Abstract
A model that calculates calibration curves (probe response functions) of reflection type optical probes for the measurement of solids volume fractions is presented. The reflection from a single surface is calculated from a relaxed inverse square law to allow the introduction of the effects of multiple reflections that occur in the cavities of rough surfaces, represented as an assembly of spherical particles. The probe response function is then calculated as the summation of the reflections of several successive surfaces with correction for obscuration. The probe response function obtained agrees reasonably well with experiments using aqueous suspensions of aluminium hydroxide particles, with a surface volume mean diameters of 75 and 20 μm. For 200 μm diameter sand particles good agreement was found for solids volume fractions greater than 5%. The difference between the predictions and experiments for low solids volume fraction suspensions of large particles was shown to be related to the large interparticle distances in comparison to the fibre diameter. When applied to a suspension of the same solids in air, the method gives a probe response function that is different from that obtained in water, especially at low solids volume fractions. The departure of the probe response function from the power law rule at low solids volume fraction, observed experimentall, is replicated by the model.
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