Length-based NDF

This average property of the distribution is defined through the number density itself and it represents the mean particle size with respect to the number of particles in the system. Of course, other definitions of the mean particle size are possible, as will become clear below. If we define the th moment of the length-based NDF as 

The mean particle length calculated from this volume-fraction density function is 

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In the literature on particle aggregation and droplet coalescence, a mass-based NDF nmf, X, M) is often preferred because mass is a conserved quantity. For these systems, it is possible to relate the mass of a particle to its characteristic length using M = kuLPf where 1 < Df < 3 is he fractal dimension. Using the procedure outlined above, we can show that the length-based and mass-based NDF are related by l(T) =... 

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