Top Navigation Bar

Article Request Page ASABE Journal Article

Development of a Size Reduction Equation for Woody Biomass: The Influence of Branch Wood Properties on Rittinger’s Constant

L. J. Naimi, S. Sokhansanj, X. Bi, C. J. Lim

Published in Transactions of the ASABE 59(6): 1475-1484 (doi: 10.13031/trans.59.11347). Copyright 2016 American Society of Agricultural and Biological Engineers.

Submitted for review in May 2015 as manuscript number ES 11347; approved for publication by the Energy Systems Community of ASABE in December 2015.

The authors are Ladan J. Naimi, ASABE Member, Graduate Research Associate, Department of Chemical and Biological Engineering, University of British Columbia, Vancouver, British Columbia, Canada; Shahab Sokhansanj, ASABE Fellow, Adjunct Professor, Department of Chemical and Biological Engineering, University of British Columbia, Vancouver, British Columbia, Canada, and Distinguished Research Staff, Environmental Sciences Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee; Xiaotao Bi, Professor, and C. Jim Lim, ASABE Member, Professor, Department of Chemical and Biological Engineering, University of British Columbia, Vancouver, British Columbia, Canada. Corresponding author: Shahab Sokhansanj, Department of Chemical and Biological Engineering, University of British Columbia, 2360 East Mall, Vancouver, BC, Canada V6T 1Z3; phone: 604-827-5347; email:

Abstract. Size reduction is an essential but energy-intensive process for preparing biomass for conversion processes. Three well-known scaling equations (Bond, Kick, and Rittinger) are used to estimate energy input for grinding minerals and food particles. Previous studies have shown that the Rittinger equation has the best fit to predict energy input for grinding cellulosic biomass. In the Rittinger equation, Rittinger’s constant (kR) is independent of the size of ground particles, yet we noted large variations in kR among similar particle size ranges. In this research, the dependence of kR on the physical structure and chemical composition of a number of woody materials was explored. Branches from two softwood species (Douglas fir and pine) and two hardwood species (aspen and poplar) were ground in a laboratory knife mill. The recorded data included power input, mass flow rate, and particle size before and after grinding. Nine material properties were determined: particle density, solid density (pycnometer and x-ray diffraction methods), microfibril angle, fiber coarseness, fiber length, and composition (lignin and cellulose glucan contents). The correlation matrix among the nine properties revealed high degrees of interdependence between properties. The kR value had the largest positive correlation (+0.60) with particle porosity across the species tested. Particle density was strongly correlated with lignin content (0.85), microfibril angle (0.71), fiber length (0.87), and fiber coarseness (0.78). An empirical model relating kR to particle density was developed.

Keywords.Aspen, Douglas fir, Fiber length, Grinding, Knife mill, Lignin content, Particle size, Pine, Poplar, Rittinger, Size reduction, Specific energy.

The increasing demands for energy and the negative impacts of fossil fuels on the environment are among the factors stimulating development of new energy sources, including biomass. According to ANSI/ASABE Standard S593.1 (ASABE, 2011), biomass originates from biological materials that can be reproduced in a short time and thus are considered renewable. Size reduction is an unavoidable operation for preparing raw biomass for drying and the production of pellets, biofuels, and other bioproducts. Size reduction ranks second in energy consumption after drying in a typical pelleting operation. One of the major challenges encountered during size reduction is the difficulty in predicting the grinder performance and product quality due to variability in the structure and presumably the composition of the biomass. To deal with these uncertainties, size reduction equipment is often over-designed in terms of power input to handle a wide range of biomass species. This leads to disproportionate capital and operating costs when compared to other equipment in the plant. This research is an attempt to identify factors that may have a major role in determining the power requirement for size reduction.

In previous studies on grinding biomass, polynomial or power correlations of various degrees (Mani et al., 2004; Miao et al., 2011; Adapa et al., 2011; Bitra et al., 2009) were proposed to represent the data of energy consumption and particle size. The equations were specific to a particular type of biomass and type of grinder. The three grinding equations of Kick, Rittinger, and Bond have built-in fundamental mechanisms, but each of these equations has one constant whose value must be estimated from experimental size reduction data.

Our previous study showed that the Rittinger equation had a better fit to the grinding data than the other two equations for grinding Douglas fir and willow chips with a knife mill (Naimi et al., 2013). This was confirmed by Temmerman et al. (2013), who studied grinding of pine, spruce, oak, and beech wood chips using a hammer mill.

The Rittinger theory was introduced in 1867 (Bond, 1952, 1961) based on the hypotheses that the work done in grinding and crushing is directly proportional to the new surface area produced. The original form of the Rittinger equation is:


where E is the specific energy input (J g-1), Lp and LF are the representative sizes of product particles and feed particles, respectively (mm), and kR is Rittinger’s constant (J mm g-1).

In many situations, the feed particle size is not well defined. Equation 1 is rearranged in terms of the product particle size (Lp) as follows:


where CR is the intercept for a given feed particle size.

Equations 1 and 2 show that kR is independent of the feed and product particle sizes. However, our previous experiments (Naimi et al., 2013) showed a wide variation in kR when wood chips of Douglas fir and willow were ground in a knife mill. The objective of this research is to examine the dependence of Rittinger’s constant (kR) on the physical and compositional properties of raw biomass samples and ground samples.

Composition and Structure of Wood in Relation to Grindability

Density, microfibril angle, and chemical constituents are basic properties of the cell walls that affect the mechanical strength of a woody biomass (Simpson and TenWolde, 1999). The chemicals that make up a woody biomass include water, cellulose, hemicellulose, lignin, extractives, and inorganics (ash). All cell walls are composed of cellulose surrounded by lignin and hemicellulose. Cellulose is the most available compound in woody biomass, with a range from 40% to 50%. Hemicelluloses and lignin contents have a range of 22% to 35% in hardwood and softwood. Extractives and inorganics make up 22% to 44% of the bark. Lignin, which glues cellulose fibers together, ranges from 22% to 34% in white wood and from 15% to 30% in bark (Gravelsins, 1998). Hemicelluloses help strengthen the cell walls through their interaction with cellulose and lignin (Scheller and Ulvskov, 2010). Zhang et al. (2013) removed hemicelluloses from a substrate of wood using successive treatments with NaOH and observed a decreasing trend for the tensile strength of the wood fibers. Gindl and Teischinger (2002) showed that cell wall compression strength increases with an increase in lignin content, and this relationship is strong in developing wood but weak in mature wood.

The mechanical properties of wood are strongly linked to the angle between the orientation of the fibers and the applied compression or tensile stress (Nielsen et al., 2009). The angle between the microfibrils and the cell axis is called the microfibril angle (MFA) (fig. 1). The MFA plays a major role in wood’s mechanical properties (Ye, 2007; Salmén and Burgert, 2009; Deng et al., 2012). Large MFA values are associated with low tensile strength (fig. 1). Rigid materials have a smaller MFA.

Mansfield et al. (2007) reported a strong dependence of the modulus of elasticity on the density, moisture content, and MFA of western hemlock. The MFA is an indication of stiffness or resistance to flexibility, where a large MFA indicates low stiffness. Young tree branches of softwoods have a higher MFA and thus are less stiff compared to older, harder wood. Bjurhager et al. (2010) observed that the stiffness of wood decreased due to a decrease in density. They stated that the most important mechanical properties that affect grinding performance are the properties associated with shear and fracture of the tissue.

Figure 1. Schematic definition of microfibril angle (MFA) in relation to a single cell. A small MFA represents a rigid structure. A large MFA represents a ductile structure.

Materials and Methods

Branches of Douglas fir, pine, aspen, and poplar (fig. 2) were collected from forests or from tree plantations in western Canada. The exact age of the branches was not known. Pieces of branches within a narrow range of diameters of 61.5 to 81.9 mm were saw-cut to lengths ranging from 200 to 400 mm. The cut pieces were debarked by hand using a manual debarker. The debarked samples were oven-dried at 50°C until the sample moisture decreased to 8% to 10% w.b. Using a bandsaw, the debarked dried branches were cut perpendicular to the grain into disks of 3.5 mm thickness. Each disk was then cut into quarter-disk pieces. Figure 3a shows debarked samples, and figure 3b shows quarter-disk pieces.

Wood Density Before Grinding

The particle density and solid density of the wood samples were measured prior to the grinding tests. The volume (Vp) of each 3.5 mm disk was calculated from the diameter and thickness of these pieces. The mass of each disk (m) was measured using an electronic balance accurate to 0.01 g. Particle density of the disk (?p) was estimated from the ratio of mass of a disk divided by its volume:


Douglas firPine
Figure 2. Branches of four species of wood as they were received in the lab. The leaves were removed. The branches were cut to length for debarking, drying, and storage.

Figure 3. (a) Wood samples were manually debarked, oven-dried at 50°C, and cut to lengths ranging from 30 to 110 mm. (b) Using a bandsaw, the samples were cut crosswise into 3.5 mm disks and then into quarter-disk pieces.

The solid density of a quarter-disk (?s) was calculated by replacing Vp in equation 3 with the volume (Vs) measured using a gas comparison pycnometer (Quantachrome Instruments, Boynton Beach, Fla.). The pycnometer measured and recorded the solid volume of a quarter-disk placed in a nitrogen gas pressurized cell. Porosity (e) of the wood pieces was calculated from:


Grinder Setup

The grinder was a knife mill (model SM100, Retsch, Inc., Newtown, Pa.). The cutting action was achieved with three blades on the rotor and four stationary cutting strips embedded in the periphery of the housing. The internal volume of the mill was approximately 0.0012 m3 (1200 cm3). The rated power of the knife mill was 1500 W. A removable perforated screen covered 120° around the lower section of the rotor housing. Screens with square perforations of the following sizes were used: 2, 4, and 6 mm. The grinder was equipped with a vibratory feeder (model-15A, Eriez Mfg. Co., Erie, Pa.). The feeder speed was controlled by varying the applied voltage. To feed the quarter-disk pieces into the knife mill, three 500 g lots were prepared. Each 500 g lot was gradually fed to the vibratory feeder tray by manually placing the pieces on the feeder tray until all the pieces had been placed. The feeding duration and power consumption were recorded.

Power Measurement

The input power was calculated by measuring the line voltage and current. The system consisted of a wattmeter (model PCI-118E, Ohio Semitronics, Inc., Hilliard, Ohio), a data acquisition card (CIO-DAS08, Techmatron Instruments, Mississauga, Ontario, Canada), and a desktop computer. Specifications for the wattmeter input were 0 to 2500 W, 0 to 25 A, and 0 to 150 V. The output of the wattmeter ranged between 4 and 20 mA, corresponding to the minimum and maximum power drawn. The current output was connected to a 250 O resistance. The voltage at the resistance was recorded by the data acquisition card. The voltage readings were read and saved in a computer file.

The grinder’s net power consumption was calculated by subtracting the parasitic power input, i.e., the power while running empty (PE, J s-1), from the total recorded power (P, J s-1). Specific energy consumption (E, J g-1) was calculated by dividing the net power consumption by the feeding rate (F, g s-1):


Particle Size Analysis

A sieve shaker (Ro-Tap model RX-94, W.S. Tyler, Mentor, Ohio) was used to fractionate particles based on their sizes. The sieves were wire mesh with square holes. The sieve motion was rotational with tapping caused by a hammer in the sieve shaker. The electronic scale used for weighing the samples could weigh up to a maximum of 1000 g with a precision of 0.01 g. ASABE Standard S319.3 (ASABE, 2007) defines geometric mean diameter or median size of particles by mass (dgw) for expressing particle size of ground biomass. Throughout this article, dgw is used to represent the mean size of the particles.

Moisture Content

Moisture content of the wood was determined gravimetrically using a convection-drying oven following ASABE Standard S352.1 (ASABE, 2012). The method consisted of placing a pre-weighed sample in the oven at 103°C ±2°C for 24 h. The dried sample was weighed, and the moisture content was calculated based on the weight loss of the sample.

Chemical Composition

In the analysis of the chemical composition of wood, cellulose and hemicellulose can hardly be separated quantitatively without degradation. The chemical composition reported for a certain species of wood also depends on the method of separation and the source of wood. In this study, a representative sample of 100 g was chosen from each species of wood. The sample was ground using a Wiley mill (model 4, Thomas Scientific, Swedesboro, N.J.) with a 2 mm screen. Three replicates of 2 to 4 g of air-dried sample were weighed. The acetone-soluble non-volatile material in the sample was removed by extraction using the NREL method (Sluiter et al., 2005) and TAPPI Test Method T280 pm-99 (TAPPI, 1999). The extracted substrates were used for chemical analysis. The acid-insoluble residue was evaluated based on ASTM Standard E1721-01 (ASTM, 2004). Chemical analysis of the wood was performed based on the NREL method (Sluiter et al., 2011) and ASTM Standard E1758-01 (ASTM, 2007). Chemical analysis consisted of the percentages of monomers of sugars, soluble lignin, and insoluble lignin of oven-dry and extractive-free wood meal. It included the glucan content. Glucan in wood comes from cellulose and hemicellulose. The percentages of hemicellulose were calculated from the mass balance using the hemicellulose mannose:glucose ratios reported by Fengle and Wegner (1989).

Wood Microstructure

SilviScan tests and fiber quality analysis (FQA) tests were performed at the PFInnovations Value Tree Laboratory on the campus of the University of British Columbia in Vancouver, Canada. The SilviScan tests comprise of a group of instruments that measure the physical structure of wood (Lawrence and Woo, 2005). The system was first developed by Evans et al. (1995, 2000) to investigate structural differences among species. SilviScan combined three techniques: x-ray densitometry, x-ray diffraction, and image analysis (Chen and Evans, 2010). Image analysis of fiber cross-sections was performed by x-ray absorption and x-ray diffraction (Lundqvist et al., 2007). A cell scanner with a video microscope was used for collecting information on the numbers and sizes of fibers and vessels, as well as the orientations of annual rings. The x-ray absorption images provided information on the wood density. The x-ray diffraction images provided information on the orientations of microfibrils in the wood matrix. MFA measurement requires fibers to be perpendicular to the x-ray beam. Literature showed that the results from SilviScan analyses have been used to determine the mechanical properties of wood. Jayawickrama (2001) and Lindström et al. (2004) studied the suitability of wood for sawn products in relation to stiffness using SilviScan. SilviScan was also used to prove that properties such as wood density, MFA, and their variations within stems may have a crucial role in drying (Ball et al., 2005).

For conducting the tests, pieces of 80 to 100 mm thickness were cut from the branches with a bandsaw. These pieces were delivered to the SilviScan laboratory. The output of the SilviScan analysis provided data on local density and MFA for the cross-section of each piece from the pith to the cambium (Defo et al., 2009).

The FQA consisted of determining fiber length and fiber coarseness. A bandsaw was used to cut pieces of wood approximately 15 mm thick, 15 mm wide, and 60 to 70 mm long. A pulp sample was prepared from each species by removing extractives and pulping the wood. The ground wood sample was extracted first by deionized water and then by a maceration solution consisting of a 1:1 ratio of glacial acetic acid and 35% technical-grade hydrogen peroxide (Woo, 2012; Naimi, 2016). The pulp samples were placed in aluminum weighing dishes to dry at room temperature for one or two days. The dried weight was recorded. A sample of 30 mg for softwood or 15 mg for hardwood was weighed. A fiber quality analyzer (OpTest Equipment, Hawkesbury, Ontario, Canada) was used with a fiber frequency of 20 to 40 events per second (EPS) for hardwoods and 10 to 20 EPS for softwoods (Woo, 2012). The FQA software reports the length-weighted fiber length and fiber coarseness of the samples and their standard deviations. Length-weighted mean fiber length is calculated as the sum of individual fiber lengths squared divided by the sum of the individual fiber lengths. Fiber coarseness is the mass of fiber per meter of fiber length.

Table 1. Particle and solid densities and estimated porosity of quarter-disk particles prior to being ground in knife mill.
(kg m-3)
(kg m-3)
Douglas firMean[a]708115038.4
CV (%)1511
CV (%)126
CV (%)413
CV (%)76

    [a]    Population means are significantly different at p = 0.05.

    [b]    n = 6.

    [c]    n = 5.

    [d]    n = 3.

    [e]    n = 4.

Statistical Analysis

Analysis of variance (ANOVA) and Tukey’s post-hoc test were performed (OriginLab, Northampton, Mass.) on the data. First, an ANOVA was performed to determine whether groups in the sample differed (p = 0.05). Tukey’s post-hoc test was performed to identify which groups in the sample differed significantly if the results showed that there was a significant difference among the groups.


Physical Characteristics of Wood Samples

Table 1 lists the means and standard deviations for particle density and solid density of quarter-disk samples. The mean particle density ranged from 474 kg m-3 for poplar to 708 kg m-3 for Douglas fir. Standard deviations between samples produced a coefficient of variation (CV) ranging from 4% for aspen to 15% for Douglas fir. Variations in solid density were less than variations in particle density, indicating the effects void spaces on wood density. This is reflected in the relatively large variation in porosity, ranging from 38.4% for Douglas fir to 61.6% for poplar. The result of the ANOVA test (p = 0.05) on sample particle density showed that the population means were significantly different.

Microstructure of Wood Samples

Table 2 lists the mean density and MFA values of wood samples as determined using the SilviScan method. The mean density ranged from 473 kg m-3 for poplar to 716 kg m-3 for Douglas fir. These values are in agreement with the density calculated from the measured mass and volume in table 1. The SilviScan method scans a cross-section and senses the local density along the scanned path. Figures 4 and 5 show the density profiles of Douglas fir and aspen, respectively, across a section of wood. Sharp changes in density are recorded for both species, although the signal variations for Douglas fir are much larger than the signal variations for aspen. The peaks represent solid density, and the valleys represent empty spaces within the wood. The mean density of aspen is lower than the mean density of Douglas fir. Marchal et al. (2009) observed that the cross-sections of softwoods were more heterogeneous than the cross-sections of hardwoods, which affected the uniformity of peeled veneers.

Table 2. Density and microstructure of quarter-disk samples measured using SilviScan and fiber quality analyzer.
(kg m-3)
(mg m-1)[b],[c]
CV (%)161540
CV (%)131880
CV (%)4768
CV (%)81147

    [a]    Density and MFA were measured with SilviScan; n = 6 repeated measurements. Population means of average densities are significantly different at p = 0.05.

    [b]    Measured by fiber quality analysis (FQA); n = 3 repeated measurements. Population means are significantly different at p = 0.05.

    [c]    Tukey’s post-hoc test indicated that paired means of a hardwood and a softwood are significantly different. The paired means of two hardwoods or two softwoods are not significantly different (p = 0.05).

Table 2 lists the MFA values for the four wood species as measured using SilviScan methods. The MFA ranged from 11.5° for aspen to 32.1° for Douglas fir. A higher MFA results in lower stiffness and a more flexible wood structure. The MFA of pine measured in this study was 29.9°, which falls in the range of 12.3° to 39.3° reported for loblolly pine (Bendtsen and Senft, 1986). The variability in MFA among the samples tested ranged from 7% for aspen to 15% for Douglas fir.

As expected, table 2 lists longer fiber lengths of 1.31 and 1.17 mm for Douglas fir and pine, respectively, than the fiber lengths of 0.65 and 0.73 mm for aspen and poplar, respectively. The measured fiber coarseness of softwood was higher than that of hardwood. This observation is consistent with common knowledge in the wood science literature (Kollmann and Côté, 1968; Kettunen, 2006; Butterfield, 2006). Hakkila (1989) reported fiber lengths of 0.96 mm for aspen and poplar branch wood, compared to the measured values of 0.65 to 0.73 mm in this study. Hakkila (1989) also reported that fiber lengths of softwood branches ranged from 1.14 to 1.7 mm. Longer fibers increase the wood’s modulus of elasticity. The results of the ANOVA tests on fiber length and fiber coarseness showed that the population means were significantly different at p = 0.05. However, the results of Tukey’s post-hoc test showed that the paired means of fiber length and fiber coarseness were not significantly different for the two hardwoods (aspen and poplar) and the two softwoods (Douglas fir and pine).

Figure 4. Density profile across the cross-section of a Douglas fir branch 75 mm diameter
Figure 5. Density profile across the cross-section of an aspen branch 100 mm diameter.

Composition of Wood Samples

Table 3. Chemical composition of wood species tested in this study (oven-dry, extractive-free).
Glucan in
CV (%)0.400.42
CV (%)0.150.44
AspenMean46.7045.6326.47 (21.2[d])27.90
CV (%)1.302.48
PoplarMean50.3749.224.27 (31.7[d])26.53
CV (%)1.002.27

    [a]    Population means of glucan content are significantly different at p = 0.05. Tukey’s post-hoc test indicated that all paired means are different except for the means of glucan content from pine and Douglas fir.

    [b]    Percentages of hemicellulose were calculated using mass balance.

    [c]    Tukey’s post-hoc test indicated that all lignin content paired means are different except for pine and Douglas fir lignin content means.

    [d]    Values from Fengel and Wegener (1989).

Table 3 summarizes the constituents of the tested oven-dry extractive-free wood samples. We measured glucan content and lignin content. Glucan represented the cellulose content. Glucan in wood comes mainly from cellulose; apart from cellulose, the other major source of glucose is hemicellulose in the form of glucomannan (Fengel and Wegener, 1989). The ratio of mannose to glucose is 3 to 1 in softwood hemicellulose and 2 to 1 in hardwood hemicellulose. Using these ratios, the glucan from cellulose was estimated and is listed in table 3. The glucan from cellulose ranged from 34.9% to 38.4% in the softwood samples and from 45.6% to 49.2% in the hardwood samples. The ANOVA test on glucan content showed that the population means are significantly different at p = 0.05 (95% confidence). The results of Tukey’s post-hoc test showed that all paired means are different except for the paired means of Douglas fir and pine.

The lignin content ranged from 26.5% for poplar to 36.2% for Douglas fir. It is well known that hardwoods have lower lignin content than softwoods. The result of the ANOVA test on lignin content showed that the population means were significantly different at p = 0.05. The results of Tukey’s post-hoc test showed that all paired means were different except the paired means of Douglas fir and pine. The low CV for each species indicates that, unlike the large variation in structural properties, the variations in chemical composition within each species were small.

Table 5. Correlation coefficient matrix of nine wood properties measured in this research.
Particle density1.00--------
Solid density0.211.00-------
Lignin content0.850.37-0.521.00-----
Density (x-ray)1.000.20-0.770.85-0.791.00---
Fiber length0.870.43-0.501.00-0.980.870.841.00-
Fiber coarseness0.780.63-0.290.96-0.930.780.930.971.00

Hemicellulose fractions were calculated from mass balance. The hemicellulose values shown in parentheses in table 3 are from Fengel and Wegener (1989). The difference between the numbers in parentheses and the values calculated in this study are due to differences in method of measurement, part of the tree (branch or stem), and location of the tree.

Correlation of Rittinger’s Constant with Wood Properties

The mean power input for no-load operation of the knife mill varied little, with a value at about 510 W (SD = 5 W). The CV for the parasitic power was 0.009. The no-load energy consumption was around 50% of the power consumption when the grinder was fully loaded. Equation 5 shows the calculation of the specific energy use. Table 4 summarizes the data from grinding the four species on three screen sizes (2, 4, and 6 mm). Using the 2 mm screen, the specific energy input ranged from a minimum of 156 J g-1 to grind Douglas fir to a maximum of 276 J g-1 to grind poplar. Using the 6 mm screen, the specific energy input dropped significantly to 42 to 87 J g-1 for Douglas fir and poplar, respectively. The CV values were generally larger for the 2 mm screen than for the 6 mm screen. The geometric mean diameters of aspen and poplar were similar at 0.65 mm. The difference between geometric mean diameters for the 4 and 6 mm screens was not significant.

Table 4 also lists Rittinger’s constant (kR), the intercept (CR), and the coefficient of determination (R2, eq. 2). The kR value ranged between 203 and 398 J mm g-1, with the smallest value for Douglas fir and the largest value for pine. The intercept (CR) ranged from -309 to -141 J g-1. The coefficient of determination (R2) ranged from 0.93 to 0.96, indicating good linearity between E and 1/dgw. Theoretically and from equations 1 and 2, kR should be independent of particle size. We therefore speculate that the range and variability of kR among wood species indicated the influence of wood properties on species energy input.

The nine properties of wood listed in tables 1, 2, and 3 are highly interdependent. Table 5 shows a correlation matrix for the nine properties. The correlation analysis was performed using the CORREL function in Microsoft Excel. Table 5 shows that the strongest correlation was between particle density measured manually and particle density measured using the SilviScan x-ray method. Among physical features, MFA had a strong correlation with density and fiber length but a weak correlation with porosity. Most of the measured properties using SilviScan had positive correlations with lignin but negative correlations with cellulose content (glucan).

Figure 6 shows the correlation of kR with the nine measured properties of the wood samples. The strongest positive correlations were with porosity, solid density, and fiber coarseness. On the negative side, the strongest correlation were between kR and particle density and x-ray density. Particle density was strongly correlated with lignin content (0.85), MFA (R = 0.71), fiber length (0.87), and fiber coarseness (0.78). It is reasonable to assume that kR is also positively dependent on these properties, although the direct correlations were not as strong as the correlation with porosity (or particle density). The relationship between kR (J mm g-1) and particle density (?, kg m-3) can be explained with a second-order polynomial with a high coefficient of determination (R2 = 0.99):


More data on density versus power input is needed to develop a more robust relationship. The validity of equation 6 is limited to the range of particle densities measured in this research.

Table 4. Grinder screen size, geometric mean diameter, specific energy input, and estimated parameters for Rittinger equation (eq. 2).
Specific Energy
(J g-1)
(J mm

    [a]    At p = 0.05 level, the population means of specific energies of grinding using the screen size are significantly different.

    [b]    Tukey’s post-hoc test indicates that all paired means are different except the specific energy of grinding means of pine and aspen, and of poplar and aspen on a 2 mm screen.

    [c]    Tukey’s post-hoc test indicates that all paired means are different except the specific energy of grinding means of pine and Douglas fir on a 4 mm screen.

    [d]    Tukey’s post-hoc test indicates that all paired means are different except the specific energy of grinding means of aspen and Douglas fir on a 6 mm screen.

Figure 6. Correlation of Rittinger’s constant (kR) with wood properties. The largest positive correlation was with wood porosity, and the largest negative correlation was with wood density.


Woody biomass samples from tree branches that may represent logging residue are highly variable in their structural properties. The effect of particle density can be explained by examining the density profiles of softwoods and hardwoods from the SilviScan analyses shown in figures 4 and 5. Figure 4 shows the density profile of Douglas fir from pith to cambium, where sharp changes in density are observed (mean = 838 kg m-3, SD = 201 kg m-3). Figure 5 shows the density profile across a 100 mm diameter aspen branch (mean = 469 kg m-3, SD = 59 kg m-3) for which the average density was lower than that of Douglas fir and the variations in density were smaller as well. Marchal et al. (2009) observed that the cross-sections of softwoods were more heterogeneous than the cross-sections of hardwoods, which affected the uniformity of peeled veneers.

Tree branches also vary in structure depending on whether they come from hardwood or softwood trees. Structurally, leaning tree branches are classified as reaction wood. In hardwoods, reaction wood is grouped as tension wood that is characterized by a higher density and tensile strength in the upper cross-section of the branch. In softwoods, reaction wood develops as compression wood in the lower cross-section of the branch (Butterfield and Meylan, 1980; Hakkila, 1989; Kettunen, 2006). Nati et al. (2010) studied grinding of branches and logs of poplar and pine using a drum chipper with installed screens. Branch wood produced less accepted pulp chips with excessive fines and oversize particles compared to logs.

In this research, sample moisture contents were maintained at around 9%. Temmerman et al. (2013) showed that the value of Rittinger’s constant (kR) increased with increasing moisture content. This can be attributed to the increased binding forces and stickiness of moist particles (softened lignin), which require more energy to crush. Nevertheless, moisture content is an important characteristic of woody biomass and needs to be studied in detail.


Previous studies showed that among the three industrial grinding equations (Kick, Rittinger, and Bond), the Rittinger equation best explains the grinding of cellulosic biomass. Rittinger’s constant (kR) is obtained by fitting the Rittinger equation to the experimental specific energy (J g-1) versus size ratio. To explore the potential dependency of kR on wood characteristics, nine physical properties of four species of woody biomass were determined, including particle density, solid density, porosity, lignin content, cellulose (glucan) content, density (x-ray method), microfibril angle (MFA), fiber length, and fiber coarseness. The wood species tested were two softwoods (Douglas fir and pine) and two hardwoods (aspen and poplar). The following conclusions can be drawn from this research.

Specific energy input to the grinder ranged from 156 kJ kg-1 (43 kW t-1) to 276 kJ kg-1 (77 kW t-1), indicating a wide variability in power use among the species tested. Similarly, the estimated value of kR ranged from a minimum of 203 J mm g-1 for Douglas fir to a maximum of 398 J mm g-1 for pine.

All nine properties were highly variable within each sample as well as between samples. The MFA, which is responsible for the stiffness of wood, varied from 11.5° for aspen to 32.1° for Douglas fir, indicating the inflexibility of aspen branches versus the flexibility of Douglas fir. The fiber length of Douglas fir and pine (1.17 to 1.31 mm) was almost twice that of aspen and poplar (0.65 to 0.73 mm).

The nine properties were all interdependent (highly correlated). Density had a strong correlation with lignin content, and fiber length had a strong correlation with cellulose content. As a result, kR had the strongest positive correlation with porosity and a strong negative correlation with density. An empirical equation relating kR as a function of density was developed and is suggested for use as a means of designing and operating grinders.


BioFuelNet and the Natural Sciences and Engineering Research Council of Canada provided funding for this research. Oak Ridge National Laboratory sponsored the PI of this project and Dr. Shahab Sokhansanj’s research. The authors would like to thank Mohammad Emami and Bahman Ghiasi for their help in the experiments and Nelson Uy and Shannon Huntley of FPInnovations for measurement of microstructural properties.


Adapa, P., Tabil, L., & Schoenau, G. (2011). Grinding performance and physical properties of non-treated and steam-exploded barley, canola, oat, and wheat straw. Biomass Bioenergy, 35(1), 549-561.

ASABE. (2007). ANSI/ASABE S319.3: Method of determining and expressing fineness of feed materials by sieving. St. Joseph, Mich.: ASABE.

ASABE. (2011). ANSI/ASABE S593: Terminology and definitions for biomass production, harvesting and collection, storage, processing, conversion, and utilization. St. Joseph, Mich.: ASABE.

ASABE. (2012). ASABE S352.2: Moisture measurement—Unground grain and seeds. St. Joseph, Mich.: ASABE.

ASTM. (2004). E1721-01: Standard test method for determination of acid-insoluble residue in biomass. West Conshohocken, Pa.: ASTM International.

ASTM. (2007). E1758-01: Standard test method for determination of carbohydrates in biomass by high-performance liquid chromatography. West Conshohocken, Pa.: ASTM International.

Ball, R. D., McConchie, M. S., & Cown, D. J. (2005). Evidence for associations between SilviScan-measured wood properties and intraring checking in a study of 29 six-year-old Pinus radiata trees. Canadian J. Forest Res., 35(5), 1156-1172.

Bendtsen, B. A., & Senft, J. (1986). Mechanical and anatomical properties in individual growth rings of plantation-grown eastern cottonwood and loblolly pine. Wood Fiber Sci., 18(1), 23-38.

Bitra, V. S. P., Womac, A. R., Chevanan, N., Miu, P. I., Igathinathane, C., Sokhansanj, S., & Smith, D. R. (2009). Direct mechanical energy measures of hammer mill comminution of switchgrass, wheat straw, and corn stover and analysis of their particle size distributions. Powder Tech., 193(1), 32-45.

Bjurhager, I., Olsson, A.-M., Zhang, B., Gerber, L., Kumar, M., Berglund, L. A., ... Salmen, L. (2010). Ultrastructure and mechanical properties of populus wood with reduced lignin content caused by transgenic down-regulation of cinnamate 4-hydroxylase. Biomacromolecules, 11(9), 2359-2365.

Bond, F. C. (1952). The third theory of comminution. Trans. American Inst. Mining Metal. Petrol. Eng., 193, 484-494.

Bond, F. C. (1961). Crushing and grinding calculations: Part I. British Chem. Eng., 6(6), 378-385.

Butterfield, B. (2006). The structure of wood: Form and function. In J. C. F. Walker (Ed.), Primary Wood Processing (pp. 1-22). Dordrecht, The Netherlands: Springer.

Butterfield, B. G., & Meylan, B. A. (1980). Three-Dimensional Structure of Wood: An Ultrastructural Approach (2nd ed.). London, U.K.: Chapman and Hall.

Chen, F. F., & Evans, R. (2010). Automated measurement of vessel properties in birch and poplar wood. Holzforschung, 64(3), 369-374.

Defo, M., Goodison, A., & Uy, N. (2009). A method to map within-tree distribution of fiber properties using SilviScan-3 data. Forestry Chronicle, 85(3), 409-414.

Deng, Q., Li, S., & Chen, Y. P. (2012). Mechanical properties and failure mechanism of wood cell wall layers. Comput. Materials Sci., 62, 221-226.

Evans, R., Gartside, G., & Downes, G. (1995). Present and prospective use of SilviScan for wood micro-structure analysis. In Proc. Appita Annual Conf. (pp. 91-96). Rotorua, New Zealand: Technical Association of the New Zealand Pulp and Paper Industry (Appita).

Evans, R., Stringer, S., & Kibblewhite, R. P. (2000). Variation of microfibril angle, density, and fiber orientation in twenty-nine Eucalyptus nitens trees. Appita J., 53(5), 450-457. Retrieved from

Fengel, D., & Wegener, G. (1989). Wood: Chemistry, Ulrastructure, Reactions. Berlin, Germany: Walter de Gruyter.

Gindl, W., & Teischinger, A. (2002). Axial compression strength of Norway spruce related to structural variability and lignin content. Composites Part A, 33(12), 1623-1628.

Gravelsins, R. J. (1998). Studies of grinding of wood and bark-wood mixtures with Szego mill. PhD diss. Toronto, Ontario, Canada: University of Toronto.

Hakkila, P. (1989). Utilization of Residual Forest Biomass. Berlin, Germany: Springer-Verlag.

Jayawickrama, K. J. S. (2001). Breeding radiata pine for wood stiffness: Review and analysis. Australian Forestry, 64(1), 51-56.

Kettunen, P. O. (2006). Wood Structure and Properties. Zurich, Switzerland: Trans Tech Publications.

Kollmann, F., & Côté, W. A. (1968). Principles of Wood Science and Technology. New York, N.Y.: Springer-Verlag.

Lawrence, V., & Woo, K. (2005). SilviScan: An instrument for measuring wood quality. Paprican Special Report PSR 550. Vancouver, B.C., Canada: Pulp and Paper Research Institute of Canada (Paprican).

Lindström, H., Harris, P., Sorensson, C. T., & Evans, R. (2004). Stiffness and wood variation of three-year old Pinus radiata clones. Wood Sci. Tech., 38(8), 579-597.

Lundqvist, S., Hansson, A., & Olsson, L. (2007). SilviScan measurements on Maritime pine: French samples cut perpendicular to the fibers. STFI-Packforsk Report 326. Stockholm, Sweden: STFI-Packforsk. Retrieved from

Mani, S., Tabil, L. G., & Sokhansanj, S. (2004). Grinding performance and physical properties of wheat and barley straws, corn stover, and switchgrass. Biomass Bioenergy, 27(4), 339-352.

Mansfield, S. D., Iliadis, L., & Avramidis, S. (2007). Neural network prediction of bending strength and stiffness in western hemlock (Tsuga heterophylla Raf.). Holzforschung, 61(6), 707-716.

Marchal, R., Mothe, F., Denaud, L.-E., Thibaut, B., & Bleron, L. (2009). Cutting forces in wood machining - Basics and applications in industrial processes. A review COST Action E35 2004-2008: Wood machining - micromechanics and fracture. Holzforschung, 63(2), 157-167.

Miao, Z., Grift, T. E., Hansen, A. C., & Ting, K. C. (2011). Energy requirement for comminution of biomass in relation to particle physical properties. Ind. Crops Prod., 33(2), 504-513.

Naimi, L. J. (2016). A study of cellulosic biomass size reduciton. PhD diss. Vancouver, B.C., Canada: University of British Columbia.

Naimi, L. J., Sokhansanj, S., Bi, X., Lim, C. J., Womac, A. R., Lau, A. K., & Melin, S. (2013). Development of size reduction equations for calculating energy input for grinding lignocellulosic particles. Appl. Eng. Agric., 29(1), 93-100.

Nati, C., Spinelli, R., & Fabbri, P. (2010). Wood chips size distribution in relation to blade wear and screen use. Biomass Bioenergy, 34(5), 583-587.

Nielsen, N. P. K, Holm, J. K., & Felby, C. (2009). Effect of fiber orientation on compression and frictional properties of sawdust particles in fuel pellet production. Energy Fuels, 23(6), 3211-3216.

Salmén, L., & Burgert, I. (2009). Cell wall features with regard to mechanical performance: A review. Holzforschung, 63(2), 121-129.

Scheller, H. V., & Ulvskov, P. (2010). Hemicelluloses. Ann. Rev. Plant Biol., 61, 263-289.

Simpson, W., & TenWolde, A. (1999). Physical properties and moisture relations of wood. In Wood Handbook: Wood as an Engineering Material. Madison, Wisc.: USDA Forest Service, Forest Products Laboratory.

Sluiter, A., Ruiz, R., Scarlata, C., Sluiter, J., & Templeton, D. (2005). Determination of extractives in biomass. NREL/TP-510-42619. Golden, Colo.: National Renewable Energy Laboratory. Retrieved from

Sluiter, A., Hames, B., Ruiz, R., Scarlata, C., Sluiter, J., Templeton, D., & Crocker, D. (2011). Determination of structural carbohydrates and lignin in biomass. NREL/TP-510-42618. Golden, Colo.: National Renewable Energy Laboratory. Retrieved from

TAPPI. (1999). Test method T280 pm-99: Acetone extractives of wood and pulp. Peachtree Corners, Ga.:: Technical Association of the Pulp and Paper Industry (TAPPI).

Temmerman, M., Jensen, P. D., & Hébert, J. (2013). Von Rittinger theory adapted to wood chip and pellet milling, in a laboratory scale hammermill. Biomass Bioenergy, 56, 70-81.

Woo, K. (2012). FQA preparation procedure. FPInnovation resource evaluation. Pointe-Claire, Quebec, Canada: FPInnovations.

Ye, C. (2007). Spectroscopic transmission ellipsometry enables quick measurement of pulp fiber. SPIE Newsroom, doi: 10.1117/2.1200705.0646. Retrieved from

Zhang, S.-Y., Wang, C.-G., Fei, B.-H., Yu, Y., Cheng, H.-T., & Tian, G.-L. (2013). Mechanical function of lignin and hemicelluloses in wood cell wall revealed with microtension of single wood fiber. BioResoures, 8(2), 2376-2385.