Cellulose mathematical modeling

Peitersen, N. and E. W. Ross, "Mathematical Model for Enzymatic Hydrolysis and Fermentation of Cellulose by Trichoderma" Biotechnol. Bioeng. 21 (1979) 997-1017. 

To control the complex process of cooking by the sulfate process cellulose, by means of a computer, it is necessary to have a mathematical model of the process. To obtain this model for the process of cooking by the sulfate process cellulose from a mixture of soft and hardwood and deciduous trees, we have used a fractional factorial experiment. It included these seven factors xi consumption of active lye, % Na20 on completely dry wood X2 cooking temperature, °C ... 

A mathematical model has also been proposed for evaluating cellulase preparations. Sattler et al.209 describe a relationship between hydrolysis extent, reaction time, and enzyme concentration. This procedure permits the effectiveness of different enzymes and of different pretreatment methods to be ranked. This method examines cellulose hydrolysis data collected from hyperbolic functions of substrate concentration versus cellulase enzyme concentration at various timed incubations. The model is based on a double reciprocal plot of the relationship... 

The aim of the present work is to develop a mathematic model describing the behavior of a single cellulose particle when heated up under a fluidized bed condition. This may give an insight into the temperature profile of the particle in connection to the reaction heat, the characters of product gas and liquid flows, the secondary reaction of primary volatile and other important phenomena of biomass pyrolysis. 

A comprehensive mathematic model describing the pyrolysis process of single cellulose particle under a fluidized bed condition is built up by fomuilating the... 

The principal features of a mathematical model described for the enzymatic hydrolysis and fermentation of cellulose by Trichoderma reesei are the assumption of two forms of cellulose (crystalline and amorphous), two sugars (cellobiose and D-glucose), and two enzymes (cellulase and j3-D-glucosidase). An inducer-repressor-messenger RNA mechanism is used to predict enzyme formation, and pH effects are included. The model consists of 12 ordinary differential equations for 12 state variables and contains 38 parameters. The parameters were estimated from four sets of experimental data by optimization. The results appear satisfactory, and the computer programs permit simulation of a variety of system changes. 

The principal features of a mathematical model described for the enzymatic hydrolysis and fermentation of cellulose by Trichoderma reesei are the assumption of two forms of cellulose (crystalline and amorphous), two sugars... 

The mathematical model presented above can be used to select materials suitable for cellulosic wastes. Additionally, the new solvents should obey the set of constraints given on Table 2, according to the requirements set above. Mixture properties are predicted using UNIFAC at infinite dilution conditions. The consideration of xylose, glucose and acetic acid distributions would shrink the feasible solution space to the materials that their interactions with the carbonyl and carboxyl groups are tabulated. 

The mathematical model used for fitting CP/MAS C-NMR spectra recorded on isolated cellulose I use different line-shapes for different forms of cellulose. Signals from crystalline forms of cellulose I are fitted using Lorentzian line-shapes and the remaining signals, from less ordered forms of cellulose, are fitted using Gaussian line-shapes 10). 

A company called MS Ltd. desires to obtain a better control over the carboxylation process in future, which takes place in an isothermal BR. In this context, Mr. Y— the pragmatist— turns to the university and requests that a technology student develop a mathematical model for the process and design of a computer program for the simulation of the DS as a function of time in the carboxymethylation of cellulose in a BR. Miss S, a technology student, accepts the challenge. Imagine that you are Miss S ... 

Later, Kumar et al. (2011) used mathematical modeling technique to determine properties of bio-nanocomposites based on starch, proteins, and cellulosic polymers. They also discussed experimental techniques to determine the mechanical, barrier, thermal, and rheological properties of bio-nanocomposites, which are significant in assessing the performance for the application as food packaging materials. 

Figure 12.24 Stress-strain curves for cellulose nitrate at 23°C. Experimental curves (0) and calculated curves, Langevin model (e). n 1/2 = 0.30, N = 1.57 x chain m . (Redrawn from Haward, R.N. and Thackray, C. (1968) The use of a mathematical model to describe isothermal stress-strain curves in glassy thermoplastics. Proc. Roy. Soc. A, 302, 453. Copyright (1968).)...

SVR applied to mathematical modeling of cellulose affinity of dyestuff... 

Rafiei S, Maghsoodloo S, Noroozi B, Mottaghitalab V, Haghi AK (2013) Mathematical modeling in electrospinning process of nanofibers a detailed review. Cellulose Chem Technol 47(5-6) 323-338... 

Aspergillus nidulans (biA-1 sorA-2) germination time and hyphae growth rate as a function of NMR and NMR T2 relaxation times of cellulose (c), sorbose (s), and orange serum broth solids with different s c ratios at 25°C. (Source From Brown, D. and Rothery, P. Models in Biology-Mathematics, Statistics and Computing, Wiley, Chichester, UK, 1993. With permission.)... 

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