A moment methodology for coagulation and breakage problems: Part 2—moment models and distribution reconstruction

Aerosol dynamics modeling of silicon nanoparticle formation during silane pyrolysis: a comparison of three solution methods

“…For a three-point quadrature approximation, six radial (not volume) moments (M 0 -M 5 ) are required and were used in our calculations. The QMOM does not deÿne or produce an explicit size distribution and hence was used only for calculating the integral properties, but the six moments could be used with an assumed functional form for a size distribution with six degrees of freedom to produce one a posteriori (McGraw et al, 1998;Diemer & Olson, 2002).…”

“…To avoid specifying the shape of the distribution a priori, the quadrature method of moments (QMOM) developed by McGraw (1997) approximates the integral moments of the size distribution by an n-point Gaussian quadrature (Gordon, 1968;Hulburt & Katz, 1964). The QMOM does not deÿne or produce an explicit size distribution, but the moments could, in principle, be used with an assumed functional form to obtain a size distribution (Barrett & Webb, 1998;McGraw, Nemesure, & Schwartz, 1998;Diemer & Olson, 2002). For comparison to experiment or other computational methods, having only a list of higher moments and not a size distribution or an easy means of obtaining quantities like the geometric standard deviation is a signiÿcant disadvantage of the QMOM method, as discussed further below.…”

Development of Novel Crystallizer Design and Optimization Tools for Solution Crystallization

“…However, in some applications the complete PSD is not needed and the essential quantities are accessible through the lower-order moments. Moreover, starting from the first six moments, the PSD can be reconstructed, and although this is not an easy task, first results are promising [22].…”

“…In this sense, the QMOM is very similar to the classic methods proposed by Kruis et al [16] and Lee [17], where the PSD is assumed to be a monodisperse or a lognormal distribution. Besides these presumed PSD methods, other approaches to the solution of the moment closure problem exist, such as modal methods and polynomial interpolative closure (for details see [18][19][20][21][22]). Thus, the QMOM has to be viewed as a competing method that presents the main advantage of being extremely accurate and amenable for coupling with with CFD codes, as will be clearer in the following sections.…”

“…The method was ÿrst proposed many years ago by Hulburt and Katz (1964), but it has not found wide applicability due to the di culty of expressing the transport equations for the moments of the PSD in terms of the moments themselves. More recently, several approaches for contending with this "closure" problem have been developed, and a discussion of these can be found in Diemer and Olson (2002).…”