Free Volume Model of Liquid Flow

This stems from the idea that when the free volume in the liquid is zero, motion is restricted to local molecular oscillation so flow cannot occur and the material is a solid. As the temperature is increased, the decrease in density means that the free volume is increasing and flow now becomes possible with the viscosity decreasing as the free volume increases. Doolittle9 suggested an exponential relationship  

Here A and B are constants and a good fit is achieved over a wide temperature range. Using AT = T—T0 in Equation (3.28), we may write the ratio of the molecular volume to the free volume as 

An alternative model was proposed by Hildebrand10 in which he considered the highest packing region. Because the liquids became rapidly more fluid as the packing expanded from the molecular volume, i.e. at low levels of free volume, he proposed that the fluidity of the liquids was directly proportional to the ratio of the free volume to the molecular volume  

The exponential dependence on temperature was taken by Hildebrand to be due to the variation of the free volume ratio with temperature. 

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