Lamellae propagation

Two lamellae propagating in opposite directions can pass each other without changing their growth directions. 

To avoid contact of two lamellae propagating in opposite directions, the growth directions of the lamellae can change, resulting in bending of the lamellae. 

Two nonparallel lamellae propagating in a similar direction can join at a certain point. Then, they can propagate along different directions after joining. The join of these two lamellae can cause bending of the lamellae. 

Two parallel lamellae propagating in the same direction can grow toward each other and finally join together due to the tension of the polymer chains trapped between the two lamellae. After joining, these two lamellae can separate and propagate again. 

Foams may contain not just gas and liquid (and usually surfactant), but also dispersed oil droplets and/or solid particles. Figure 1.5 shows a practical aqueous foam that contains dispersed oil droplets within the foam lamellae. This can occur, for example, when a foaming solution is used for detergent action in a cleaning process (see Section 12.2) or when a foam is propagated through an underground oil reservoir as part of an enhanced oil recovery process (See Section 11.2.2). 

Equation (2.52) satisfies the requirement that the ordering of the lamellae will not affect the final result. Furthermore, the differential propagation Jones matrix for a composite material is simply the sum of the matrices, N., for each of the separate optical effects. The N matrices for different optical properties can be derived using equation (2.44). As an example, consider a birefringent material with retardation S = (InAn z) /X. One form of the Jones matrix for this material is... 

Fig. 22 Phase image showing the joining (J) and bending (B) of lamellae of BA-C8 during their growth and propagation [60]...

An increasing number of investigators are interested in the propagation of cyclic monomers without carbon. The reasons are theoretical interest and anticipation of the future need of monomer sources other than the fossil fuels. Theoretically siloxane units can be arranged into lamellae or bundles (an analogy of mica or asbestos) yielding thermoplastic materials. Another possibility could be the application of the cyclic esters of phosphoric acid [326], phosphazenes, etc. 

In polyethylene the ac-relaxation process (see Section 3.4) enables the movement of chains into and out of the crystalline lamellae. Theoretical treatments have demonstrated that it most probably proceeds by propagation of a localized twist (180° rotation) about the chain axis extending over 12 CH2 units (Fig. 6.14). As the twist defect travels along the chain, it rotates and translates the chain by half a unit cell (i.e, by one CH2 unit) - this is termed the c-shear process (Mansfield and Boyd, 1978). The activation energy for this process is about HOkJmoF1, corresponding to the extra energy required to introduce the twist defect into the crystal. Once formed, the twist can freely... 

One important and as yet not fully understood feature of CO2 foam concerns delineation of the length of the foam bank. Multiple pressure tap measurements indicated that the largest pressure drop occurred within 3 to 6 inches around the bulk CO2 phase front. These and additional studies suggest that the foam bank can be relatively short compared to the length of the core. The pressure drop decreased to very low values as brine approaches its irreducible saturation. This is reasonable, since aqueous surfactant lamella cannot form or propagate when there is no mobile brine present. 

The large amount of unmobilized oil must have reduced or prevented lamella formation and propagation. Also, the surfactant reduced interfacial tension so that capillary forces no longer dominated the gravity forces as they did in experiment No. 3. 

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