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2.4 Reconstructing the Particle Size Distribution from Moments

Given a set of moments, the most likely PSD can be obtained based on the "statistically most probable'' distribution for turbulent flames [ 23], which was adapted for crystallization problems by Baldyga and Orciuch [ 3].

The number density function $n(L)$ is expressed as


n(L) = \exp\left(\sum_{i=0}^{N-1}A_{i}L^{i}\right) (2.4-1)

The equation for the $k$th moment is now written as


m_k = \int_{0}^{\infty}L^{k}\exp\left(\sum_{i=0}^{N-1}A_{i}L^{i}\right)dL \qquad k=0, 1, \cdots, N-1 (2.4-2)

Given $N$ moments, the coefficients $A_i$ can be found by a globally convergent Newton-Raphson method to reconstruct the particle size distribution (e.g., Figure  2.4.1).

Figure 2.4.1: Reconstruction of a Particle Size Distribution
figure

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