On the use of sectional techniques for the solution of depolymerization population balances: Results on a discrete-continuous mesh

Ahamed, Firnaaz; Singh, Mehakpreet; Song, Hyun‐Seob; Doshi, Pankaj; Ooi, Chien Wei; Ho, Yong Kuen

doi:10.1016/j.apt.2020.04.032

Cited by 24 publications

(23 citation statements)

References 40 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This signifies that the above formulation cannot be used to track the true behavior of the number density and require some adjustments to predict the integral properties (zeroth-and first-order moments) accurately corresponding to the number density function. This issue will be resolved by adding two weights in the birth and death terms of the (15) which gives 1 1 . ( 16)…”

Section: Numerical Schemementioning

confidence: 99%

“…To conduct the convergence of the discrete system, first it is necessary to define the norm 1 which is given by…”

Section: Convergence Analysismentioning

confidence: 99%

“…Fragmentation is a well-known mechanism occur in many applications of aerosol [10], depolymerization [1,12], crystallization [31], pharmaceutical sciences [14,15] and chemical engineering [23,30]. The fragmentation process leads the formation of two or more smaller size particles after the disintegration of larger size particles.…”

Section: Introductionmentioning

confidence: 99%

“…The Mathematical model required to track the evolution of the number density function with time 0 corresponding to a fragmentation process is described by a linear integro-partial differential equation: (1) subject to a initial condition 0 0 0.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Finite volume approach for fragmentation equation and its mathematical analysis

Singh

Walker

2021

Numer Algor

Self Cite

View full text Add to dashboard Cite

This work is focused on developing a finite volume scheme for approximating a fragmentation equation. The mathematical analysis is discussed in detail by examining thoroughly the consistency and convergence of the numerical scheme. The idea of the proposed scheme is based on conserving the total mass and preserving the total number of particles in the system. The proposed scheme is free from the trait that the particles are concentrated at the representative of the cells. The verification of the scheme is done against the analytical solutions for several combinations of standard fragmentation kernel and selection functions. The numerical testing shows that the proposed scheme is highly accurate in predicting the number distribution function and various moments. The scheme has the tendency to capture the higher order moments even though no measure has been taken for their accuracy. It is also shown that the scheme is second-order convergent on both uniform and nonuniform grids. Experimental order of convergence is used to validate the theoretical observations of convergence.

show abstract

Section: Numerical Schemementioning

confidence: 99%

“…To conduct the convergence of the discrete system, first it is necessary to define the norm 1 which is given by…”

Section: Convergence Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Finite volume approach for fragmentation equation and its mathematical analysis

Singh

Walker

2021

Numer Algor

Self Cite

View full text Add to dashboard Cite

show abstract

“… Note : Readers are referred to the works of Ahamed et al (2019) and Ahamed (2020) for the formulation of the ML‐PBM including the balances of soluble products, enzyme‐polymer complex species, insoluble polymer species and surface‐adsorbed enzyme species, whereas Ahamed (2020), Ahamed et al (2020), Ho et al (2014), and Ho et al (2018) elucidate the numerical Fixed Pivot Technique (FPT) used to solve the depolymerization population balances over a mixed discrete‐continuous mesh. The descriptions of the key variables are given in the main text as well in the Nomenclature and explained in detail in the Supporting Information (cf.…”

Section: Modeling Frameworkmentioning

confidence: 99%

Modeling coordinated enzymatic control of saccharification and fermentation by Clostridium thermocellum during consolidated bioprocessing of cellulose

Ahamed

Song

2021

Biotech & Bioengineering

Self Cite

View full text Add to dashboard Cite

Consolidated bioprocessing (CBP) of cellulose is a cost‐effective route to produce valuable biochemicals by integrating saccharification, fermentation and cellulase synthesis in a single step. However, the lack of understanding of governing factors of interdependent saccharification and fermentation in CBP eludes reliable process optimization. Here, we propose a new framework that synergistically couples population balances (to simulate cellulose depolymerization) and cybernetic models (to model enzymatic regulation of fermentation) to enable improved understanding of CBP. The resulting framework, named the unified cybernetic‐population balance model (UC‐PBM), enables simulation of CBP driven by coordinated control of enzyme synthesis through closed‐loop interactions. UC‐PBM considers two key aspects in controlling CBP: (1) heterogeneity in cellulose properties and (2) cellular regulation of competing cell growth and cellulase secretion. In a case study on Clostridium thermocellum, UC‐PBM not only provides a decent fit with various exometabolomic data, but also reveals that: (i) growth‐decoupled cellulase‐secreting pathways are only activated during famine conditions to promote the production of growth substrates, and (ii) starting cellulose concentration has a strong influence on the overall flux distribution. Equipped with mechanisms of cellulose degradation and fermentative regulations, UC‐PBM is practical to explore phenotypic functions for primary evaluation of microorganisms’ potential for metabolic engineering and optimal design of bioprocess.

show abstract

Improved accuracy and convergence of homotopy‐based solutions for aggregation–fragmentation models

Kushwah

Saha

2022

Math Methods in App Sciences

View full text Add to dashboard Cite

We discuss the formulation of a numerical scheme based on the homotopy method to solve different aggregation–fragmentation models including the simultaneous event. Several test cases are considered and analyzed qualitatively and quantitatively to ascertain the improved accuracy and efficiency of the proposed model over the existing semi‐analytical models. The generalized solution of the truncated problem is obtained for some test cases, which in the limiting sense tends to the exact solution. A detailed convergence analysis of the scheme is also studied.

show abstract

On the use of sectional techniques for the solution of depolymerization population balances: Results on a discrete-continuous mesh

Cited by 24 publications

References 40 publications

Finite volume approach for fragmentation equation and its mathematical analysis

Finite volume approach for fragmentation equation and its mathematical analysis

Modeling coordinated enzymatic control of saccharification and fermentation by Clostridium thermocellum during consolidated bioprocessing of cellulose

Improved accuracy and convergence of homotopy‐based solutions for aggregation–fragmentation models

Contact Info

Product

Resources

About