Turbidity methods of surface area determination

When a light beam passes through a suspension the emergent intensity / is related to the intensity for a beam passing through the suspending liquid Iq by the Beer-Lambert Law  

The laws of geometric optics break down as particle size approaches the wavelength of light and a correction term has to be included to compensate for this breakdown. This is in the form of an extinction coefHcient Kr defined as the ratio of the amount of light cut off by the particle to that which would be cut off if the laws of geometric optics held. 

If there are nr particles of diameter dr in 1 gram of powder (W = 1), the volume-specific surface is given by  

According to Cauchy, for non-ie-entrant particles the ratio of the surface and projected area shape coefficients is constant and equal to 4 [4]. For re-entrant particles the surface area obtained by maldng this assumption is the envelope surface area. Applying Cauchy s theorem simplifies equation (5.8) to  

D is the maximum optical density and K is the average optical density over the size range under examination. If Km is assumed equal to unity, equation (5.9) gives the mass specific surface by photoextinction with no correction for the breakdown in the laws of geometric optics. 

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