Abstract Grammage Probabality Distributions

ABSTRACT

GRAMMAGE PROBABALITY DISTRIBUTIONS TO PREDICT THE SOURCE OF FLOC FORMATION IN PAPER

by Payal Sood

Paper formation is an important characteristic for paper. It is affected by several papermaking variables such as refining, settling times, furnishes and chemical additives. This work involved the study on how grammage probability distributions (GPD) can be useful to predict the paper formation originating from PFI fibrillation actions, settling times and differences between softwood and hardwood pulps with the help of β- radiography. It was observed that GPDs of the handsheets were positively skewed. A new method of characterizing formation based on skewed nature of the GPD is useful to predict the source of flocculation was developed. These exhibited an inverse relationship with PFI refining. However, they showed a direct relationship with settling times. Softwood had higher skewness than that of hardwood. Thus, this work introduced the usefulness of the skewed part of grammage probability distributions to predict the origin of floc formation.

GRAMMAGE PROBABALITY DISTRIBUTIONS TO PREDICT THE SOURCE OF FLOC FORMATION IN PAPER

A Thesis

Submitted to the

Faculty of Miami University

in partial fulfillment of

the requirements for the degree of

Masters of Science

Department of Paper Science and Engineering

Payal Sood

Miami University

Oxford, Ohio

2009

Advisor ______Dr. D. Steven Keller

Reader ______Dr. Douglas W. Coffin

Reader ______Dr. Shashi B. Lalvani Table of Contents Chapter 1 Background and Literature Survey Page No. 1.1 Introduction 1 1.1.1 Fiber geometry 2 1.1.2 Stock Preparation 3 1.1.3 Stock Flow 5 1.1.4 Dewatering Process 6 1.1.5 Chemical Additives 7 1.2 Formation of paper 8 1.2.1 Formation Detection Techniques 9 1.2.2 Paper formation models for structure of paper 10 1.2.3 Analyses of paper formation 14 1.2.3a Spectral analysis 14 1.2.3b Statistical Analysis 16

1.3 Grammage probability distributions 17 1.4. Skewness 18 1.5 Problem Statement 20

Chapter 2 Experimental Procedure 2.1 Stock Preparation 21 2.2 Sheet Forming 21 2.3 Radiographic Method 22

Chapter 3 Results and Discussions 3.1 Sheet formation analysis 25 3.2 Grammage maps comparisons 28 3.3 Formation spectra analysis 31 3.4 Fiber length analysis 33 3.5 Grammage probability distributions analysis 34 3.5.1 Skewness 34

3.5.2 Grammage probability distributions 37 3.5.2a Normal distributions fitting 39 3.5.2b Relative areas 44

3.5.2c Relative differential Gaussian distributions (AG2) 47

Chapter 4 Conclusion 51 Chapter 5 Suggestions for future work 52 References 53 Appendix I 60 Original GPDs varying in terms of PFI refining, settling times with their G1 and G2 overlayed for hardwood 60 Appendix II 66 Original GPDs varying in terms of PFI refining, settling times with their G1 and G2 overlayed for softwood 66

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List of Tables

Table No. Caption Page No. Table 1 Process parameters for the experiments 24

Table 2 Symbols used in GPD analysis and their explanations 40 Table 3 Relative areas for softwood with different PFI milling 45 and different settling times. Table 4 Relative areas for hardwood with different PFI milling 45 and different settling times Table 5 Grammages and standard deviations of Gaussian (G1) 46 and differential Gaussian (G2) distributions for softwood handsheets made at different PFI refining degrees and settling times

Table 6 Grammages and standard deviations for Gaussian (G1) 46 and differential Gaussian (G2) distributions for hardwood handsheets made at different PFI refining degrees and different settling times

List of Figures

Figure No. Caption Page No. Figure 1 Wavelength spectra for a softwood handsheet made at PFI 16 milling of 10000 revolutions and settling times of 0 and 2 minutes Figure 2 An example of a Grammage probabaility distribution 18 Figure 3 A typical betaradiographic image of a handsheet in the 23 Formation Masters Software

Figure 4 Schematic Representation of Experimental Design 24 Figure 5 COV of sheets formed from softwood pulp refined at var- 27 ious freeness levels and made with different settling times Figure 6 COV of sheets formed from hardwood pulp refined at var- 28 ious freeness levels and made with different settling times

Figure 7 Basis weight maps of laboratory made isotropic, unrefined 30 handsheets of 30 g/m² Figure 8 Mass distribution Spectra for softwood and hardwood 32 handsheets made under PFI refining of 10000 revolutions with different settling times Figure 9 Fiber length (mm) of softwood and hardwood stocks re- 34 fined to various freeness levels using a PFI Mill Figure 10 skewness of sheets formed from softwood pulp refined at 35 various freeness levels and produced with different settling times Figure 11 skewness of sheets formed from hardwood pulp refined at 35 various freeness levels and produced with different settling times Figure 12 An example of positively skewed distributions illustrating 36 the effect of different settling times on standard deviations. Figure 13 GPD obtained by using Better Histogram software, Nor- 38-39 malized noisy GPD and its smoothed curve Figure 14 A non fitted Gaussian distribution (G1) on the original 41 GPD Figure 15 Gaussian Distributions (G1) fitted on a positively skewed 42 GPD Figure 16 Gaussian Distribution (G2) fitted on differential area (D) 42 Figure 17 G1+G2 fitted on a skewed GPD 43 Figure 18 G1 and G2 fitted on original GPD. It shows that median 43 grammages of G1 and G2 are different Figure 19 Mean Grammage values for G1 and G2 as a function of 49 PFI refining for softwood v

Figure 20 Mean Grammage values for G1 and G2 as a function of 49 PFI refining for hardwood

Figure 21 AG2 values for softwood made at different freeness levels 50 and different settling times Figure 22 AG2 values for hardwood made at different freeness levels 50 and different settling times

ACKNOWLEDGMENT My sincere gratitude to Dr. D. Steven Keller, my research advisor, for his support, guid- ance, editorial inputs and patience throughout the course of this project.

I would also like to thank the committee members, Dr. Douglas W. Coffin and Dr. Shashi B. Lalvani for their valuable suggestions.

I would like to thank Mr.Doug Hart and Mrs.Laurie Picadio for their valuable help during my Graduate study in the Department of Paper Science and Engineering. .

I extend my thanks to the graduate students of the Department of Paper Science and En- gineering for their support. Jie, I had good time in your company. Yan, you were fun to work with. I had some of my best times in the department with you. Na. thank you for always complimenting me! By the way, you are a good shopping partner!!! Gloria, with you, I had some of my best interactions. Good luck with your future studies. Bo, thank you, for always solving my MS Excel problems with patience! I know I have come to you with some of the silliest questions about it, but you always welcomed me with a smile. Sami, you were fun to talk with and a very nice person with a positive outlook. Kingsley, thanks for being there as a good friend. Yan2 (no matter how much you get ir- ritated by this name, I will still call you Yan2), we may not have spent enough time together, but from our brief interactions, I can say that you are a fun guy to be with. I ad- mire your constant endeavor to improve.

My most special thanks to my loving parents who relentlessly supported me throughout. I am thankful to God who has been really kind to bless me with the most wonderful set of parents. Papa, you are the most optimistic person I ever met in my life. Every parent love their children, but what makes you special is the fact that you have an incredible amount of belief in me. No matter, what the circumstances, you stood by me like no other person. I would not be what I am today without your constant support and wonderful advice. My darling Mom, I cannot thank you enough! I know how tough it was for you, to send the

vii only apple of your eye so far away. But you did it, just for your daughter’s sake of happiness. Finally, thank you Papa and Mom, for instilling the best values in me which kept me grounded and connected to the roots, in spite of being so far away from home.

I would like to extend my special note of appreciation to Shomz, Pama, Neha, Gaytri, Aanchal, Praveen and Aisha for their special friendships and neverending support throughout the years. Shomz, you made me feel that USA is the best place to live. You were the best roommate I ever had. Thanks for being the constant support system in my life. Pama, what would I do without you? You always patiently listened to my constant cribbing, complains, frustrations and gave me a shoulder to cry on. Pama, you are the strongest person I ever met. And how can I forget to mention our long night telephonic talks and our nonstop comments on each and every person we know. Sometimes, I won- der if we are long lost sisters. We think so much alike! I wish you all happiness in life. Neha, my childhood friend, I was thrilled to know that you are coming to USA, and trust me, you always kept me connected with our nostalgic childhood, which had become dis- tant memories, until you arrived! Gaytri, you were like an elder sister to me. You have seen me through some worst times here but stood like a pillar of support to me. Aanchal, my sweetest friend, a girl cannot ask for a better friend than you. In spite of being so far away, in heart I knew that you are always there for me. That proves correct every time, as whenever I call you, you bunk your class to talk to me! Praveen, my best online chatting friend, you are brilliant. It always amazes me as to how you have solutions for all problems. Last but not the least, Aisha, how I wish we met long time ago. I had some of my best times in Oxford with you. Moreover, you always showed an unshakeable amount of belief in me which kept me going.

My final thanks to some of my loving relatives, Bhushan Mamaji, Arvind Mamaji, Mee- na Masi, Shakti Masi, Kamini Di, Dimple Di and Richa for their neverending love and encouragement. Each one of you pampered and spoilt me a lot but that’s what relatives are for!

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Dedicated to

My loving parents, Lalit Sood and Madhu Sood

Chapter 1 Background and Literature Survey

1.1 Introduction

Formation or paper uniformity is one of the most important characteristics of paper in terms of quality. It can be described as mass distribution or grammage variations in the plane of a paper sheet [1]. Poor formation can lead to print unevenness [2,3], poor strength properties [4,5], good opacity and smoothness [6]. Recognizing the importance that sheet formation has on paper quality, numerous methods have been used to measure and analyze formation [7].

Paper formation depends, for the most part, on the flocculation of fibers during the forming process [8]. By definition, flocculation is just an aggregation of fibers together in a suspension [9]. Fibers tend to flocculate due to a number of reasons. These are: the composition of the fiber suspension, known as the furnish, the preparation process used to precondition the stock, the conditions of flow of the stock in the approach system; in the forming zone before fibers are dewatered into a coherent web, and the chemistry of the fibers and fines in solution. Regarding the furnish, fibers and fiber length greatly affects flocculation [10]. For stock preparation, refining/beating causes defibrillation which in turn affects paper formation [11]. An increase or decrease in speed of flow of stock through the headbox influences flocculation [9,12]. During dewatering in the forming zone, low drainage as indicated by low freeness values, results in increased flocculation

[13]. Finally, the addition of retention aids such as polyacrylamides [14] and micropar- ticles [15,16] influence flocculation. Wet strength resins [17] also influence flocculation.

Extensive research has been done to study all of these factors that affect formation.

An aspect that has been sought, but difficult to achieve, is the ability to separate the con- 1 tribution of various flocculation mechanism to the network structure by analyzing only the formation of the paper. Our work focuses on a method to separate several of these effects. Meanwhile, a review on each of these floc causing techniques is given below:

1.1.1 Fiber Geometry

Fiber properties play an important role in the formation of flocs. The lengths of fibers influence flocculation [10]. To demonstrate this, Kerekes et al. [10] observed an improvement in formation as fiber length was decreased. They performed fiber length and coarseness (mass per unit length) analysis on unbeaten kraft pulps produced from different species of wood. They attributed this to a decrease of size of flocs with decrease in fiber length. Kerekes [18] introduced an important parameter that describes flocculation, referred to as the crowding factor (N). The crowding factor indicates the tendency of a fiber suspension to form flocs. It is given by a relationship between fiber length, L, mass consistency, Cm, and fiber coarseness, w. in the formula

N = 5 *Cm *L²/w (1)

As one can see from the above equation, the crowding factor is a function of the square of fiber length. There is an inverse relationship between paper formation and crowding number as long fibers tend to become more entangled and hence form floccy sheets.

Waterhouse [17] observed that hardwood handsheets showed better formation than those formed with softwood. He attributed this to presence of short and less coarse fibers in hardwood sheets. Dodson [19] studied the effect of fiber length on formation distribution for commercial and random papers (simulated) [20] and found that the coefficient of variation of commercial paper was lower than for the ideally random paper.

1.1.2 Stock Preparation

Another factor that affects flocculation is stock preparation which includes refining.

Refining causes the defibrillation of fibers by mechanical action. It plays a major role in determining the paper formation [ 13,17,21,22]. Dodson et al. [23] studied the effect of refining on formation of paper. They predicted that an increase in refining will improve formation by 8-10%.

Norman et al. [24] refined bleached softwood pulps to different degrees by using an industrial double disc refiner. They observed that fibers are shortened during refining.

Further, Beghello et al. [21] performed image analysis on bleached kraft pulp of three different beating levels and inferred that an increase in beating decreased the size of flocs thereby resulting into better formation. Also, Helmer et al. [13] performed experiments on bleached eucalyptus kraft pulps by beating them to different freeness levels using a valley beater. They observed that as beating is increased, the coefficient of variation of basis weight decreased. The coefficient of variation or COV is equal to the standard deviation of basis weight divided by the mean basis weight [25]. Lower values of COV indicate better formation. Further, Kaji et al. [22] had cut the softwood pulp at different length intervals to produce slurries of different fiber lengths. They gave PFI milling of

6000 revolutions to each of them, and compared the COV values of unbeaten and beaten slurries. They observed lower COV for the latter case. They attributed this to the fiber flexibility imparted by the PFI mill. A detailed analysis on effect of PFI milling on fiber flexibility has been studied elsewhere [26]. The PFI mill is the most commonly used laboratory refiner and can be defined as a high energy and low intensity device where compressive forces acting on fibers result in internal fibrillation of fibers [27]. The geo-

3 metry of a PFI mill has been explained elsewhere [28]. Nazhad et al. [5] performed PFI milling at different levels to bleached softwood pulp and observed that better formation resulted. Waterhouse [17] studied the effect of PFI milling of softwood and hardwood on paper formation and found that paper formation was improved. Kerekes et al. [11] conducted experiments by producing handsheets made out of bleached kraft softwood pulp under criteria of using two different refiners (PFI and Escher Wyss laboratory refiner), standard handsheet making conditions and at headbox consistency. They deduced that increased PFI refining had an improving effect on the formation of standard handsheets made out of whole pulp.

Mohlin [29] presented paper on effect of industrial refining on different kinds of bleached softwood and hardwood kraft pulps using β-radiography [30] for formation evaluation. The STFI formation method measures grammage variations as a function of wavelength. It was found that formation numbers in the shorter wavelength region 0.3-

3mm decreases with increase in refining. She attributed this to an increase in the number of smaller particles or fines (due to refining in an industrial refiner) which produced a self healing structure in handsheets and hence exhibited good formation.

Taking into consideration the important role that refining plays in determining floc formation of sheets while we attempt to separate several of the effects on paper formation, we decided to study refining as one of the variables causing difference in mass distributions in a sheet and statistically analyzing the same.

1.1.3 Stock Flow

The pulp stock prepared in a stock preparation section of a paper mill proceeds to the forming section where the wet web is consolidated via the approach system and the headbox. The headbox plays a major role in controlling the physical qualities in paper, such as the distribution of material across the machine and in smaller areas that determine the formation. This makes control of flow one of the major tasks for a headbox. Thus, an insufficient amount of turbulent flow of the dilute pulp suspension in headbox becomes primary cause of fiber flocculation [12], as first demonstrated by Mason [9]. He introduced the mechanical aspect to flocculation, and proved that the governing factors for flocculation were fiber entanglement and the dispersion of fibers caused by turbulent mo- tion of liquid. Further, Mason also studied individual fibers and observed that average size of flocs diminished with an increase in turbulence, or the level of shear force. Thus, he found that fibers rotate, and become entangled to form flocs and due to shear force or turbulence acting on them, they disentangle and redisperse. These findings were verified and summarized by Hubey et al. [31] and Robertson et al. [32]. These concepts helped to demonstrate the importance of turbulence effects in the headbox and the influence on fiber flocculation.

Recognizing the effects of turbulence in the headbox on flocculation [12], and of flocculation on paper formation [18], one can easily see that the headbox plays an important role in determining paper quality. In order to study this relationship further, Karema et al. [33], Kerekes et al. [12] studied stock flow effects on flocculation and concluded that turbulence in headbox prevents flocs from forming and hence improved paper uniformity. Huber et al. [34] studied the characterization of floc size distribution of pulp

5 suspensions taking into consideration the fiber flocculation and sheet formation. Five flowing suspensions of dilute pulps, including hardwood, softwood and three mixtures thereof varying in terms of different flow speeds and different concentrations were analyzed using light transmission formation analysis. They inferred that the relationship between flocculation and formation is not linear.

Considering the importance of turbulence in headbox in determining paper formation, in this research investigation it was decided to introduce stock relaxation following turbulence, commonly called settling times, in the handsheet mold to study its effect on paper formation and statistically analyze the same. The settling times mentioned here refer to the time lag between turbulent agitation and the drainage in the sheet mold. Nor- man et al. [35] studied the effects of different settling times on softwood pulp flocculation by constructing formation spectra and observed that there was an increase in fiber flocculation as settling times were increased.

1.1.4 Dewatering process

From an operational point of view, the drainage/forming process is a key variable on paper machine. The speed of the paper machine is governed by drainage rate, while at the same time, the quality of the paper cannot be compromised. The most important effect of drainage is the formation of a fibrous mat on the web. Due to the dilute fibrous suspension, fibers are initially free to move. Hence drainage takes place via the filtration process which results in a uniform layered structure of fibers. But as the number of fiber contacts increase, they tend to become immobilize and drainage occurs by a thickening process.

This forms floccy networks, thereby worsening formation. Thus, the drainage rate plays a significant role in determining the paper formation. This has been verified by Corte [8]

6 who observed lowest coefficient of variation of basis weight for random paper where drainage takes place via filtration process. However, while studying the effect of dewatering process on paper formation, when Norman et al. [36] calculated the mass distribution wavelength spectra for both random and real sheets, they noticed more mass unevenness in random sheets as compared to real sheets in the small scale range of wavelength. This difference in observations by Corte and Norman was may be due to difference in aperture sizes of beta radiographic source. Corte used 1mm aperture while Norman used 0.1 mm.

1.1.5 Chemical Additives

Chemical additives can also promote or deter flocculation. The effects of some of the chemical additives such as wet strength resins, retention aids such as polyacrylamides and microparticle retentions, on flocculation are summarized below.

Wet strength resins are used as paper strengthening agents and consist of a wide range of cationic polymers. An increase in amount of wet strength agents used would lead to flocculation. In order to ascertain this, Waterhouse [17] conducted analysis by measuring the formation of handsheets (softwood and hardwood) produced by different types of laboratory formers and at different levels of freeness, with and without addi- tional wet strength resin (polyaminoamide- epichlorohydrin (PAE)). Delayed drainage was also tested in these experiments. Both resulted in poorer formation.

Another group of cationic polymers that are commonly used as a papermaking additives are polyacrylamides which are used as retention aids. To study its effect of fiber flocculation, Wågberg et al. [37] performed image analysis on fiber flocs formed by add- ing c-PAM. They attributed this formation of flocs to the bridging behavior of c-PAM. In this mechanism, oppositely charged surfaces (fibers- anionic, polymer- cationic) attract

7 each other to form bridges which cause fibers to form flocs. Also, Hartley et al. [38] studied the effect of c-PAM dosage on virgin pine fibers and observed that an increase in retention aid dosage increased the rate of fiber flocculation.

A contemporary form of retention aids known as microparticle retention also influences flocculation. This was demonstrated by Wågberg et al. [39] when they performed image analysis on unbleached cellulosic fibers in order to study the state of flocculation as c-PAM in combination with an anionic bentonite clay (a microparticle) was introduced to fibers. They observed that inducement of microparticle based retention aid resulted into higher degree of fiber flocculation.

Therefore, it can be concluded that flocculation is affected by various factors which ultimately influences paper formation. This research deals with separating several of these effects and statistically analyzing the uniformity of mass distributions. In the next few sections, I will discuss in detail paper formation measurement techniques, paper formation models suggested for structure of paper and analyses of formation.

1.2 Formation of paper

Paper formation is one of the most important parameters for papermakers. As discussed in earlier parts of this study, it plays a major role in determining paper properties

[2,4,6]. As demands for higher paper quality increased, a need was felt to quantitatively measure paper formation. Thus, a number of analytical techniques were developed [40-

45]. A brief overview on some of the existing techniques is given below:

1.2.1 Formation Detection Techniques

Tomimasu et al. [40] studied and compared the four imaging techniques namely as electrography [41], X - radiography [42], β - radiography [43] and light transmission

[44], by taking newsprint as the paper sample. They found that in terms of spatial resolution, β- radiography and electrography are superior to light transmission. X-radiography gave the poorest contrast. Furthermore, light transmission methods do not detect true grammage values of a chosen measured region due to sensitivity to the presence of fillers and calendaring. The β - rays on the other hand, do not scatter to the extent that visible light does. β-radiation gives a much closer approximation of the true grammage variations in a paper sample. A typical β-radiograph consists of a grey level map which is converted into a grammage map by using Mylar standards of different thickness and grammage exposed under same conditions as that of paper sample.

Since the early 1960s’, X-ray film radiography using radioactive 14C has been recognized as the foremost technique to image the paper formation [42]. Tomimasu et al. [45] identified some of the drawbacks of X-ray film radiography, for example the variability of exposure, development and suggested the use of electron beams and fluorescing screens as viable alternative that also included a digitization process. A contemporary approach to β-radiographic imaging involved the use of a storage phosphor imaging systems, referred to as computed radiography that was developed for paper by Keller et al.

[43]. This method was employed in this research project to image the distribution of mass in the sample.

Computed Radiography [43]

Johnston et al. [46] studied the application of phosphor imaging plates in autoradiography. The mechanism of phosphor imaging involves the use of BaFBr:Eu complex imbedded in the detector screen. This screen is exposed to radiation energy that trans- forms the Europium to an excited state. Photostimulated phosphorescence takes place thereafter when small areas of the plate are exposed to visible red laser emission. Johns- ton also reported that sensitivity of storage phosphor screens was about 60 times higher than that of X-ray film.

Storage phosphor imaging has many performance advantages over other imaging sensors [47]. Storage phosphor plates exhibit higher resolution as compared to other imaging devices. Imaging data is directly obtained from the imaging plate using digital values which can be easily processed by computer. Results are reproducible unlike X-Ray film which is affected by slight changes in development conditions. Also, imaging plates are reusable. Once irradiated with visible light, the residual image on imaging plates can be erased to allow repeated use.

1.2.2 Paper formation Models for structure of paper

The structure of paper can be described as a stochastic network of fibers. Paper formation plays an important role in the field of structure of paper. Further elaborating this, the network descriptors such as fiber crossings [48] ( total number of fiber to fiber contacts), number of fiber crossings per fiber, number of fiber crossings per square mm, average fiber length are some of the geometrical scales which determine mechanical, opt- ical properties of paper. The above discussed descriptors like fiber crossings per square mm depends on the number of fibers passing through that particular square mm which in

10 turn depend on the non uniformity or non uniform distribution of fibers in a plane of sheet. Thus formation of paper becomes an underlying player in the field of structure of paper.

Models for paper formation provided relationships correlating various papermaking variables to mass distributions. Recently, significant advances in modeling formation have been made by Dodson et al. [49-51]. Further, in one of the earliest studies of geometrical structure of paper, in order to perform statistical geometric analysis on a two dimensional flocculated sheets, Corte et al. [48] provided an accurate definition for random network of fibers and predicted that in a random network, the fibers are layered indepen- dently of each other, they have an equal probability of appearing at the same point in the plane of the sheet and fibers can choose to make any angle with the fiber axis which means that they have random orientation. Further, in order to provide a relationship between coefficient of variation of basis weight for flocculated commercial papers in nar- row ranges of basis weights and that of random paper, Dodson [50] gave the equation

0.5 COVfloc (β) = nf x COVrandom (β) (2)

Where β = local basis weight

nf = formation index ( variancecommercial / variancerandom) [49]

COV (β) = coefficient of variation where the subscript denotes an

ideal random or commercial paper

Thus, eq. (2) correlates grammage variations of the commercial and an ideal random paper. Also, the equation was found to hold true for commercial papers over the range of 16 g/m² to 260 g/m².

In another paper, to study the relationship between fiber length, mass consistency and formation index, Schaffnit et al. [51] presented a study in which a new quantita- tive relationship was established between formation index (nf) and two wet end papermaking variables which were crowding number for headbox and mean fiber length. The relationship was given by

nf = 2.6 +0.13 nc – 1.34L (3)

Where nc ( crowding number ) = πc*L²/6w (4)

c = volumetric consistency

L = mean fiber length

w = mass coarseness

They concluded that formation index is positively correlated with crowding number and negatively correlated with fiber length. To elaborate on this, as seen in eq. (4), crowding number contains squared mean fiber length and the mass consistency. Hence, from eq. (3), Schaffnit et al. predicted a decrease in nf at constant consistency and a stated change in mean fiber length. Further, they also predicted an increase in nf under stated change in consistency at constant fiber length.

Sampson et al. [52] presented a statistical analysis of the influence of paper formation on various structural parameters, such as skewness of coverage distributions of fibers, and the prediction of pinholes [53]. For modeling purposes, he used the term coverage which implies the number of fibers covering a single point in the plane of sheet.

While performing statistical analysis, he used the following formula for calculating the skewness of the coverage distribution of fibers

0.5 Sk = 2nf -1/(c̅ *nf) (5)

Where Sk = skewness of coverage of fibers

nf = formation number or formation index

c̅ = mean coverage

The probability of increase in pinholes (P*(0)) in a given

network at coverage = 0 is given by

-c/n 1 P*(0) = nf f- (6)

Thus from eq. (5) and eq. (6), one can see that the skewness of a distribution of coverage of fibers increases with an increase in flocculation which in turn influences pinholes in paper and gives a rise to them. The purpose of discussing this work was to demonstrate that there has been a study on influence of paper formation on skewness. How- ever, in this research work, the effect of different PFI refining degrees, settling times and different furnishes on skewness of mass distributions was studied. This will be further elaborated in next few sections of this study.

In another paper, Farnood et al. [54] presented a physical model which they termed as random disk model [55]. This model refers to spherical flocs in a sheet which take up the shape of a disk on random deposition in a forming process. To prove its utility, they ran β-radiography on the commercial paper samples varying in terms of mean disk grammages and disk diameters (small loose flocs) and plotted the calculated disk diame- ter versus mean disk grammage. They showed that low disk grammages and small disk diameters gave better formation. As both parameters start to increase the sheet becomes cloudier.

Thus, the literature discussed above contained mathematical and physical models relating mass uniformity to various papermaking variables. Also, all the models men-

13 tioned above predict poor paper formation as flocculation increases. However, my research deals with a study of the analysis of mass uniformity with the help of grammage probability distributions. This will be explained in further sections. Hence, in order to explain the structure of paper, various handsheet samples under different degrees of PFI refining, different settling times and two furnishes (softwood and hardwood) were prepared. Formation testing on the samples was performed using storage phosphor system.

In the next section, a brief discussion of the analyses of paper formation will be given.

1.2.3 Paper Formation analyses

Paper formation can be characterized in many ways. To demonstrate this, Kajanto et al. [7] presented a paper summarizing the statistical parameters used for characterizing paper formation and also applied power spectra [56] to evaluate paper formation.

The paper formation characterization can be classified as either spectral or statistical analysis.

1.2.3a Spectral Analysis

Norman et al. [56] were the first to use power spectrum technique to characterize paper formation. Power spectra, or frequency spectra, indicates how the variance of a signal (read as mass uniformities) is distributed over different frequency ranges. In other words, it is a representation of mass or fiber distribution in a given sheet. Further, some of the stochastic variables such as basis weight, turbulence in the headbox, concentration of fibers in the dilute stock and hence their frequencies will vary in each phase which needs to be characterized. This is where power spectrum comes into the picture. It gains importance from the fact that any periodic variations in the structure of paper will appear

14 as prominent peaks in a power spectrum. To sum it up, the power spectrum represents the contributions of the small and large flocs to the variability in a paper sheet.

To interpret the variance at each length scale (in a power spectrum) more expli- citly, Norman et al. [56] came up with transformation of frequency spectrum into wavelength spectrum. A detailed discussion on how this transformation takes place is well explained by Norman et al. [56]. Further, its utility comes from the fact that it is possible to directly evaluate the geometrical scales in mass variation that is the flocs formed in paper sheets. The final results are independent of the speed of scanning device. An example of the wavelength spectra is shown in Figure 1.

To show an example of wavelength spectra, we performed wavelength spectra analysis on ordinary (zero min) and delayed drainage (two min) handsheets with an average basis weight of 30 g/m2 by running beta radiography, to obtain Figure 1 , which gave all information about the basis weight variation over different wavelengths. The dashed curve which represents the flocculated handsheet showed how flocculation increases at long wavelengths. Thus the wavelength spectra give information about the floc size distributions. We used the wavelength spectra to characterize different mass distributions obtained due to different settling times. We constructed the wavelength spectra, as a function of settling times, in order to illustrate an example of the effect of settling times on fiber flocculation

100.00

10.00 sw 0 min sw 2min

Spectral density, 1/m 1.00

0.10 0.10 1.00 10.00 100.00 Wavelength, mm

Figure.1 Wavelength spectra for a softwood handsheet made at PFI milling of 10000 revolutions and settling times of 0 (dotted line) and 2 (dashed line) minutes.

1.2.3b Statistical Analysis

In early years, work in this area has been done by Corte [8,57]. In his findings,

Corte recognized the use of random distribution of fibers in a paper sheet as a reference

distribution for characterizing formation. As discussed earlier, paper formation exhibits

the non-uniformities of a paper sheet and defined as the mass distribution in a paper

sheet. In order to quantify and characterize paper formation, Wahren [25] introduced the

16 utility of the statistical parameter coefficient of variation of local basis weight in order. It can be determined by using various mass variation measurements and is given by the formula:

COV = ơ/BW (7)

Where ơ = standard deviation of basis weight (g/m²)

BW = mean basis weight (g/m²)

In my research work for analyses of paper formation, I measured the COV as one of the statistical parameters to characterize different mass uniformities obtained due to use of different PFI milling degrees, different settling times and two furnishes (softwood and hardwood) with the help of β - radiography. Meanwhile, in the following sections, I will discuss the grammage probability distributions, skewness and the objective of my research work. .

1.3 Grammage Probability Distributions

Figure 2 illustrates an example of the grammage probability distribution for a softwood handsheet made at 0 PFI refining degree and settling time of 0 min with both axes normalized with respect to the average grammage. As we can see from Figure 2, the right hand tail to the mean (30 g/m²), is heavier than the left hand one,thereby indicating positive skewness.The concept of skewness will be explained in next section.

Earlier studies [52], have shown the effect of paper formation on skewness of coverage distributions. However, the aim of this study is to investigate the influence of

PFI refining, settling times and differences in softwood and hardwood on grammage probability distributions and how can they be proved useful to analyze the different mass distributions.

0.90

0.80

0.70

0.60

0.50

0.40 EXPERIMENTAL Frequency Gaussian 0.30

0.20

0.10

0.00 0 10 20 30 40 50 60

Grammage, g/m²

Figure 2. An example of a Grammage probabaility distribution.

1.4 Skewness

As shown in Fig.8, the distribution is positively skewed; Skewness can be defined as asymmetry of data around the mean. It can be either positive or negative. Positive skewness has more data spread out towards the right hand side of mean and vice versa for negative skewness. The figure shown below illustrates positive and negative skewed distributions.

The skewness of a distribution is generally quantified as

y=E(x-µ)³ / ơ³ (8)

where µ = mean of x,

ơ = standard deviation of x,

and E(t) represents the expected value of the quantity t.

In my work, skewness was used as one of the primary statistical tools to analyze different mass distributions resulting from using different PFI refining, settling times and two furnishes, namely, softwood and hardwood.

1.5 Problem Statement

Kajanto et al. [7] gave detailed analysis on several statistical parameters

(coefficient of variation, standard deviation, specific perimeter) which characterized paper formation and how they can be used to define relation between formation and different functional properties such as smoothness, opacity, printability and strength. They em- phasized that as different functional properties are important for different paper grades, therefore only one parameter describing formation should not be employed. Instead more formation parameters will be required.

Therefore, in a broadened way, my research objective was to discover a new parameter to characterize mass uniformity with the use of grammage probability distributions, obtained for handsheets made at different PFI refining degrees, settling times and with softwood and hardwood. Hence my hypothesis was:

Hypothesis

Statistical analysis of grammage probability distributions can be used to predict the origin of floc formation.

Objective of thesis

To analyze how grammage probability distributions (GPD) can be useful to predict the paper formation originating from PFI fibrillation actions, dilute stock relaxation following turbulence and differences between softwood and hardwood pulps. In next few sections, I will describe the experimental procedure, results and their discussions, conclu- sions of this work and suggestions for future work.

Chapter 2 Experimental Procedure

2.1 Stock Preparation

Two kinds of furnishes, namely softwood and hardwood pulps (supplied by Mo- hawk Paper Mill, Ohio), were beaten to various degrees (0, 2500, 5000, 10000) using a

PFI Mill. The stock was prepared in accordance with the TAPPI Standard (T 248 cm-85).

The freeness values of the beaten stocks were measured using a Canadian Standard freeness tester according to the TAPPI Standard (T 227 om-94). No filler or any other chemical additives were used.

Samples of stocks (prepared under different refining degrees) were sent to Beckett mill (Mohawk Fine Paper Inc.), Hamilton Ohio for fiber length testing. Relative weighted average fiber length was determined using a Kajaani FS-100 instrument.

2.2 Sheet Forming

The handsheets were prepared from the PFI refined pulps in accordance with

TAPPI standard (T 205-95) using a British handsheet mold. For this work, the departures from the T 205-95 method were- first, the selected grammage of handsheets was reduced from 60 g/m² to 30 g/m², second, different settling times (zero min, one min, two min) following turbulence were introduced during the handsheet preparation. As already discussed in earlier part of this study, settling times mentioned here refer to time lag between agitation and drainage in the sheet mold. Earlier studies have shown that settling times have well known effects on formation as it gives rise to flocculation in pulp suspension [35]. A number of sheets were formed at each operating conditions.

2.3 Radiographic Method

Keller et al. [43] explained β-radiographic method using storage phosphor system but a brief description of the data collecting procedure and the formation testing equip- ments is present here.

The imaging plates (phosphor screens) were cleared of any remaining images using

Image Eraser. The β - emitter was a carbon 14 source mounted on a 102mm x 102mm x

1mm polymethyl methacrylate film. The storage phosphor screen consisted of a 20 x 25 cm active polymer screen mounted on a rigid aluminum plate. As described in earlier in- vestigations [46] the sample was held between 14C radiation source and storage phosphor screens (Molecular Dynamics Sunnyvale, Ca USA) which act as an image receptor. I chose an exposure time of 30 minutes. After 30 minutes, storage phosphor screens were slid into the PhosphorImager (Molecular Dynamics) and thus developed and digitized to give scanned images. The scanner took approximately a scan time of 7 minutes at 100

µm pixel size to scan a handsheet image stored on phosphor screen. The images were then calibrated against the Mylar Standards and analyzed using MATLAB software. Fig- ure 3 shows an image of the custom software called Formation Masters [58] used for this research work. This software provides options for obtaining statistical and spectral data of β - radiographic images which included coefficient of variation of mass (COV) or formation numbers, wavelength spectra, average grammage, grammage histograms of the selected scanned area on image. The repeatability of mass measurements COV was 0.5% or better. This software [58] provided grammage maps which were further used to obtain grammage probability distributions (GPD). Each GPD was constructed by using a grammage grid of 300x300 (around 90,000 data points), so that the number of detected

grammage points remained essentially constant. Figure 4 gives a schematic representa-

tion of the experimental organization. Also, Table 1 summarizes the process parameters

used in this study.

Figure.3 A typical β - radiographic image of a handsheet in the Formation Masters Soft- ware

Handsheets prepara- β - radiography or Pulping at different tion according to formation testing on refining degrees TAPPI Std handsheets

Run formation master Figure.4 Schematic Representation of Experimental Organization on β - radiographic

images

Table 1. Process parameters for the experiments Raw material Softwood and hardwood

PFI refining degrees 0,2500,5000,10000

Settling times, minutes 0,1 and 2

Exposure time for β – radiography 30 minutes

Chapter 3 Results and Discussions

As the means to characterize paper formation, I measured the COV values of basis weight and plotted them as a function of PFI refining, settling times and hardwood and softwood. Further, grammage maps of softwood and hardwood were compared. Also, we constructed the formation spectra for softwood and hardwood, to show the effect of different settling times on flocculation. Fiber length analysis was also performed on softwood and hardwood. Lastly, as per the objective of my research work, to study the usefulness of GPDs in predicting origin of floc formation, GPDs were analyzed and explained.

3.1 Sheet formation analysis

In the introductory part of this study, I have already discussed the importance of paper formation and effects of papermaking variables such as PFI refining, settling times and furnishes (softwood, hardwood) on it. I therefore calculated the COVs of grammage and studied the effect of papermaking variables on them in order to characterize paper formation. I found that they were in good agreement with previous studies [13]. The detailed explanations are given below:

Figure 5 illustrates the effects of PFI refining and different settling times on softwood pulp. It shows that COV (Coefficient of variation) decreases as refining increases and freeness decreases, which indicates that formation of sheets improved as refining is increased. This improvement in mass uniformity may be due to the internal fibrillation of fibers by the PFI mill which lead to finer scale variations in the sheet. Somewhat similar trends were observed in the previous research of Waterhouse [17], although COV result that he found for bleached northern softwood handsheets refined at different levels and

25 made using TAPPI standard showed significantly lower COV values when compared with my values. This can be attributed to the fact that he used a grammage of 60 g/m² whereas in this study the handsheet mean grammage is 30g/m² which explain the difference in COV values. Also at 10000 revolutions, a significant increase in COV was noticed in his work, which he attributed to longer drainage time occurring at low freeness levels and hence flocculation taking place. However, in this study, the formation number results for softwood handsheets shows an improvement of 10-15% in formation as refining is progressed from 0 revolutions up to 10000 revolutions. This is in agreement with what Dodson [23] predicted for formation improvement. Further, from Fig. 5 we can see that different handsheet settling times were used and their effects on sheet formation were studied. It is evident that COV increases as settling time is increased. This can be attributed to the fact that at a settling time of one min and two min, flocs are formed which leads to poor formation, whereas at zero min handsheets shows fine grammage variations and hence show better formation than the other two settling times. Hence Figure 5 shows that different handsheet settling times and various refining degrees affect paper formation and longer drainage time at high refining levels may not play any role to influence formation. This is not in agreement with the results of Waterhouse [17]. He concluded that the occurrence of longer drainage time was a reason behind the rapid deterioration of formation at high refining levels.

Figure 6 shows the effect of PFI milling and different settling times on hardwood pulp where a decrease in COV occurs as PFI refining is increased. As mentioned earlier, formation improvement can be attributed to the fibrillation action and the fiber flexibility imparted by the PFI mill. Also, hardwood fibers are short and shorter fibers generally

26 give finer scale variation [59]. Previous studies [13] have shown similar effect of beating on COV values of hardwood. Also, from Fig. 6 effect of different settling times on COV values of hardwood can be clearly seen. An increase in settling times led to fiber flocculation and hence poor formation.

From Fig. 5 and Fig. 6, when COV values of softwood and hardwood were compared, it was noticed that COV for softwood were higher than that for hardwood. Longer and coarser fibers, in case of softwood, led to poor formation. Similar predictions were made by Waterhouse [17]. Although in his work, COV values for softwood and hardwood were much lower as compared to what I obtained. This can be attributed to the fact that he used an aperture of 1 mm to measure mass variations while the aperture size of storage phosphor system (used in this study) was 100 µm.

20 19 18 17 16 15 0 min 14 1 min 13

Coeff of of CoeffVariation, % 2 min 12 11 10 0 100 200 300 400 500 600

Freeness, CSF

Figure.5 COV of sheets formed from softwood pulp refined at various freeness levels and made with different settling times

13 0 min

11 1 min

Coeff of of Coeff Variation,% 2 min 9

5 0 100 200 300 400 500

Freeness, CSF

Figure.6 COV of sheets formed from hardwood pulp refined at various freeness levels and made with different settling times

3.2 Grammage maps

Importance of paper formation is well known. Its also known that paper formation is the grammage variations in a sheet of paper. Also, the research objective of this study was to determine the usefulness of grammage probability distributions constructed from the grammage maps to predict the origin of floc formation.An example β - radiographic grammage maps of softwood and hardwood pulps with different settling times is provided in Fig. 7.

Effect of settling time

When Sample A and B are visually observed, we notice that A has better formation than B as evidenced by the more uniform appearance. This difference is large enough to 28 appear in formation number ( 17.0% for SampleA, 19.5% for Sample B). The reason behind this can be attributed to formation of flocs in the latter case. Introducing a settling time of two min, allows dense and coarse flocs to be formed in the pulp suspension which is clearly visible in Sample B map. In case of Sample C and D, again the sheet formation of former is better than the latter. This difference shows up in their formation numbers

(9.1% for Sample C, 11.4% for Sample D). For Samples A,B,C,D, the contrast was enhanced in order to make the images appear more clearly. This change in no way affects the final results since the same contrast correction was applied to all samples.Also, the same β - radiographic conditions were used to generate all images.

Effect of furnish

In Fig. 7, visual comparison between Sample A and C, clearly indicates that due to presence of highly variable light and dark (flocs) zones in softwood sheet, shows a poorly formed sheet. Softwood handsheets contain denser and coarser flocs than the hardwood because of long fibers. Long fibers tend to form large flocs and hence poor formation. Similar observation can be noticed while comparing Sample B and D. Sample

D has better formation than Sample B.This can be attributed to presence of short fibers in case of hardwood which leads to good formation

A B

C D

Figure. 7 Grammage maps of laboratory made isotropic, unrefined handsheets of 30 g/m² A. Softwood, Settling time = 0 min B. Softwood, Settling time = 2 min C. Hardwood, Settling time = 0 min D. Hardwood, Settling time = 2 min

3.3 Formation Spectra Analysis

Fiber geometry, which includes length of fibers contributes to pulp flocculation.

Also, settling time has well known contribution to pulp flocculation. In order to demonstrate this, I plotted formation spectra for softwood and hardwood handsheets made under different settling times. In Figure 8, the effects of differences in softwood and hardwood and different settling times on floc size distributions can be clearly seen. Hereafter, the floc size distribution will be discussed for two wavelength regions, short (0.1 mm- 1 mm) and long (1mm – 30mm). It was assumed that fiber flocculation play a role in longer wavelength region. Hence by creating the two wavelength regions W (0.1-1) and W (1-30), effect of fiber flocculation was separated.

The two spectra shown in Fig. 8 for softwood handsheets indicate that two min handsheets contain more of the large flocs in W (1-30) but actually fewer of the smallest flocs in W (0.1-1) when compared with zero min handsheets. When whole floc size range is considered, zero min softwood sheets were found to be more even with a formation number of about 14% compared with about 16% for the two min softwood sheets. Thus, it shows that wavelengths for two min sheets are higher than that of zero min sheets due to presence of larger flocs in the former case, thereby supporting the occurence of flocculation when time lag is introduced. While studying the delayed drainage effects on kraft pulp, Norman et al. [35] observed similar trends in their research, when the unbleached kraft pulp was beaten to different degrees and handsheets (40 g/m²) prepared with time lags of 0 min, 1 min, 6 min.

Inspection of hardwood spectra reveals that zero min and two min handsheets contained almost same amount of smaller flocs in W(0.1-1). However, in the long wave-

31 length region (1mm -30 mm), the presence of more of the larger flocs is observed for two min handsheets when compared with zero min sheets. This indicates the occurrence of flocculation, as delayed drainage was introduced.

Comparing the hardwood and softwood spectra, one can see that softwood spectra tail elongates towards the long wavelength region. This is due to presence of larger flocs as compared to that of hardwood spectra. Also, some of the predominant wavelengths, appearing as peaks in the formation spectra must be due to characteristic sizes of furnish or some specific step in the experimental procedure.

100.00

sw 0 min 10.00 sw 2min hw 0 min hw 2min

Spectral density, 1/m 1.00

0.10 0.10 1.00 10.00 100.00 Wavelength, mm

Figure 8. Mass distribution Spectra for softwood and hardwood handsheets made under PFI refining of 10000 revolutions with different settling times

3.4 Fiber Length Analysis

In the introductory part of this study, the importance of fiber length in determining paper formation was discussed in detail. Also, the effect of PFI refining on fiber lengths of wood species and its improving effect on paper formation was also mentioned. There- fore it was decided to study the effect of PFI refining on fiber length as a part of the pre- liminary research. The fiber lengths of hardwood and softwood pulp samples made at different PFI refining degrees were tested on Kajaani FS 100. The weight weighted average fiber lengths [60] are plotted as a function of PFI refining.

Figure 9 illustrates the effect of PFI milling on fiber lengths of softwood and hardwood. It can be seen that fiber lengths of both softwood and hardwood decreased as PFI milling was increased. It can be attributed to the internal fibrillation action of PFI mill.

Similar trends were noticed for hardwood when Helmer et al. [13] performed beating via valley beater on bleached eucalyptus pulp and observed its effect of fiber length of the pulp. Although, greater fiber shortening was observed in their work than from what I noticed for my work, but it can be attributed to the fact that a PFI mill applies compressive forces on fibers which leads to an internal fibrillation to the fibers, whereas a valley beater performs fiber cutting.

A study on effect of refining performed by industrial refiners on fiber length of softwood and hardwood has been done previously [4,24]. They all showed fiber shortening as refining was increased.

Figure 9. Fiber length (mm) of softwood and hardwood stocks refined to various freeness levels using a PFI Mill

3.5 Grammage probability distributions analysis

3.5.1 Skewness

Skewness has already been discussed in the introductory part of this study. In the initial part of this project, the skewness of grammage maps was obtained and plotted as a function of papermaking variables such as different PFI refining, different settling times as shown in Fig. 10 and Fig. 11 for softwood and hardwood pulps respectively. It was observed that the skewness values were all positive. In next few sections, GPD, their Nor- mal distributions, relative areas and its analysis will be discussed.

0.35

0.3

0.25

0.2 0 min 0.15 SKEWNESS 1 min

0.1 2 min

0.05

0 0 100 200 300 400 500 600

freeness, CSF

Figure.10 skewness of sheets formed from softwood pulp refined at various freeness levels and produced with different settling times

0.3

0.25

0.2

0.15 0 min

Skewness 1 min 0.1 2 min

0.05

0 0 100 200 300 400 500

Freeness, CSF

Figure.11 skewness of sheets formed from hardwood pulp refined at various freeness levels and produced with different settling times.

The focus of this research focus was to statistically analyze the grammage probability distributions (GPD) in order to see its usefulness in predicting floc formation. There- fore, when I constructed the GPDs as a function of PFI refining, settling times and hardwood and softwood, I noticed different standard deviations and different skewness of basis weight in GPDs. An example illustrating this is shown in Fig. 12. One can clearly see in Fig. 12 that dashed curve has lower standard deviation than the continuous one. This was due to the effect of an increase in settling times. Also, the skewness of both the curves appears different. My interest was in the skewed part of the GPDs and hence to study the influence of PFI refining, settling times and differences in softwood and hardwood on them. Also I analyzed how these GPDs can be useful in predicting origin of floc formation.

0.9

0.8

0.7

0.6

0.5

0.4 0 min Frequency 2 min 0.3

0.2

0.1

0 0 10 20 30 40 50 60

Grammage, g/m²

Figure 12. An example illustrating the effect of different settling times on standard deviations. It shows that different standard deviations and different skewness of basis weights for both curves.

3.5.2 Grammage probability distributions

The GPDs were constructed with a help of software called as “Better Histo- gram_20070222_2050” which used the grammage maps obtained from Matlab to get grammage histograms that appear similar to that shown in Figure 13 (top plot). Further, to normalize the area under the curve, the abscissa was normalized with respect to grammage values as shown in eq. (9)

Normalized grammage = bin width x 30 g/m2 (9)

Mean grammage

The grammage bin width was chosen to be 0.1 g/m2. Further, the ordinate contained frequency values normalized as shown in eq. (10) given below

Normalized frequency = each frequency x 100 x mean grammage (10)

Sum of frequencies x 30 g/m²

Thus, a representative GPD is shown in Fig. 13 (center plot). Further, it was noticed that these GPDs were not smooth (see center plot in Fig. 13). Hence, I applied a smoothing function which applied a 5 point moving average which yielded a smoothed curve without disturbing the characteristics of the original curve (see bottom plot in Fig. 13).

Figure 13 shows both the original and the smoothed curve. Note the grammage probability distributions contained heavy tail to the right hand side of mean grammage (30 g/m²).

Better Histogram 800

700

600

500

400

Frequency 300

200

100

0 0.1080.2160.3240.4320.6480.7560.8640.540.9721.1881.2961.4041.0801.5121.7281.8361.9441.622.0522.2682.3762.4842.162.5922.8082.9163.0243.1323.3483.4562.73.5643.243.6723.8883.9964.1043.784.2124.4284.5364.6444.324.7524.9685.0765.1844.865.2925.5085.6165.7245.8326.0486.1565.46.2645.946.3726.5886.6966.8046.486.9127.1287.2367.3447.027.4527.6687.7767.8847.567.9928.2088.3168.4248.5328.7488.8568.18.9648.649.0729.2889.3969.5049.1810.0449.61210.1529.82810.3689.93610.4769.7210.58410.69210.2610.90811.01611.12411.23211.44811.55610.811.66411.77211.3411.98812.09612.20412.31211.8812.52812.63612.74412.85212.4213.06813.17613.28413.39212.9613.60813.71613.82413.93214.14814.25613.514.36414.47214.0414.68814.79614.90415.01214.5815.22815.33615.44415.55215.1215.76815.87615.98416.09215.6616.30816.41616.52416.63216.84816.95616.217.06417.17216.7417.38817.49617.60417.71217.2817.92818.03618.14418.25217.8218.46818.57618.68418.79218.3619.00819.11619.22419.33219.54819.65618.919.76419.87219.4420.08820.19620.30420.41219.9820.62820.73620.84420.95220.5221.16821.27621.38421.49221.0621.70821.81621.92422.03222.24822.35621.622.46422.57222.1422.78822.89623.00423.11222.6823.32823.43623.54423.65223.2223.86823.97624.08424.19223.7624.40824.51624.62424.73224.94825.05624.325.16425.27224.8425.48825.59625.70425.81225.3826.02826.13626.24426.35225.9226.56826.67626.78426.89226.4627.10827.21627.32427.43227.64827.75627.86427.97227.5428.18828.29628.4042728.51228.0828.72828.83628.94429.05228.6229.26829.37629.48429.59229.1629.80829.91630.02430.13230.34830.45629.730.56430.67230.2430.88830.99631.10431.21230.7831.42831.53631.64431.75231.3231.96832.07632.18432.29231.8632.50832.61632.72432.83233.04833.15632.433.26433.37232.9433.58833.69633.80433.91233.4834.12834.23634.34434.45234.0234.66834.77634.88434.99234.5635.20835.31635.42435.53235.74835.85635.135.96436.07235.6436.28836.39636.50436.61236.1836.82836.93637.04437.15236.7237.36837.47637.58437.69237.2637.90838.01638.12438.23238.44838.55637.838.66438.77238.3438.98839.09639.20439.31238.8839.52839.63639.74439.85239.4240.06840.17640.28440.39239.9640.60840.71640.82440.93241.14841.25640.541.36441.47241.0441.68841.79641.90442.01241.5842.22842.33642.44442.55242.1242.76842.87642.98443.09242.6643.30843.41643.52443.63243.84843.95643.244.06444.17243.7444.38844.49644.60444.71244.2844.92845.03645.14445.25244.8245.46845.57645.68445.79245.3646.00846.11646.22446.33246.54846.65645.946.76446.87246.4447.08847.19647.30447.41246.9847.62847.73647.84447.95247.5248.16848.27648.38448.49248.0648.70848.81648.92449.03249.24849.35648.649.46449.57249.1449.78849.89650.00450.11249.6850.32850.43650.54450.65250.2250.86850.97651.08451.19250.7651.40851.51651.62451.73251.94852.05651.352.16452.27251.8452.48852.59652.70452.81252.3853.02853.13653.24453.35252.9253.56853.67653.78453.89253.4654

Data Value (Grammage, g/m²)

Normalization of Grammage histogram

Smoothing function was applied to the original GPD

1.20

1.00

0.80

0.60

frequency Experimental

0.40

0.20

0.00 0 20 40 60

Grammage, g/m²

Figure 13. GPD obtained by using the Software “Better Histogram” (top), Norma- lized original GPD (center) and after smoothing it (bottom)

3.5.2a Normal Distributions fitting

Normal distributions were fitted on each positively skewed GPD of the handsheets made at different PFI refining degrees, different settling times and softwood and hardwood. These are referred to as Gaussian distributions, G1, (see Fig. 15). The reason for arbitrarily fitting G1 on skewed GPDs’ is shown in Fig. 14. which shows a not so proper- ly fitted Normal distribution (G1). By proper fitting, I mean the perfect alignment of

Normal distribution on the front edge to the left side of mean grammage. The reason I decided to fit it along the front edge was, to show that residue was left on the right side

39 of the mean grammage of the GPD because as already seen from Figure 11 and Figure

12, the skewness is positive as a function of PFI refining, settling times and softwood and hardwood. Further, for proper fitting, I had to slightly alter the standard deviations and mean grammage values of the original GPDs. Hereafter, I will denote the residue as the differential area, D = GPD - G1. Further, the differential areas were plotted and smoothed in a similar manner to the GPD. Normal distributions were fitted on the differential areas

(see Figure 16). These will be denoted as differential Gaussian distributions, G2. In order to fit their heights equal to the height of GPD, the frequency values of G1 and G2 were scaled by an arbitrary scaling factor. All the symbols and their explanations for GPD analysis are summarized in Table 2.

To illustrate the analysis of GPD peak shape, an example showing a Gaussian

(G1) and differential Gaussian (G2) is shown in Figure 15 and Figure 16, respectively.

Thus the overall skewed GPD was divided into two parts, G1 and G2. However, I considered an occurrence of a third part which from Figure 16 is the difference between differential area (D) and G2 termed the residue (R). I summed up G1 and G2 and fitted them on the GPD. This is shown in Figure 17 in order to clearly show that R = 0. Also, in order to clearly show that the median grammage values of G1 and G2 are different, they were fitted on the original GPD, as shown in Figure 18. The median grammage values and standard deviation values for G1 and G2 as a function of PFI refining, settling times and softwood and hardwood are provided in Table 5 and Table 6.

Table 2. Symbols used in GPD analysis and their explanations

Terms Symbols Explanations Grammage probability distributions GPD See section 5.2 Gaussian Distribution G1 Distribution fitted on a GPD Differential area D Residual Area due to heavy tail on right hand side of mean grammage (30 g/m2) of a GPD Differential Gaussian Distribution G2 Distribution fitted on a differential D= GPD-G1

Total GPD Area ATotal

Residual area R R = ATotal – (G1+G2) Relative Gaussian Area, % AG1 G1/ATotal*100 Relative Differential Gaussian AG2 G2/ATotal*100 Area, %

Relative residual (D-G2) area, % AR R/ATotal*100

0.80

0.70

0.60

0.50

0.40 Experimental Frequency 0.30 G1

0.20

0.10

0.00 0 10 20 30 40 50 60

Grammage, g/m²

Figure 14 A non fitted Gaussian distribution (G1) on the original GPD. 41

0.90

0.80

0.70

0.60

0.50

0.40 EXPERIMENTAL Frequency G1 0.30

0.20

0.10

0.00 0 10 20 30 40 50 60

Grammage, g/m²

Figure 15 Gaussian Distributions (G1) fitted on a positively skewed GPD. On right hand side of the mean grammage (30 g/m²), the area between G1 and heavy tail showed by dashed curve was termed as Differential area (D)

0.20

0.15

0.10

Differential Area Frequency 0.05 G2

0.00

-0.05 0 10 20 30 40 50 60

Grammage, g/m²

Figure 16 Distribution (G2) fitted on differential area (D).

0.80

0.70

0.60

0.50

0.40

Experimental Frequency 0.30 G1+G2

0.20

0.10

0.00 0 10 20 30 40 50 60

Grammage, g/m²

Figure 17. G1+G2 fitted on a skewed GPD.

0.80

0.70

0.60

0.50

0.40 Experimental

Frequency 0.30 G1 G2 0.20

0.10

0.00 0 10 20 30 40 50 60

Grammage, g/m²

Figure 18 G1 and G2 fitted on original GPD. It shows that median grammages of G1 and G2 are different.

3.5.2b Relative areas

As the part of the overall research objective of investigating the GPDs’ usefulness to determine the origin of floc formation, the relative areas under G1, G2 were quantified and denoted as AG1 and AG2 respectively. The total GPD area (ATotal) remained approximately constant. The areas G1, G2 and ATotal were calculated by using the formula shown in eq. (10),

Areas (G1, G2 and ATotal), g/m² = sum of Normalized frequencies x grammage bin width

(10)

R was calculated by using eq. (11) given below.

R, g/m² = ATotal – (G1+G2) (11)

Its relative area was denoted by AR. Further, I calculated the relative areas in % as shown in eq. 12

Relative area (AG1, AG2, AR ) % = distribution areas (G1, G2, R) x 100 (12)

GPD area (ATotal)

The summation of the relative areas gives,

Sum, % = AG1 + AG2 + AR (13)

In my work, I found R to be negligible in all cases. Meanwhile, based on eq. (12) and Eq. (13), Table 3 and Table 4 contained the relative areas (AG1, AG2, AR) and their summations as a function of different PFI refining degrees and settling times for softwood and hardwood, respectively.

The standard deviations and mean grammages of G1 and G2 for softwood and hardwood are shown in Table 5 and Table 6. As expected, the standard deviations of ba-

sis weights decreased as PFI refining was increased and increased as settling times were

increased. Also, standard deviations of softwood were higher than that of hardwood.

Table 3. Relative areas for softwood with different PFI milling and different settling times.

Softwood Refining levels 0 revolutions 2500 revolutions 5000 revolutions 10000 revolutions

Settling (min) 0 1 2 0 1 2 0 1 2 0 1 2

AG1 91.0 90.0 88.0 93.0 91.6 89.5 94.0 92.7 91.4 95.9 94.6 93.3

AG2 9.0 10.0 11.8 7.0 8.4 10.5 6.0 7.3 8.5 4.0 5.3 6.6

AR 0.0 0.0 0.2 0.0 0.0 0.0 0.0 0.0 0.1 0.1 0.1 0.1 Sum 100.0 100.0 100.0 100.0 100.0 100.0 100,0 100.0 100.0 100.0 100 100

Table 4. Relative areas for hardwood with different PFI milling and different settling times

Hardwood Refining levels 0 revolutions 2500 revolutions 5000 revolutions 10000 revolutions

Settling (min) 0 1 2 0 1 2 0 1 2 0 1 2

AG1 96.0 94.9 92.9 97.9 95.9 94.5 98.4 96.5 95.5 99.2 98.0 97.5

AG2 3.8 5.0 7.0 1.9 3.9 5.4 1.6 3.2 4.3 0.8 1.9 2.4

AR 0.2 0.1 0.1 0.2 0.2 0.1 0.0 0.2 0.2 0.0 0.1 0.1 Sum 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0

Table 5. Grammages and standard deviations of Gaussian (G1) and differential Gaussian (G2) distributions for softwood handsheets made at different PFI refining degrees and settling times

Softwood Settling times, 0 1 2 min G1 G2 G1 G2 G1 G2 Refining le- w1, w2, w1, w2, w1 w2 vels g/m² g/m² g/m² g/m² g/m² g/m² (Ơ1) (Ơ2) (Ơ1) (Ơ2) (Ơ1) (Ơ2)

0 27.6 37.0 28.8 37.3 27.5 37.5 (4.7) (4.3) (4.8) (4.4) (5.6) (5.4) 2500 29.2 36.3 26.8 36.6 28.0 39.0 (4.5) (3.8) (4.6) (4.2) (5.2) (4.9) 5000 28.5 36.3 29.4 37.0 29.1 36.3 (4.3) (3.6) (4.5) (3.7) (4.9) (4.5) 10000 29.6 37.4 27.8 37.7 28.0 34.8 (4.2) (3.1) (4.4) (3.6) (4.8) (4.3)

Table 6. Grammages and standard deviations for Gaussian (G1) and differential Gaussian (G2) distributions for hardwood handsheets made at different PFI refining degrees and different settling times. w denotes average grammages Ơ denotes standard deviations

Hardwood Settling times, 0 1 2 min G1 G2 G1 G2 G1 G2 Refining le- w1, w2, w1, w2, w1 w2 vels g/m² g/m² g/m² g/m² g/m² g/m² (Ơ1) (Ơ2) (Ơ1) (Ơ2) (Ơ1) (Ơ2)

29.5 36.6 32.1 35.4 29.5 36.6 0 (3.4) (3.6) (3.6) (3.8) (4.5) (4.3) 2500 28.9 36 28.0 35.6 30.2 35.9 (3.2) (3.1) (3.5) (2.9) (4.0) (3.3) 5000 31.9 35.5 32.1 35.0 29.8 35.4 (2.9) (1.8) (3.0) (2.2) (3.3) (2.5) 10000 29.3 35.3 29.0 36.5 28.6 35 (2.7) (1.7) (2.9) (2.0) (3.2) (2.4) 46

3.5.2c Relative Differential Gaussian distributions (AG2)

As already known, G1 and G2 are Normal distributions which depend on the mean grammage values and standard deviations. Hence, I decided to plot the mean grammage values of G1 and G2 as function of refining, settling times for softwood and hardwood.

But, it was noticed that mean values appeared to be closely overlapped for each of settling time (zero min, one min and two min) at a given freeness level. Hence, these three

(each for zero min, one min and two min) values were averaged and plotted as a function of refining for both softwood and hardwood, shown in Fig. 19 and Fig. 20 respectively. It was observed that these mean values did not change with refining for both softwood and hardwood. However, from Table 3 and 4, one can see that AG2 values (symbolizing skewed part of a GPD) were influenced by PFI refining, settling times and softwood and hardwood. Therefore, it was decided to study the differential areas (G2). Hence, I decided to analyze G2 which denotes the skewed/residual/differential part of the GPD (see Figure

16). Also, from eq. (12), AG2 is merely the relative area in % between G2 and Total area,

ATotal. Therefore, AG2 represents a parameter which can be used to characterize paper formation. Values for AG2 were therefore plotted as a function of PFI milling, settling times and softwood and hardwood as shown in Figure 21 and Figure 22 respectively.

Impact of papermaking variables

Refining and furnish

In Figure 21, it is evident that, softwood handsheets made at zero min settling time, shows a decrease of about 54%. in AG2 values, as refining is progressed from 0 revolutions to 10000 revolutions This can be attributed to the internal fibrillation action and fiber flexibility imparted by the PFI mill. This gives us an idea about the usefulness of

47 these GPDs in predicting the effect of refining on floc formation. Therefore, it can then be said that paper formation improved as these relative differential areas get reduced as a function of refining. From Figure 22, we can see that similar effect of PFI refining was observed for hardwood sheets prepared at zero min, although their AG2 values were found to be lower than that of softwood zero min handsheets. This can be attributed to the fact that hardwood contains smaller and less coarse fibers than softwood and hence better formation. Hence, skewed GPDs, can prove useful to predict floc formation as a function of furnish and refining.

Settling times

Comparing zero min, two min and two min softwood AG2 values from Figure 21, I noticed that areal distribution values increases as settling time is increased. This can be attributed to formation of flocs in two min and one min sheets, whereas zero min handsheets show fine grammage variations and hence lower AG2 values than former. A similar trend was observed for hardwood AG2 values as settling times were increased, see Figure 22.

However those AG2 values were found to be lower than that of softwood due to presence of short fibers in hardwood. Thus, relative differential area distributions can be used to predict floc formation as a function of settling time. Hence, one can say that mean grammage values is not important but area is. I saw how the positively skewed GPDs were influenced by PFI refining, settling times and softwood and hardwood. In other words, positively skewed part of GPDs can prove useful in predicting origin of floc formation.

It was already observed that AG2 values decreased with increasing PFI refining or settling time. AG2 values of softwood were lower than that of hardwood. Thus, AG2 is new method to assess formation.

40 38 36

² 34 32 30 28 G1

Grammage, g/m 26 G2 24 22 20 0 100 200 300 400 500 600

Freeness

Figure 19. Mean Grammage values for G1 and G2 as a function of PFI refining for softwood

40 38 36

² 34 32 30 28 G1

Grammage, g/m 26 G2 24 22 20 0 100 200 300 400 500

Freeness

Figure 20 Mean Grammage values for G1 and G2 as a function of PFI refining for hardwood 49

14.00

12.00

10.00

8.00 %

G2 sw 0 min

A 6.00 sw 2 min 4.00 sw 1 min

2.00

0.00 0 100 200 300 400 500 600 Freeness, CSF

Figure 21 AG2 (Relative Differential Gaussian Area) values for softwood made at different freeness levels and different settling times

14.00

12.00

10.00

8.00 %

G2 hw 0 min

A 6.00 hw 2 min 4.00 hw 1 min

2.00

0.00 0 100 200 300 400 500 Freeness, CSF

Figure 22 AG2 (Relative Differential Gaussian Area) values for hardwood made at different freeness levels and different settling times 50

Chapter 4 Conclusion

The different mass distributions obtained as a function of papermaking variables such as PFI refining, settling times and differences in softwood and hardwood were statistically analyzed. The GPDs of the mass distributions were constructed from the grammage maps obtained from Matlab software. The GPDs exhibited different standard deviations and skewness of grammages. However, the prime interest of this research was skewness of GPDs. It was observed that all the GPDs exhibited positive skewness. It was shown that skewed part of GPDs was influenced as a function of PFI refining, settling times and softwood and hardwood. It is represented by the relative differential Gaussian area (symbolizing the skewed part of GPD, AG2). It was found to be useful to characterize paper formation. Hence, it can be called as a new formation assessment tool. Thus, the method exhibited an inverse relationship with PFI refining. This was attributed to the fiber flexibility and internal fibrillation imparted by a PFI mill. However, it showed a direct relationship with settling times due to an increase in flocculation with increase in settling times. Due to presence of longer and coarser fibers, softwood had higher assessment value than that of hardwood. Thus, it was demonstrated that the skewed part of the

GPDs can be useful to predict the origin of floc formation.

Chapter 5 Suggestions for future work

1. I suggest that the usefulness of GPDs in predicting the floc formation influenced by

chemical additives should be studied. This research work proved the utility of GPDs in

determining the origin of floc formation influenced by PFI refining, stock relaxation fol-

lowing turbulence and differences in softwood and hardwood. As flocculation is also

caused by chemical additives, hence utility of GPDs in predicting it can be a good subject

to study.

2. I suggest that the utility of GPDs in predicting floc formation influenced by industrial re-

fining should be investigated. I used a PFI mill, which is a high energy but low intensity

device and its effect on paper formation is much more subtle than what an industrial re-

finer imparts. Hence an effect of industrial refining on different mass distributions using

GPDs can be an interesting subject to study.

3. I suggest a use of increased exposure times during beta radiography, for formation analy-

sis. In my work, I used an exposure time of 30 minutes for formation testing. But the

resolution of the scanner is approximately 13.5 bit, which yield around 10,000 grey level

units per pixel. This work employed 30 minutes, so this resulted in only small number of

GLU per pixel. Hence an increase in exposure time will yield more GLU per pixels,

hence better analysis. Thus, in future study, exposure times can be increased and its effect

on the analysis of mass distributions using GPDs can be assessed.

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Appendix I – Original GPDs varying in terms of PFI refining, settling times with their G1 and G2 overlayed for hardwood

hw 0 rev 0min

1.20

1.00

0.80

0.60 Experimental frequency G1 0.40 G2

0.20

0.00 0 10 20 30 40 50 60

Grammage, g/m²

hw 0 rev 1 min 1.20

1.00

0.80

0.60 Experimental

frequency G1 0.40 G2

0.20

0.00 0 10 20 30 40 50 60

Grammage, g/m²

hw 0 rev 2min 1.20

1.00

0.80

0.60 Experimental frequency G1 G2 0.40

0.20

0.00 0 10 20 30 40 50 60

Grammage, g/m²

hw 2500 rev 0min 1.20

1.00

0.80

0.60 Experimental

frequency G1 0.40 G2

0.20

0.00 0 10 20 30 40 50 60

Grammage, g/m²

hw 2500 rev 1 min 1.20

1.00

0.80

0.60 Experimental frequency G1 0.40 G2

0.20

0.00 0 10 20 30 40 50 60

Grammage, g/m²

hw 2500 rev 2min 1.20

1.00

0.80

0.60 Experimental frequency G1 0.40 G2

0.20

0.00 0 10 20 30 40 50 60

Grammage, g/m²

hw 5000 rev 0min 1.60

1.40

1.20

1.00

0.80 Experimental frequency 0.60 G1 G2 0.40

0.20

0.00 0 10 20 30 40 50 60

Grammage, g/m²

hw 5000 rev 1 min 1.60

1.40

1.20

1.00

0.80 Experimental frequency 0.60 G1 G2 0.40

0.20

0.00 0 10 20 30 40 50 60

Grammage, g/m²

hw 5000 rev 2 min 1.20

1.00

0.80

0.60 Experimental frequency G1 0.40 G2

0.20

0.00 0 10 20 30 40 50 60

Grammage, g/m²

hw 10000 rev 0min 1.60

1.40

1.20

1.00

0.80 Experimental frequency 0.60 G1 G2 0.40

0.20

0.00 0 10 20 30 40 50 60

Grammage, g/m²

hw 10000 rev 1 min 1.40

1.20

1.00

0.80 Experimental 0.60 frequency G1

0.40 G2

0.20

0.00 0 10 20 30 40 50 60

Grammage, g/m²

hw 10000 rev 2 min 1.40

1.20

1.00

0.80 Experimental 0.60 frequency G1

0.40 G2

0.20

0.00 0 10 20 30 40 50

Grammage, g/m²

Appendix II – Original GPDs varying in terms of PFI refining, settling times with their G1 and G2 overlayed for softwood

0.80 sw 0 rev 0 min 0.70

0.60

0.50

0.40 Experimental

Frequency 0.30 G1 G2 0.20

0.10

0.00 0 10 20 30 40 50 60

Grammage, g/m²

sw 0 rev 1 min 0.80

0.70

0.60

0.50

0.40 Experimental

frequency 0.30 G1 G2 0.20

0.10

0.00 0 10 20 30 40 50 60

Grammage, g/m²

sw 0 Rev 2min 0.80

0.70

0.60

0.50

0.40 Experimental frequency 0.30 G1 G2 0.20

0.10

0.00 0 10 20 30 40 50 60

Grammage, g/m²

sw 2500 rev 0min 0.90

0.80

0.70

0.60

0.50 Experimental 0.40 frequency G1 0.30 G2 0.20

0.10

0.00 0 10 20 30 40 50 60

Grammage, g/m²

sw 2500 rev 1 min 0.80

0.70

0.60

0.50

0.40 Experimental frequency 0.30 G1 G2 0.20

0.10

0.00 0 10 20 30 40 50 60

Grammage, g/m²

sw 2500 Rev 2min 0.80

0.70

0.60

0.50

0.40 Experimental frequency 0.30 G1 G2 0.20

0.10

0.00 0 10 20 30 40 50 60

Grammage, g/m²

sw 5000 rev 0min 0.80

0.70

0.60

0.50

0.40 Experimental frequency 0.30 G1 G2 0.20

0.10

0.00 0 10 20 30 40 50 60

Grammage, g/m²

sw 5000 rev 1 min 0.90

0.80

0.70

0.60

0.50 Experimental 0.40 frequency G1 0.30 G2 0.20

0.10

0.00 0 10 20 30 40 50 60

Grammage, g/m²

sw 5000 rev 2min 0.80

0.70

0.60

0.50

0.40 Experimental frequency 0.30 G1 G2 0.20

0.10

0.00 0 10 20 30 40 50 60

Grammage, g/m²

sw 10000 rev 0min 1.00 0.90 0.80 0.70 0.60

0.50 Experimental frequency 0.40 G1 0.30 G2 0.20 0.10 0.00 0 10 20 30 40 50 60

Grammage, g/m²

sw 10000 rev 1 min 0.90

0.80

0.70

0.60

0.50 Experimental 0.40 frequency G1 0.30 G2 0.20

0.10

0.00 0 10 20 30 40 50 60

Grammage, g/m²

sw 10000 REV 2min 0.80

0.70

0.60

0.50

0.40 Experimental frequency 0.30 G1 G2 0.20

0.10

0.00 0 10 20 30 40 50 60

Grammage, g/m²