Synthesis of silicon nanoparticles with a narrow size distribution: A theoretical study

Menz, William J.; Shekar, Shraddha; Brownbridge, George P.E.; Mosbach, Sebastian; Körmer, Richard; Peukert, Wolfgang; Kraft, Markus

doi:10.1016/j.jaerosci.2011.10.005

Cited by 20 publications

(23 citation statements)

References 57 publications

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“…Stochastic methods solve the population balance equations by modelling how the particle processes alter an ensemble of computational particles. This method has been well-documented (Balthasar & Kraft, 2003;Morgan et al, 2006;Shekar et al, 2012) and takes advantage of various features such as linear process deferment (Patterson et al, 2006), a binary tree cache (Goodson & Kraft, 2002) and the concept of majorant rates with fictitious jumps (Eibeck & Wagner, 2001) to accelerate the solution of the population balance model. Coupling with the gas-phase is accomplished using the technique of operator splitting (Celnik et al, 2007;Shekar et al, 2012).…”

Section: Population Balancementioning

confidence: 99%

“…This method has been well-documented (Balthasar & Kraft, 2003;Morgan et al, 2006;Shekar et al, 2012) and takes advantage of various features such as linear process deferment (Patterson et al, 2006), a binary tree cache (Goodson & Kraft, 2002) and the concept of majorant rates with fictitious jumps (Eibeck & Wagner, 2001) to accelerate the solution of the population balance model. Coupling with the gas-phase is accomplished using the technique of operator splitting (Celnik et al, 2007;Shekar et al, 2012). Performance of the model and its numerical convergence behaviour have been addressed in Celnik et al (2007), Shekar et al (2012), and Menz et al (2013Menz et al ( , 2014.…”

Section: Population Balancementioning

confidence: 99%

“…Coupling with the gas-phase is accomplished using the technique of operator splitting (Celnik et al, 2007;Shekar et al, 2012). Performance of the model and its numerical convergence behaviour have been addressed in Celnik et al (2007), Shekar et al (2012), and Menz et al (2013Menz et al ( , 2014.…”

Section: Population Balancementioning

confidence: 99%

“…Various models-from gas-phase kinetic to particle population balances-have been proposed to describe the formation of nanoparticles from silane (Menz et al, 2012;Onischuk et al, 2000;Swihart & Girshick, 1999). In all of these models, it is common to find model parameters which have uncertain values.…”

Section: Introductionmentioning

confidence: 99%

“…In all of these models, it is common to find model parameters which have uncertain values. Examples include empirical expressions for sintering (Chen et al, 2013;Menz et al, 2012;Shekar et al, 2012).…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Global sensitivity analysis of a model for silicon nanoparticle synthesis

Menz

Brownbridge

Kraft

2014

Journal of Aerosol Science

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Section: Population Balancementioning

confidence: 99%

Section: Population Balancementioning

confidence: 99%

Section: Population Balancementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Global sensitivity analysis of a model for silicon nanoparticle synthesis

Menz

Brownbridge

Kraft

2014

Journal of Aerosol Science

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Properties of the solutions of delocalised coagulation and inception problems with outflow boundaries

Patterson

2015

J. Evol. Equ.

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Well posedness is established for a family of equations modelling particle populations undergoing delocalised coagulation, advection, inflow and outflow in a externally specified velocity field. Very general particle types are allowed while the spatial domain is a bounded region of d-dimensional space for which every point lies on exactly one streamline associated with the velocity field. The problem is formulated as a semi-linear ODE in the Banach space of bounded measures on particle position and type space. A local Lipschitz property is established in total variation norm for the propagators (generalised semi-groups) associated with the problem and used to construct a Picard iteration that establishes local existence and global uniqueness for any initial condition. The unique weak solution is shown further to be a differentiable or at least bounded variation strong solution under smoothness assumptions on the parameters of the coagulation interaction. In the case of one spatial dimension strong differentiability is established even for coagulation parameters with a particular bounded variation structure in space. This one dimensional extension establishes the convergence of the simulation processes studied in [Patterson, Stoch. Anal. Appl. 31, 2013] to a unique and differentiable limit.

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