Water volume-conductivity fraction curves

InrxLiences of alcohol isomery on the conductivity - water volume fraction curve (symbols are the same as those for Figure 4). 

The relationship of the thermal conductivities of fabrics and volume fractions of water in the interfiber spaces was expressed by a quadratic curve when the heat flow was normal to the fabric surface and by a straight line when the flow was parallel to the warp yarns. Except for hairy wool fabrics, the thermal conductivity of various wet fabrics may be calculated from the equations of Naka and Kamata (J3). An earlier investigation used an environmentally controlled room as a periodic heat source, and observed conductivities of 1-2 x 10 l cal/cm-sec °C for cotton, linen, and wool fabrics, and changes to 2-10 x 10 when the water content of these fabrics were increased ( ). After correcting for anisotropic effects, good agreement between actual conductivity measurements of wool fabrics and those calculated from a mathematical model of a random arrangement of fibers was observed. 

In the first case (when using butanol), the curve can be analysed using the percolation theory of conductivity [18]. In this model, the effective conductivity is practically zero as long as the volume fraction of the conductor (water) is below a critical value (the percolation threshold). Beyond this value, k suddenly takes a non-zero value and increases rapidly with further increase in In the above case (percolating microemulsions), the following equations were derived theoretically. 

It would be more helpful if the predictions obtained from those equations can be quantitatively compared with the experimental results. Figure 26 shows the calculated and experimental dielectric constant vs. frequency for nitrobenzene/water emulsion. The nitrobenzene volume fraction is 0.5. The parameter used for calculation is that the dielectric constant and conductivity of nitrobenzene and water is 35.15, 6.249 xlO S/cm, 78.0, 7.286 xiO S/cm, respectively. The experimental data were obtained at temperature 20 C. All calculated curves are similar, and the only difference is the relaxation strength. 

Figure 5.6 Variations of electrical conductivity K (a) and rate constant kg (b) with w<, for water/chlorobenzene/alkylbenzenedime-thyl ammonium chloride microemulsions surfactant alkyl chain C12 (o) Ci4 (+) Cie ( ). Numbers on the curves indicate volume fraction of dispersed phase for onset of electrical percolation. Surfactant concentration 0.27 M T = 20°C. Reprinted with permission from Reference 105, copyright 1989, American Chemical Society.

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