Lamella number

To describe the process of an oil phase emulsifying into foam lamellae, one could adopt an equilibrium thermodynamic approach analogous to that employed to obtain S and E. Such an approach produces the result that emulsification is only favored (negative AG) for negative values of the interfacial tension. In an alternative approach, the tendency of an oil phase to become emulsified and imbibed into foam lamellae has been described through a simplified balance of forces by the lamella number, L (37). For foam lamellae flowing in porous media, it is predicted that oil will be drawn in and pinched off to produce emulsified drops inside foam lamellae when L > 1, where... 

The physical basis for the lamella number is that a combination of capillary suction in the Plateau borders and the influence of mechanical shear cause the oil-phase distortion and pinch off into droplets. This result is in accord with the observations of emulsification and imbibition by Lobo et al. (50), French et al. (54), and Schramm and Novosad (37). The mechanical shear may come from several sources, including the flow... 

Figure 9. Relation between foam breakage frequencies in a microvisual cell and the lamella number for four different oils. (Reproduced with permission from reference 47. Copyright 1992 Elsevier Science Publishers.)...

The emulsification—imbibition of oil into foam, which the lamella number is intended to describe, has been noticed or predicted by a number of authors and was illustrated in Chapter 2. Lobo et al. (50) emphasized the importance of this phenomenon for foam stability. Rater-man (28) predicted that emulsification—imbibition would be important in constant quality preformed foam injection floods. In the core-flood studies of French et al. (54), they observed that the contacting of foam with crude oils produced emulsified droplets of oil within the foam lamellae. Schramm et al. (40) determined MRFs for a number of foams flowing in Berea sandstone cores containing residual light crude oil and found a strong correspondence with the micromodel results (Figure 10). This work was the first to show that foams that are quite stable to oil in the micromodel are also quite effective in core-floods and vice versa. 

Figure 11 shows all of these core-flood foam performance results plotted versus the logarithm of the lamella number. A strong correspondence is obtained with the logarithm of lamella number. That the trend between mobility reduction and lamella number is so consistent among the different systems is remarkable considering that the core-flood results... 

Plotting the same foam stability data versus lamella number (39) shows that for these four oils, the same variation of foam breakage frequency with lamella number is observed. Thus, even though for a given foaming surfactant solution the foam does not have the same stability in the presence of each oil, the stability is still well predicted by the surface properties, as reflected in the lamella number (equations 4 and 5). Also, using the surface properties allows the effects of the dodecane to be... 

APf/AP , mobility reduction factor monolayer coverage of surfactant monolayer coverage of solvent K APIctL, capillary number based on pressure reference capillary number for shear thinning p v /a, water capillary number PgVg/a, gas capillary number lamellae number per unit volume pressure... 

Lamella Number. A dimensionless parameter used to predict the likelihood that a combination of capillary suction in plateau borders and the influence of mechanical shear will cause an oil phase to become emulsified and imbibed into foam lamellae flowing in porous media (reference [19]). 

Figure 1.11 The growth rate of seven individual lamella (numbers 1-7) from isothermal crystallization of PE at various times [76].

Polypropylene molecules repeatedly fold upon themselves to form lamellae, the sizes of which ate a function of the crystallisa tion conditions. Higher degrees of order are obtained upon formation of crystalline aggregates, or spheruHtes. The presence of a central crystallisation nucleus from which the lamellae radiate is clearly evident in these stmctures. Observations using cross-polarized light illustrates the characteristic Maltese cross model (Fig. 2b). The optical and mechanical properties ate a function of the size and number of spheruHtes and can be modified by nucleating agents. Crystallinity can also be inferred from thermal analysis (28) and density measurements (29). 

Small micelles in dilute solution close to the CMC are generally beheved to be spherical. Under other conditions, micellar materials can assume stmctures such as oblate and prolate spheroids, vesicles (double layers), rods, and lamellae (36,37). AH of these stmctures have been demonstrated under certain conditions, and a single surfactant can assume a number of stmctures, depending on surfactant, salt concentration, and temperature. In mixed surfactant solutions, micelles of each species may coexist, but usually mixed micelles are formed. Anionic-nonionic mixtures are of technical importance and their properties have been studied (38,39). 

According to Hosemann-Bonart s model8), an oriented polymeric material consists of plate-like more or less curved folded lamellae extended mostly in the direction normal to that of the sample orientation so that the chain orientation in these crystalline formations coincides with the stretching direction. These lamellae are connected with each other by some amount of tie chains, but most chains emerge from the crystal bend and return to the same crystal-forming folds. If this model adequately describes the structure of oriented systems, the mechanical properties in the longitudinal direction are expected to be mainly determined by the number and properties of tie chains in the amorphous regions that are the weak spots of the oriented system (as compared to the crystallite)9). 

Hoffman assumes that aj, has the same interpretation as for infinite chain length, that is the surface tension of the fold surface. However, as pointed out above, effects of a non-folded surface are already included in AH[ Tm(0, p)] and AS[ 7, (0, p)], and at best a e could be regarded as the contribution to the surface tension from just the folds, but more realistically as a parameter which is related to the surface tension but which also varies with the thickness of the lamella, that is as the proportion of the number of folds to free ends in the surface changes. 

The average thickness may easily be measured as the average stem length in the bulk part of the lamella, and the growth rate is the mean distance moved by the growth front during a number of Monte Carlo time-steps, nt, divided by nt. 

The intermediate-mobility pectin can exist in any space in the cell wall more than 2nm away from cellulose microfibrils. It could therefore be in the middle lamella, cell comers or between layers of microfibrils in addition to the above proposal. The pectin seen in this part of the spectram are probably a heterogeneous mixture from a number of locations. 

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