) relation... 

Finally we should comment that it is necessary to employ in the calculation of the spreading coefficient (which is often used as a stability criterion) accurately measured values of the various tensions operative in the pseudoemulsion film to determine whether oil is spreading or nonspreading in the three phase foam structure. 

Colloidal liquid aphrons (CLAs), obtained by diluting a polyaphron phase, are postulated to consist of a solvent droplet encapsulated in a thin aqueous film ( soapy-shell ), a structure that is stabilized by the presence of a mixture of nonionic and ionic surfactants [57]. Since Sebba s original reports on biliquid foams [58] and subsequently minute oil droplets encapsulated in a water film [59], these structures have been investigated for use in predispersed solvent extraction (PDSE) processes. Because of a favorable partition coefficient for nonpolar solutes between the oil core of the CLA and a dilute aqueous solution, aphrons have been successfully applied to the extraction of antibiotics [60] and organic pollutants such as dichlorobenzene [61] and 3,4-dichloroaniline [62]. 

Crosslinked low-density polyethylene foams with a closedcell structure were investigated using differential scanning calorimetry, scanning electron microscopy, density, and thermal expansion measurements. At room temperature, the coefficient of thermal expansion decreased as the density increased. This was attributed to the influence of gas expansion within the cells. At a given material density, the expansion increased as the cell size became smaller. At higher temperatures, the relationship between thermal expansion and density was more complex, due to physical transitions in the matrix polymer. Materials with high density and thick cell walls were concluded to be the best for low expansion applications. 16 refs. 

Acetal translucent crystalline polymer is one of the stiffest TPs available. It provides excellent hardness and heat resistance, even in the presence of solvents and alkalies. Its low moisture sensitivity and good electrical properties permit direct competition with die-cast metal in a variety of applications. In addition, acetal has extremely high creep resistance and low permeability. Acetal is also available as a copolymer (Hoechst Celanese Corp. s Celcon) for improved processability. The homopolymer (DuPont s Delrin) has a very low coefficient of friction and its resistance to abrasion is second only to nylon 6/6. Acetals are frequently blended with fibers such as glass or fluorocarbon to enhance stiffness and friction properties. Acetal is not particularly weather-resistant, but grades are available with UV stabilizers for improved outdoor performance. Acetal, whether homopolymer or copolymer, is not used to any significant degree in forming structural foams. 

The relationship between the structure of the disordered heterogeneous material (e.g., composite and porous media) and the effective physical properties (e.g., elastic moduli, thermal expansion coefficient, and failure characteristics) can also be addressed by the concept of the reconstructed porous/multiphase media (Torquato, 2000). For example, it is of great practical interest to understand how spatial variability in the microstructure of composites affects the failure characteristics of heterogeneous materials. The determination of the deformation under the stress of the porous material is important in porous packing of beds, mechanical properties of membranes (where the pressure applied in membrane separations is often large), mechanical properties of foams and gels, etc. Let us restrict our discussion to equilibrium mechanical properties in static deformations, e.g., effective Young s modulus and Poisson s ratio. The calculation of the impact resistance and other dynamic mechanical properties can be addressed by discrete element models (Thornton et al., 1999, 2004). 

For the process of foam accumulation involving capillary drying, an equation relating the water flooding coefficient to the structural parameters of the foam can be derived [67]. 

Foaming properties can be quantitatively related to surfactant chemical structure, surfactant physical properties, and test conditions using the technique of multiple correlation analysis.(11) The current studies were restricted to linear correlation equations to permit the analyses to be performed on a small microcomputer. While non-linear equations having higher correlation coefficients than obtained herein can be developed, theoretical insights are often limited due to the complexity of the various terms of such equations. The quality of the correlations were assessed using the correlation coefficient (r ) criteria of Jaffe (12)... 

The limitation of the use of one atmosphere foaming experiments to rank order the predicted surfactant performance in permeable media rather than in quantitatively or semi-quantitatively predicting the actual performance of the surfactants under realistic use conditions has already been mentioned. Multiple correlation analysis has its greatest value to predicting the rank order of surfactant performance or the relative value of a physical property parameter. Correlation coefficients less than 0.99 generally do not allow the quantitative prediction of the value of a performance parameter for a surfactant yet to be evaluated or even synthesized. Despite these limitations, multiple correlation analysis can be valuable, increasing the understanding of the effect of chemical structure variables on surfactant physical property and performance parameters. 

Several other experimental findings support the existence of a microceliular structure in oligomeric foams. Thus, Oween and Denis ) observed an anomalous pattern (in the expression of the authors) for certain types of silicone surfactants the liquid foam system consists of gas bubbles the sizes of which differ by several orders of magnitude. The possibility of formation of very small gas bubbles after a marked reduction of the surface tension coefficient in poly-lurethane formulations has been reported by Dubyaga and Tarakanov ). 

Here p and p are the liquid and gas densities, respectively, g is the vector of the gravitational acceleration, and AP is the capillary rarefaction given by (7.1.10) and (7.1.15). The kinetic coefficient H was called the coefficient of hydroconductivity and calculated for polyhedral foam models [245, 246]. Generally speaking, the variable H is a tensor, but usually the isotropic approximation is used, where this parameter is a scalar. Various expressions for the coefficient H were proposed and made more precise in [125, 214, 245]. Thus, different approaches used to calculate the coefficient of hydroconductivity were analyzed in [488]. For example, the structure of spherical and cellular foam was studied under the assumption that liquid flows through a porous layer according... 

---