Modeling of particle size distribution in emulsion co-polymerization: comparison with experimental data and parametric sensitivity studies

Immanuel, Charles D.; Cordeiro, Cajetan F.; Sundaram, Sekhar S.; Meadows, Edward S.; Crowley, Timothy J.; Doyle, Francis J.

doi:10.1016/s0098-1354(02)00031-5

Cited by 74 publications

(45 citation statements)

References 26 publications

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“…In particular the linearized models of the crystallization processes or the ploymerization processes have the form given in (2.1), see [14,28]. The constructed Lyapunov functionals, apart from the proof for the essential result, are potentially utilizable for proving stability of nonlinear systems as well as for future control design.…”

Section: Remark 22mentioning

confidence: 99%

“…[23,29]). To obtain final products of high quality it becomes necessary to supervise and control the evolution of the corresponding dynamical processes based on more sophisticated models, established by the population balance or the conservation law (see [14,28]). The typical examples of these chemical engineering processes are crystallization processes and polymerization processes.…”

Section: Introductionmentioning

confidence: 99%

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Exponential stability of distributed parameter systems governed by symmetric hyperbolic partial differential equations using Lyapunov's second method

Tchousso

Besson

2008

ESAIM: COCV

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Abstract. In this paper we study asymptotic behaviour of distributed parameter systems governed by partial differential equations (abbreviated to PDE). We first review some recently developed results on the stability analysis of PDE systems by Lyapunov's second method. On constructing Lyapunov functionals we prove next an asymptotic exponential stability result for a class of symmetric hyperbolic PDE systems. Then we apply the result to establish exponential stability of various chemical engineering processes and, in particular, exponential stability of heat exchangers. Through concrete examples we show how Lyapunov's second method may be extended to stability analysis of nonlinear hyperbolic PDE. Meanwhile we explain how the method is adapted to the framework of Banach spaces L p , 1 < p ≤ ∞.

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Section: Remark 22mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Exponential stability of distributed parameter systems governed by symmetric hyperbolic partial differential equations using Lyapunov's second method

Tchousso

Besson

2008

ESAIM: COCV

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“…By means of the OCFE method, the PBE is semi-discretized and transformed into a system of differential algebraic equations (DAEs), whose unknowns are the values of the number density function at the collocation points. The reader is referred to references [30,47,124,130] for details on the implementation of this numerical technique. As shown in Table 1, the OCFE method has mostly been used in coagulation-free models.…”

Section: Finite Elementsmentioning

confidence: 99%

Modeling particle size distribution in emulsion polymerization reactors

Vale

McKenna

2005

Progress in Polymer Science

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A review of the use and limitations of Population Balance Equations (PBE) in the modeling of emulsion polymerisation (EP), and in particular of the particle size distribution of the dispersed system is presented. After looking at the construction of the general form of PBEs for EP, a discussion of the different approaches used to model polymerization kinetics is presented. Following this, specific applications are presented in terms of developing a two-dimensional PBE for the modeling of more complex situations (for example the particle size distribution, PSD, and the composition of polymerizing particles). This review demonstrates that while the PBE approach to modeling EP is potentially very useful, certain problems remain to be solved, notably: the need to make simplifying assumptions about the distribution of free radicals in the particles in order to limit the computation complexity of the models; and the reliance of full models on approximate coagulation models. The review finishes by considering the different numerical techniques used to solve PBEs.

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“…Table 2 is the scale on which these systems can be analyzed. Polymerization reactor models can be developed using input-output representations (Parker et al, 2001a) or based on detailed descriptions of the individual polymer particles and their interactions (Immanuel et al, 2003). Analogous models can be developed for microbial fermentors where lumped descriptions of cellular process are provided by unsegregated models (Henson and Seborg, 1992) and detailed descriptions of the individual cells are provided by cell population models (Henson, 2003).…”

Section: Integration Of Biological Systems Contentmentioning

confidence: 99%

Integration of Biological Systems Content into the Process Dynamics and Control Curriculum

Doyle

Henson²

2004

IFAC Proceedings Volumes

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The evolution of the chemical engineering discipline motivates a reevaluation of the process dynamics and control curriculum. A key requirement of future courses is the introduction of theoretical concepts and application examples relevant to emerging areas such as complex biological systems. We outline the critical concepts required to integrate biological content within the traditional framework of process dynamics and control. Our initial experience with three courses is outlined to demonstrate alternative approaches to achieve this integration. The paper concludes with a discussion of open issues which require further attention from the process control and biological systems communities.

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Modeling of particle size distribution in emulsion co-polymerization: comparison with experimental data and parametric sensitivity studies

Cited by 74 publications

References 26 publications

Exponential stability of distributed parameter systems governed by symmetric hyperbolic partial differential equations using Lyapunov's second method

Exponential stability of distributed parameter systems governed by symmetric hyperbolic partial differential equations using Lyapunov's second method

Modeling particle size distribution in emulsion polymerization reactors

Integration of Biological Systems Content into the Process Dynamics and Control Curriculum

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