A mathematical model for neutral sulfite pulping of various broadleaved wood species

Summary A mathematical model for neutral sulfite pulping process was derived. This model represented by a linear logarithmic relationship of the main pulping characteristics (yield and lignin content) to time and temperature parameters, both determined by the H-factor, is expressed by a logarithmic straight line equation. The relationship of yield to lignin content in the high yield pulps after neutral sulfite pulping is also expressed by a logarithmic straight line equation. A suitable way to calculate the main characteristics of neutral sulfite pulping is the power form of the logarithmic straight line equation for the dependence of the ratio yield/lignin vs. lignin content, yield/H-factor vs. H-factor, lignin/H-factor vs. H-factor and their mathematical equivalents (i.e. reciprocal ratio and/or product). A set of power equations characterizing the relationships yield vs. lignin content as well as yield and lignin content vs. H-factor for woodpulps prepared by neutral sulfite pulping of various broadleaved wood species are given.     

Effect of impact velocity on the fracture of wood as related to the mechanical pulping process

 The fiber separation step in refining is crucial for energy consumption in subsequent refining where the pulp properties are developed. The size reduction of chips during refining is dependent on refining intensity and chip strength. Factors affecting these two parameters are discussed in a literature review. The impact strength of chips and the break down of chips to separate fibers are also discussed. Specifically the effect of impact velocity on the fracture of wood has been studied by use of a falling weight impact tester. Samples were prepared from a freshly cut log of Norway spruce, Picea abies, and the impact strength was measured using an instrumented falling weight impact tester. An increase in impact velocity from about 2.7 to 4.8 m/s resulted in an increase in impact strength of about 50%. Received 23 August 1999     

A mathematical model of mould growth on wooden material

Summary A mathematical model for the simulation of mould fungi growth on wooden material is presented, based on previous regression models for mould growth on sapwood of pine and spruce. Quantification of mould growth in the model is based on the mould index used in the experiments for visual inspection. The model consists of differential equations describing the growth rate of the mould index in different fluctuating conditions including the effect of exposure time, temperature, relative humidity and dry periods. Temperature and humidity conditions favourable for mould growth are presented as a mathematical model. The mould index has an upper limit which depends on temperature and relative humidity. This limiting value can also be interpreted as the critical relative humidity needed for mould growth depending also on the mould growth itself. The model enables to calculate the development of mould growth on the surface of small wooden samples exposed to arbitrary fluctuating temperature and humidity conditions including dry periods. The numerical values of the parameters included in the model are fitted for pine and spruce sapwood, but the functional form of the model can be reasoned to be valid also for other wood-based materials. Received 18 May 1997     

Studies on the effect of prehydrolysis and amine in cooking liquor on producing dissolving pulp from jute (Corchorus capsularis)

Dissolving pulps are the raw materials for the production of many different end-products. Jute is a very good source of cellulose. In this investigation, jute fiber was subjected to pulping in soda process in order to produce dissolving pulp under different prehydrolysis conditions and compared with prehydrolysed kraft pulp from jute. An increase of the prehydrolysis temperature or H₂SO₄ in prehydrolysis liquor increased the α-cellulose content and decreased the viscosity of pulp. The effect of ethylenediamine in soda liquor was also investigated when producing dissolving pulp. Jute fiber produced pulp having 90–97% α-cellulose. Ethylenediamine in soda liquor produced pulp of higher yield, viscosity and higher α-cellulose content than that of prehydrolysis soda or kraft pulp. The α-cellulose content and viscosity were increased with the increase of amine in soda liquor. The kappa number of dissolving pulp from jute was very low (9–5), which indicated that less bleaching chemicals are required for bleaching. The bleachability of soda-ethylenediamine pulp was lower than prehydrolysed soda and kraft pulp in ECF bleaching sequences. The bleachability of soda-ethylenediamine pulp was improved at the sacrifice of pulp yield when prehydrolysis was done prior to pulping. The alkali solubility S ₁₀ and S ₁₈ were 4–9 and 2–4%, respectively.     

A literature-based study on the loss tangent of wood in connection with mechanical pulping

In mechanical pulping, wood is dynamically loaded, which causes large heat losses due to wood viscoelasticity. The heat losses depend on the loss tangent (tan δ) of wood. The loss tangent has a temperature-dependent behaviour, especially in the lignin glass transition region. The glass transition softens wood, and is therefore necessary for gentle mechanical pulping, but at the same time, the loss tangent shows a maximum called the α-peak. The transient peak depends on temperature, loading frequency and moisture content. The temperature where the peak is found can be lowered with chemical treatments, but they also increase the magnitude of the peak. Thermal treatment in the presence of water also increases the magnitude. The loss tangent of wood depends, amongst other things, on the chemical structure of lignin, width of cellulose crystals, microfibril angle, and extractives in the cell wall.     

寻找平板内气泡的数学方法

介绍了寻找平板内气泡的数学方法，该方法在测量山体、水坝、隧道等内部结构的气泡问题时具有一定的作用。     

A mathematical model linking tree sap flow dynamics to daily stem diameter fluctuations and radial stem growth

To date, models for simulating sap flow dynamics in individual trees with a direct link to stem diameter variation include only the diameter fluctuation driven by a change in stem water storage. This paper reports results obtained with a comprehensive flow and storage model using whole-tree leaf transpiration as the only input variable. The model includes radial stem growth based on Lockhart's equation for irreversible cell expansion. It was demonstrated that including growth is essential to obtaining good simulation results. To model sap flow dynamics, capacitance of storage tissues was assumed either constant (i.e., electrical analogue approach) or variable and dependent on the water content of the respective storage tissue (i.e., hydraulic system approach). These approaches resulted in different shapes for the desorption curve used to calculate the capacitance of storage tissues. Comparison of these methods allowed detection of specific differences in model simulation of sap flow at the stem base (F(stem)) and stem diameter variation (D). Sensitivity analysis was performed to select a limited subset of identifiable parameters driving most of the variability in model predictions of F(stem) and D Both the electrical analogue and the hydraulic system approach for the flow and storage model were successfully calibrated and validated for the case of a young beech tree (Fagus sylvatica L.). Use of an objective model selection criterion revealed that the flow and storage model based on the electrical analogue approach yielded better predictions.     

The formation of LC and other aromatic end-group structures in <Emphasis Type="Italic">O</Emphasis>-alkyl-substituted cellulose during kraft pulping conditions

Ultraviolet resonance Raman spectroscopy (UVRRS) was used to study the formation of aromatic and/or lignin-carbohydrate (LC) structures at the reducing end groups of O-alkyl-substituted cellulose under conditions simulating the initial phase of kraft pulping. The derivatives studied were methyl cellulose (MC) with degree of substitution (DS) of 1.64–1.95, carboxymethyl cellulose (CMC) with DS ∼0.6, and a lignin model compound, creosol. The total alkali concentrations in the treatments were 0.1 M and 0.5 M and the sulfidities were 1%, 10%, and 30%. HS⁻ ions and creosol are both strong nucleophiles and they compete for the hot-alkali-generated unsaturated electrophilic reaction sites in the reducing end groups of the polysaccharides. The results indicated that conditions similar to those in the initial phase of conventional kraft cooking (high OH⁻ and low HS⁻ ion concentrations) increased the aromatic nature of the end groups and conditions similar to those in the initial phase of super batch cooking (low OH⁻ and high HS⁻ ion concentrations) partly inhibited the formation of aromatic and LC end groups.     

银杏叶中芦丁含量快速定量数学模型的建立

利用傅里叶变换近红外透射光谱收集了19批不同产地银杏叶样品的近红外光谱图,运用OPUS 6.5分析软件对其进行一阶导数和多元散射校正预处理。在7 500~6 099 cm-1和5 450~4 249 cm-1范围内,因子数选择7,采用偏最小二乘法(PLS)对芦丁的含量进行了快速定量测定,根据超高效液相色谱-串联质谱测定的芦丁含量结果,建立了银杏叶中芦丁含量的定量数学模型。近红外模型预测结果与色谱检测结果相吻合,模型均方差为0.194,预测集的平均回收率为98.40%。本方法快速、简便,可应用于银杏叶药材的质量控制和大批量产品的检测。     

Gremmeniella-infected Pinus contorta as raw material in the production of kraft pulp

Pinus contorta, logs with occluded cankers caused by the pathogen Gremmeniella abietina, as well as logs from unaffected trees were sampled from a 23-year-old plantation in Sweden and compared in terms of their paper properties. Damaged wood gave kraft pulp with poor paper properties: it required a larger amount of beating energy and resulted in paper with low tear strength, air permeability, tensile stiffness, burst strength, and poor light-scattering properties. However, small amounts of damaged wood mixed in with a large amount of healthy wood can pass almost unnoticed. The use of trees with a larger content of damaged wood will lead to serious processing problems and give a pulp with poor paper properties. Thus, wood damaged by Gremmeniella should be sorted out and classed as low-grade raw material.     

Determination of the distribution and reaction of polysaccharides in wood cell walls by the isotope tracer technique VII: Double radiolabeling of xylan and pectin in magnolia (Magnolia kobus DC) and comparison of their behaviors during kraft pulping by radiotracer technique

myo-Inositol-[2-³H] and d-glucuronic acid-[6-¹⁴C] were administered simultaneously to a growing stem of magnolia (Magnolia kobus DC) to label xylan and pectin, respectively, in the cell wall. Determination of the radioactivity of nitrobenzene oxidation products and sulfuric acid hydrolysates of the newly formed xylem indicated that xylan and pectin were labeled with ³H and ¹⁴C, respectively. The doubly labeled wood tissue was treated to kraft pulping, and the radioactivity of the pulping black liquor and treated wood tissue were determined at various stages of the pulping to compare the dissolving behavior between pectin and xylan during the pulping. The results showed that pectin was not dissolved as easily as xylan and was not redeposited on pulp fiber at the late stage of the pulping.Part of this report was presented at the 40th Lignin Symposium at Tsukuba, October 1995     

Distribution of chemical components in the walls of kraft and bisulphite pulp fibres

Summary Fines removed from the surfaces of Pinus radiata fibres by beating were identified and characterised in terms of microfibril orientations in the surfaces of beaten fibres. Fines fractions subjected to chemical analyses were selected so that chemical component data could be related to specific layers or lamellae in fibre walls.Carbohydrate distributions within the walls of kraft fibres differed from those in bisulphite fibres. In the kraft fibres, glucomannan increased and other hemicelluloses decreased from the primary wall to the outer lamellae of the S₂ layer of the secondary wall. In the bisulphite fibres, hemicelluloses were uniformly distributed throughout the outer wall layers, i. e., the primary wall and the S₁ and outer lamellae of the S₂ layers of the secondary wall. More galactan but less arabinan, xylan, and glucomannan were found in the outer layers than in the inner layers of the bisulphite fibres. Carbohydrate distributions were determined for a range of bisulphite pulp yields (53 to 80 percent).The outer layers of the bisulphite fibres contained more Klason lignin than the inner layers. Acid-soluble lignin contents were similar in the inner and outer layers.Helpful discussions with Dr. V. D. Harwood are gratefully acknowledged.     

A mathematical verification of the reinforced-matrix hypothesis using the Mori-Tanaka theory

This article presents a theoretical verification of the reinforced-matrix hypothesis derived from tensor equations, σ ^W = σ ^f + σ ^m and ε ^W = ε ^f = ε ^m (Wood Sci Technol 32:171–182, 1998; Wood Sci Technol 33:311–325, 1999; J Biomech Eng 124:432–440, 2002), using classical Mori-Tanaka theory on the micromechanics of fiber-reinforced materials (Acta Metall 21:571–574, 1973; Micromechanics — dislcation and inclusions (in Japanese), pp 141–147, 1976). The Mori-Tanaka theory was applied to a small fragment of the cell wall undergoing changes in its physical state, such as those arising from sorption of moisture, maturation of wall components, or action of an external force, to obtain 〈σ ^A〉_D = ϕ·〈σ ^F〉_I + (1−ϕ)·〈σ ^M〉_D−I. When the constitutive equation of each constituent material was applied to the equation 〈σ ^A〉_D = ϕ·〈σ ^F〉_I + (1−ϕ)·〈σ ^M〉_D−I, the equations σ ^W = σ ^f + σ ^m and ε ^W = ε ^f = ε ^m were derived to lend support to the concept that two main phases, the reinforcing cellulose microfibril and the lignin-hemicellulose matrix, coexist in the same domain. The constitutive equations for the cell wall fragment were obtained without recourse to additional parameters such as Eshelby’s tensor S and Hill’s averaged concentration tensors A^F and A^M. In our previous articles, the coexistence of two main phases and σ ^W = σ ^f + σ ^m and ε ^W = ε ^f =ε ^m had been taken as our starting point to formulate the behavior of wood fiber with multilayered cell walls. The present article provides a rational explanation for both concepts.     

Early selection in eucalypt breeding in Australia – optimum selection age to minimise the total cost of kraft pulp production

Optimum ages for early combined-trait selection were derived for a breeding objective of reducing the total cost of unbleached eucalypt kraft pulp, assuming typical heritabilities and age-age genetic correlations for basic density and growth. The optimum biological selection age, the selection age where average annual gain is maximised, was four years for an assumed rotation age of 15 years. The optimum economic selection age, the selection age where the present value of all future gains is maximised, was three years. These conclusions were relatively robust to changes in assumptions used in analysis.     

Empirical specification of cost reductions associated with accumulated knowledge in the Swedish kraft paper industry

This paper presents an alternative approach in estimating the effect that technological knowledge has on the cost structure facing individual firms. The suggested method is applied to the Swedish kraft paper industry and relies on a comprehensive dataset for eight individual integrated kraft paper mills. The developed model is based on a two-step process. Step one, the estimation of a pure cost reduction index is derived using a flexible variable cost function which is utilising mill-specific dummy variables. In addition, this approach allows for an estimation of the pure unit cost reduction index that is devoid of scale and price effects which, if not dealt with can produce spurious results when estimating learning effects. Step two, is the estimation of a two factor dynamic learning curve model (2FDLC) using the estimated pure unit cost reduction index as dependent variable. The results suggest that the Swedish kraft paper industry has relatively little to gain in terms of cost reduction through a further technological learning. However, the method performed well, producing intuitive and statistically significant estimates indicating its usefulness in further analyses.     

ZimFlores: A model to advise co-management of the mafungautsi forest in Zimbabwe

ZimFlores (version 4) is the outcome of a participatory modelling process and seeks to provide a shared factual basis for exploring land-use options for the communal lands surrounding the Mafungautsi forest. The ZimFlores experience underscores the importance of a sharing a common problem and a common location in which all participants have an interest. Participatory modelling has proved an effective way to consolidate a diverse body of knowledge and make it accessible. Results demonstrate the importance of model outputs that are diagnostic, and which offer insights into the issues under consideration. Many people contributed in many ways to help realize ZimFlores. Some of the people who contributed include Elias Ayuk, Ivan Bond, Ephraim Chabayanzara, Muyeye Chambwera, Vijay Datadin, Wil de Jong, Peter Frost, James Gambiza, Jode Garbe, Peter Gondo, Emmanuel Guveya, Chiedza Gwata, John Hansell, Gideon Kamumvuri, Godwin Kowero, Dominic Kwesha, Chris Legg, Tim Lynam, Hilton Madevu, Simba Mandota, Everisto Mapedza, Frank Matose, Gutura Matoso, Chipo Mlambo, John Mudekwe, Maxwell Mukwekwerere, Dorcas Mungwari, Tendayi Mutimukuru, Mkhululi Ngwenya, Richard Nyirenda, Bill Ritchie, Lizwelabo Sibanda, Manasa Sibanda, Fergus Sinclair, Jivas Sithutha, Jasper Taylor, Michael Thomas, Zivanai Tsvuura and Steve Twomlow. We are grateful to the UK’s Department for International Development (DFID) and the European Community for financial support of this project.     

Effect of the presence of lignin on the structure and reactivity to hydrolysis of lignincarbohydrate complexes of poplar wood obtained by sulfate pulping

Summary Lignincarbohydrate complexes (LCC) of poplar wood obtained by sulfate pulping and containing lignin in amounts of 0.9–8.3% have been studied by X-ray diffractometry. Heterogeneous hydrolysis methods have been used to determine their reactivity. The content of the crystalline fraction in LCC depends on the lignin removal and increases with the decrease of the lignin content. The degree of crystallinity of cellulose in sawdust and in LCC is fairly high and changes slightly with the lignin removal. The presence of lignin plays a blocking role in the heterogeneous hydrolysis and decreases the rate constant. It is suggested that lignin is bonded to cellulose on the outer surfaces of the crystalline part of the cellulose fibril. Some possible variants of these bonds are discussed.     

The use of diffuse-reflectance laser-flash photolysis to study the photochemistry of the kraft pulp treated with hydrogen peroxide under alkaline and acidic conditions

 The diffuse-reflectance laser-flash photolysis method together with ground state diffuse reflectance spectroscopy have been used to study the effect of pH and temperature of the hydrogen peroxide treatment on oxygen delignified softwood kraft pulp. Received 20 December 1999