Proportionality factors, mean properties

There has been a recent revival in interest in the use of ethanol-diesel fuel blends (E-diesel) in heavy-duty vehicles as a means to reduce petroleum dependency, increase renewable fuels use, and reduce vehicle emissions [27]. E-diesel blends containing 10-15% ethanol could be prepared via the use of additives. However, several fuel properties that are essential to the proper operation of a diesel engine are affected by the addition of ethanol to diesel fuel - in particular, blend stability, viscosity and lubricity, energy content and cetane number (increasing concentrations of ethanol in diesel lower the cetane number proportionately) [28]. Materials compatibility and corrosiveness are also important factors that need to be considered. 

For-inatiy practical applications, the power law relationship (8.1 requires an appropriate proportionality constant or coefficient. Consider the case of nionodisperse primaty particles of radius ft,o which fonn power law agglomerates according to a process whose statistical features are independent of r ,o. The statistical properties of the agglomerates produced by this process do not depend on the magnitude of fl o. That is, if were multiplied by a factor of 10, the value of Df would not be affected nor would all of the other higher-order particle correlation functions that are not considered in this analysis. This means that the system should scale as R/apo so that (8,3) becomes... 

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