What is the formula of paper ash

N.C. State UniversityDept. of Forest Biomaterials
Wet-End and Colloidal Chemistry, WPS 527, Fall 2002

Worksheets Note: As of 2017, these worsheets are optional.


Complete the following assignments and submit the result by e-mail, FAX, or hard copy if you wish to. You DO NOT have to be neat, use correct grammar, or spelling for this part. But you MUST SHOW YOUR COMPLETE WORK (equations, units, logic, etc.). Here are links to quickly scroll down to other worksheets: WS#2; WS#3, WS#4; WS#5; WS#6


First-Pass Retention
The goal of this exercise is to make sure that everyone is "on board" with the definitions of first-pass retention, first-pass ash retention, ash content, filler content, and over-all or "net" retention.
Imagine that this is your first day on the job as shift superintendent. The regular staff of the "test lab" called in sick. A summer employee, "Sal," has been assigned to be the substitute. Sal has faithfully followed the written procedure for first-pass retention and has recorded the following data:

Full Weight (g)423857
Tare Weight (g)5186
Dry Filter Paper (g)1.0211.017
Moist Filter Pad (g)15.38110.001

Dried Filter Pad (g) (with paper)


A. Which item in the table above is not needed to calculate first-pass retention?

B. What is the percent headbox consistency? (Show your work! Show the units!) (Note that "consistency" is the same as "percent solids" based on oven drying at 105 oC.

C. What is the percent tray solids? (Show your work).

D. What is the first-pass retention? (Show your work).

E. You know that the mineral content of the paper is almost 100% calcium carbonate and that ashing at 900 oC causes the following reaction: CaCO3 goes to CaO (ash) + CO2 (gas). Atomic masses are as follows:
Ca = 40
O = 16
C = 12

What is CaCO3's ignition factor (ash mass over dry filler mass)?

F. Assume that the filter paper was "ashless" and that the entire samples have been incinerated at 900 oC. Sal shows you the following data:

Crucible Tare Mass (g)3.6213.589
Crucible + air-dry solids with filter paper (g)6.6535.219
Crucible + dry ash (g)3.8063.725

Which item in the table above (if any) is not needed to calculate percent ash retention?

G. What is the percent filler content of the headbox SOLIDS? (Show your work.) [Clue: Use data from the very first table to get the oven-dry mass of headbox solids.]

H. Calculate the percent ash of the tray solids.

I. Calculate the percent first pass ash retention. Show your work. [Hint: Use the equation for first-pass ash retention given in your course-pack.]

J. In your opinion, based only on this number, is there a sufficiently high amount of retention aid being used on this paper machine? Why or why not?


The Critical Coagulation Concentration and the Ionic Double Layer Thickness
These concepts can seem rather abstract, so it can help to work some numbers and get a feeling of how different salt concentrations (and different ions) have some practical effects that we can roughly predict.

A. A representative from one of the chemical vendors who services your mill thinks she knows why you are getting sediment in your TiO2 slurry dilution tank. She says it is because of the hardness of the water used for dilution. Please explain in two or three sentences why this makes sense.

B. Your co-op student from N.C. State University has added 10 ml of TiO2 slurry to each of five beakers containing 90 ml of aqueous solution. The following table gives final Ca2+ levels and turbidity levels after settling of any agglomerated pigment:



Turbidity (NTU)


0.00001 M



0.00003 M



0.00010 M



0.00030 M



0.00100 M


Using Fig. 5.44 from your WPS527 course-pack as a guide, what is the approximate value of the critical coagulation concentration for the calcium ion in this case?

C. Your co-op student suggested that monovalent ions also be considered. Your records show the following typical levels:
[Na+] = 0.0001 M
[K+] = 0.00002 M

Based on the Shultz-hardy rule, what is your estimate of the critical coagulation concentration of this TiO2 slurry in the case of monovalent cations?

D. The water used to dilute the TiO2 has a hardness of 150 parts per million as CaCO3 equivalents. What is this in terms of molar equivalents? [Atomic masses are as follows: Ca = 40, C = 12, O = 16.]

E. Based on your answer to part B, is the Ca2+ concentration high enough to cause a significant increase in the agglomeration rate of the TiO2 slurry?

F. The content of excess polyacrylate dispersant in the TiO2 slurry is 0.005 M. Does this information affect your opinion about your answer to part D? (Please give a reason; various conclusions can be justified.)

G. Using a table that you can find in Part 5 of the Coursepack, please roughly estimate the thickness of the electrical double layer in the diluted TiO2 slurry (1 / kappa). Give about two sentences of explanation.

H. Depending on the first letter of your last name answer one of the following questions pertaining to the following Assigned Reading article. You can get a PDF copy from the WebCT System by clicking on "Assigned Readings."

Ström, G., and Kunnas, A., "The effect of cationic polymers on the water retention value of various pulps," Nordic Pulp Paper Res. J. 6 (1): 12 (1991).

A-G: These authors found that cationic polymers decreased the water retention value (WRV) of certain pulps. Please describe the type and location of water that seems to be affected by the polymer addition.
H-M: Cationic starch did not affect the WRV in the absence of fiber fines. Cationic starch reduced WRV values in the presence of fines. Why?
N-S: What evidence do the authors show to demonstrate that cationic polymers added to kraft pulp get into small pores and get between fibrils?
T-Z: How can you account for the fact that higher-mass polyethyleneimine polymers were more effective in reducing WRVs (Fig. 6 of the article)?

I. Depending on the first letter of your last name answer one of the following questions pertaining to the following Assigned Reading article:

Suty, S., Alince, B., and van de Ven, T. G. M., "Stability of ground and precipitated CaCO3 suspensions in the presence of polyethyleneimine and salt," J. Pulp Paper Sci. 22 (9): J321 (1996).

A-G: These authors used the "percent transmittance" of a pigment slurry to obtain information about colloidal stability. What did the authors conclude about stability in cases when the percent transmittance increased?
H-M: How did the ground calcium carbonate samples differ from the precipitated calcium carbonate samples? Is there evidence that these differences affected the interactions of the mineral with polyethyleneimine (PEI)?
N-S: What is the meaning of log W? Why was it reasonable for the authors to express their main findings in terms of log W?
T-Z: Why was there a minimum in the plot of log W versus PEI dosage in the case of ground calcium carbonate (Fig. 6 of the article) but not precipitated calcium carbonate (Fig. 7)?


Relative Bonded Area and Factors Affecting Dry Strength
The purpose of this exercise is to give practice in the calculation of "relative bonded area" (RBA). You may recall that RBA is a key term in Page's equation for tensile strength (Tappi 52, 4: 674, 1969). Every paper chemist should have a working familiarity with the Page equation. This is a practical, semi-empirical equation. It helps to "make sense" out of tensile strength data and the effects of chemicals and furnish variables. The concept of RBA was already introduced earlier by Parsons (Paper Trade J. 115, 25: 35, Dec. 17, 1942). She observed that the light-scattering ability of dry fibers is roughly proportional to their surface area. Sheets that are well bonded tend to scatter less light than "non-bonded" sheets. Parsons formed "non-bonded" sheets from n-butyl alcohol.

The first step the exercise is to calculate the scattering coefficient of a non-bonded sheet and a regular paper sheet made from the same fibers with water. To explain this subject fully would require a whole course. Instead, we will just use some of the most useful results from a theory developed by Kubelka and Munk (Zeits. f. tech. Physik. 12: 593, 1931; see also Robinson, J. V., Tappi 58, 10: 152, 1975). The main equations that we will be using are as follows:

s = 0.5 ln[ (c+1) / (c-1) ] / (W b)
a = 0.5 [ (1/Rinf) + Rinf ]
b = 0.5 [ (1/ Rinf) - Rinf ]
c = (1 - a Ro) / (b Ro)

where s is the scattering coefficient, often expressed with units of cm2/g, W is the basis weight in mass per unit area (consistent units always), Rinf is the reflectivity of a thick stack of paper, and Ro is the reflectance of a single sheet backed by a black cavity (a perfect black background).

Here are the data:

 Regular Sheet No. 1Non-Bonded Sheet
Basis weight (g/m2)75.074.6
Ro74.75 %81.20 %
Rinf80.00 %84.00 %

A. Calculate a, b, c, and s of Sheet No. 1. Show your work. Remember to convert the reflectance values into fractions (because the equations don't use "percent" information).

B. Calculate the same information for the non-bonded sheet.

C. Calculate the relative bonded area [(snonbonded - sregular ) / snonbonded]. Show work.

D. In an attempt to increase paper strength for a new grade, refining energy was doubled. Standard handsheets were prepared under the same conditions, with water. The following data were obtained for "Sheet No. 2."

Ro = 72.4 %
Rinf = 78.55 %
W = 75.23 g/m2
s = 465.2

Calculate the relative bonded area of the sheet. How does it compare vs. No. 1?

E. Based on the Page equation (see course-pack), what is your estimate of how the extra refining affected tensile strength? Give a numerical estimate and state your main assumption(s).

F. A representative for a chemical company tells you that they can increase your paper strength without sacrificing opacity by adding a chemical. Based on the Page equation, does this statement make sense? Please explain.

G. Depending on the first letter of your last name answer one of the following questions pertaining to the following Assigned Reading article:

Marton, J., "Mechanistic differences between acid and soap sizing," Nordic Pulp Paper Res. J. 4 (2): 77 (1989).

A-G: What mechanism can explain the results in Table 1, i.e. a decrease in attachment of rosin soap size with increasing pH in the range 4.6 to 6.8?
H-M: What type of rosin product, investigated by this author, had a higher negative charge density? What evidence do you have for this?
N-S: Why was this author so concerned about levels of fiber fines and fillers?
T-Z: Why was this author also concerned about affects of temperature (different reasons, depending on the type of rosin)?

H. Depending on the first letter of your last name answer one of the following questions pertaining to the following Assigned Reading article:

Stratton, R. A., "Dependence of sheet properties on the location of adsorbed polymer," Nordic Pulp Paper Res. J. 4 (2): 104 (1989).

A-G: Did fiber fines have a negative affect on paper strength? What evidence does the author present relative to this issue?
H-M: Can you think of a reason why it makes more sense to add a strength aid after refining, rather than before refining?
N-S: Explain why the use of dry-strength chemicals can affect the appearance of a ripped edge of paper.
T-Z: What does the author mean when he says that his results support a "reinforcement" mechanism rather than a "protection" mechanism? (Note: internal addition was more effective than surface treatment of the paper.)


Case Studies Related to the Appearance of Paper
This case study comes from the end of Part 8 of the Coursepack. Your assignment is to write a one-paragraph (no more than half page) essay for each of the following cases:

A. First case: "Speckled Appearance"
Your goal: Recommend steps to find the root cause and solve the problem.
Situation: To eliminate color in its wastewater, Mill "D" switched to the use of a cationic direct blue dye. A new pump and tubing were installed to handle the dye concentrate. The addition point for blue was moved to the opposite side of the machine chest from the red and yellow (anionic dyes). "The paper looks speckled."

B. Second case: "Change Time"
Mill "C" produces paper with over 50 different colors during each month-long cycle. Certain runs last only two hours. Management is concerned that the transition between different color targets requires an average of 40 minutes of off-quality paper that has to be repulped and bleached. The chemical vendor has reported that the white water contains a high level of dissolved dye. Why would dye in the white water tend to slow the transitions from one color target to another? What steps do you recommend towards finding a solution? State your key assumptions about the system.

C. Depending on the first letter of your last name answer one of the following questions pertaining to the following Assigned Reading article:

Wågberg, L., and Lindström, T., "Some fundamentals of dual component retention aid systems," Nordic Pulp Paper Res. J. 2 (2): 49 (1987).

A-G: What's the difference between a "floc size" and a "floc index," based on the procedures described in this article?
H-M: Why was the author concerned with the frequency of collisions between different polymers and solid surfaces in the suspensions?
N-S: Explain in "Fig. 7" why one order of addition was more effective than the other.
T-Z: Why did the author think that the dual-polymer system based on cationic potato starch and anionic silica was very promising? Does he show any evidence that this system works by a process of "complex flocculation?"

D. Depending on the first letter of your last name answer one of the following questions pertaining to the following Assigned Reading article:

Isogai, A., Kitaoka, C., and Onabe, F., "Effects of carboxyl groups in pulp on retention of alkylketene dimer," J. Pulp Paper Sci. 23 (5): J215 (1997).

A-G: These authors worked with pulp that had been modified in an unusual way. In what respects would you expect that the pulp studied by these authors would be different from typical papermaking stock from a paper mill?
H-M: What was the charged nature of the sizing agent?
N-S: Please explain the results in Fig. 1, showing a low retention of AKD size and essentially no sizing effect when aminated pulp was treated at the default levels of the two additives.
T-Z: How would you expect the presence of carboxyl groups in the solution phase of white water to affect AKD sizing efficiency?


Formation Uniformity and the Crowding Factor

The definition of "crowding factor" is as follows:
nf = 2/3 Cv (L/D)2
Cv = volume fraction of the fibers
L = effective fiber length
D = effective fiber diameter
The idea is that the degree of mechanically induced flocculation of fibers can be predicted. Systems having the same values of the crowding factor are expected to have the same level of flocculation when they are stirred in the absence of strong attractive forces between the fibers.

A. Please calculate nf for the following data. Check your units. Show your work.
Effective length = 1.4 mm
Effective diameter = 20 micro-meters
Slurry solids (mass) = 0.54%
Effective fiber density = 1.5 (g/cm3)

B. The engineering team has proposed capital improvements to the press section. They are optimistic that this change will make it possible to decrease the amount of softwood fiber, reducing the effective fiber length from 1.4 to 1.2 mm. Assuming that the headbox solids and effective fiber diameter remain essentially unchanged, how will this change affect the value of nf? Show your work. How is the suggested change likely to affect the uniformity of formation?

C. Your senior chemist has read a report that leads him to believe he can decrease the headbox solids. This will require a modification to the headbox and application of a more effective drainage and retention chemical program. The target solids level is 0.43%. How would this change affect the value of nf? Show your work. Assume the original value for effective fiber length (1.4 mm).

D. Your team now has three options to consider: (a) do nothing, (b) make the investments needed to reduce softwood fiber content, or (c) make the investments needed to reduce headbox solids. Some of the factors that need to be considered include:
" The capital costs of options (b) and (c)
" The increased energy case of option (b) due to increased flow at the fan pump
" The increased cost of chemicals in option (c)
" Please list at least 3 additional factors that will guide your decision.

E. Depending on the first letter of your last name answer one of the following questions pertaining to the following Assigned Reading article:
Buontempo, J. T., Sherman, L. M., and St. John, M. R., "The effects of salts on the performance of cationic flocculants used as retention aids for alkaline fine paper," Proc. TAPPI 1996 Papermakers Conf., 49.

A-J: Why is it important to consider affects of increasing salt content in process water?
K-P: Which of the cationic flocculants suffered most, in terms of its efficiency as a retention aid, when the salt level was increased?
Q-Z: How did the cationic starch affect retention?

F. Depending on the first letter of your last name answer one of the following questions pertaining to the following Assigned Reading article:

Pierre, C., "Complementarity between two dewatering and retention microparticle systems: 'cationic starch/anionic colloidal silica,' and 'potato starch/aluminum salts," Proc. TAPPI 1993 Papermakers Conf., 163.

A-J: What do the authors mean by the words "complementary systems?"
K-P: Why do the authors expect that the fresh aluminum hydroxide precipitate interacts with phosphate groups on the cationic potato starch?
Q-Z: Do the authors believe that the benefits of aluminum compounds can be fully explained by charge neutralization? If not, why not?


Britt Jar Data and the Concept of Hard and Soft Fiber Flocs

The goal of this exercise is to make sure that everyone in the class can work through the graphical data of a Britt Jar study and become confident in their understanding of "reversibility" of flocculation.
A representative from the chemical company servicing your paper mill has carried out Britt Jar tests of various retention and drainage programs. They have followed the procedure used by Hedborg and Lindström (Nordic Pulp & Paper Res. J. 11, 4: 254, 1996). Here are their data for the current retention and drainage chemical program:

Agitator Speed (5 minutes)Percent Retention
300 rpm82.0
800 rpm53.1
800, then 300 rpm55.4

A. Use the data to calculate the reversibility index. Use the following figure, taken from Section 11 of the Coursepack, as your guide:

B. Does your answer to part A mean that the fiber flocs cannot be broken? Please explain with 2 to 3 sentences.

C. Based on the definitions given by Britt and Unbehend, what type of fiber flocs probably were broken at the high agitator speed in this example? (Reference: Britt, K., and Unbehend, J., Tappi 59, 2: 67, 1976; also see figures in Part 11 of WPS527 course-pack).

D. Further tests yielded the following data:

Agitator Speed
(5 minutes, rpm)

Percent Retention

Current Retention Aid SystemOption 2Option 3
800, then 30055.463.272.0

Calculate the reversibility index values for Options 2 and 3.

Please assume the following supplemental information when answering questions E-G:
"Option 1," the current retention aid system, consists of a cationic acrylamide copolymer. It is added after the pressure screens.
"Option 2" is a microparticle program with a cationic acrylamide copolymer before the screens and colloidal silica after them.
"Option 3" is a dual-polymer retention aid system with a high-charge cationic polyamine at the stuff box and an anionic acrylamide copolymer added after the screens.

E. Which of the three retention and drainage chemical programs is likely to yield the highest value of first-pass retention on the paper machine?

F. Which of the three retention and drainage chemical programs is likely to yield the most rapid drainage?

G. Which of the three retention and drainage chemical programs is likely to yield the largest fiber flocs, giving the lowest uniformity of formation?

H. Depending on the first letter of your last name answer one of the following questions pertaining to the following Assigned Reading article:

Shetty, C. S., Greer, C. S., and Laubach, G. D., "A likely mechanism for pitch deposition control," Tappi J. 77 (10): 91 (1994).

A-J: Why did the addition of cationic polymer cause the surface tension of the process water from a TMP pulp mixture to go down, according to the authors?
K-P: Do the authors expect pitch-control to be best when (a) the polymer is added at the correct dosage for coagulation, or (b) the polymer is "overdosed" so that it restabilizes the pitch suspension?
Q-Z: How did the addition of cationic polymers affect the surface of pitch particles?

I. Depending on the first letter of your last name answer one of the following questions pertaining to the following Assigned Reading article:
Sjöström, L, and Ödberg, L., "Influence of wet-end chemicals on the recyclability of paper," Papier 51 (6A): V69 (1997).

A-G: To what extent do the results of this study support or contradict the following statement: "Wet-end additives become recycled also, when paper is recycled."
H-M: Why did these authors remove the fines from the refined pulp before conducting the experiments?
N-S: Did pre-adsorption of cationic polymer during the initial sheet forming affect the amount that could be adsorbed by recycled pulp (Fig. 1)?
T-Z: How did the pre-adsorption of AKD size during the initial sheet-forming affect the amount that needed to be added to size the recycled paper (Fig. 6)?