Ceramic Processing E-zine Volume 1 Number 7 1 May 2003

Volume 1 Number 7 Dennis R. Dinger 1 May 2003

An Update

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The short courses Fine Particle Processing Using Predictive Process Control (PPC) Principles (a 3-day course), Performing Particle Calculations in MS Excel® Using the DRD Add-In Functions (a 1-day course), and Rheology for Ceramists (a 1-day course) are scheduled for 16-20 June 2003. Please check the Short Course Announcement for details and for links to the registration and hotel information forms. Don't miss out on the early registration discount which ends on the 15^th of May. If you are planning to attend, please check the comments in the Miscellany section at the end of this issue.

A 20-Minute Gelation Test

A very common gelation test is a single point measurement using a small cylindrical bob suspended on a light spring wire (a Gallenkamp-type torsion viscometer). The bob is wound 360 degrees and held stationary in a freshly stirred suspension for a given number of minutes. After the required time, the bob is released and the number of degrees of 'overshoot' are reported. The spring wire unwinds, the bob travels the 360 degrees back to the zero position, and then it continues for several more degrees while it once again tightens the spring wire. The number of degrees of travel past the zero point is the 'overshoot.' The number of degrees of travel past the zero point gives indication of the strength of the gel structure that built in the time prior to release of the bob.

Single point tests, however, do not show the buildup rate of the gel structure. They do not indicate whether the gel is building really quickly or whether it has completed building at the single point of the measurement. They simply show the strength of the gel structure at that time.

For years, we have encouraged (and continue to encourage) the use of Brookfield rotational viscometers (Brookfield, Stoughton, MA) to measure gel structures. While most ceramic companies own and use such rotational viscometers in their labs and production facilities, they may not own a Gallenkamp-type viscometer. Rotational viscometers are well-suited to measure gel properties. In fact, it can be argued that they provide more information than the single point viscometer tests. I will describe the details of this technique in the remainder of this article.

The Test

Figure 1 shows an example of the 20 minute gelation test that we recommend:

Figure 1 -- The 20 minute gelation test performed on a rotational viscometer:
10 minutes at high rpm, followed immediately by 10 minutes at low rpm.

One should always subject a slip or slurry to HID (high intensity dispersion) conditions immediately prior to starting the 20 minute measurement. The HID can be accomplished by mixing for 1 minute at medium or high speed on a milkshake mixer. Special HID blades are available to replace the standard milkshake blades for this purpose. The reason for using HID before a gelation measurement is to destroy all existing gel structure. As a result, the gel (and viscosity) will build again during the test.

Choose a spindle that covers the viscosity range of the suspension to be measured. In most cases, a single spindle can be used as the standard spindle for all gelation tests. Then select the rpms to use. The high rpm should be either 60 or 100 rpm, and the low rpm should be 1/10^th of the high rpm value. If the viscometer has both 60 and 100 rpm speeds available, use the 100 rpm setting. If you are using an automatic viscometer, program it to switch from 100 rpm to 10rpm (or 60 to 6rpm) at the 10 minute point of the 20 minute test. If you must change the rpm manually, change it at the 10 minute point with the viscometer running so the test continues uninterrupted for its 20 minute duration..

As you are building a data base of gelation curves, you will see a range of gelation rates as a function of the state of flocculation or deflocculation of the suspension. Excellent gelation behavior should show stable viscosities between ~6 to 10 minutes and between ~16 to 20 minutes as shown by the dark blue curve in Figure 1. When viscosities climb steadily and slowly from 0 to 10 minutes, and again from 10-20 minutes, (the red curve in Figure 1) gelation rates are usually very low and the gelation behavior is quite poor. If the viscosity increases quickly to a maximum (the green curve in Figure 1) and then slowly drops back to stable 10 and 20 minute values, gelation is excessive and syneresis is occurring.

Yield Stress Calculation

Although Bingham rheology is a commonly used, popular term, Bingham behavior is scarce in actual practice. The mathematical simplicity of the Bingham form of rheology, however, makes it useful to calculate yield stresses. Using the 10 minute and 20 minute data points from a 20 minute gel test, one can plot the 100 rpm and 10 rpm shear stress measurements (or dial readings) versus shear rate (or rpm) on a linear chart. Dial readings are proportional to shear stresses, and rpm values are proportional to shear rates. One then draws a straight line through the two points on the shear stress vs shear rate chart, as shown in Figure 2, and uses that line to extrapolate back to 0 rpm to calculate the yield stress t_Y and the Bingham viscosity. The yield stress in Figure 2 is the point at which the straight line crosses the Y-axis. The Bingham viscosity is the slope of the line. In this example, the yield stress corresponds to a dial reading of ~39 and the slope of the line is approximately 0.1. If the formulas are available, dial readings can be converted to shear stress units, rpms can be converted to shear rate units, and viscosities can be calculated in milliPascal seconds. If the conversion formulas are not readily available, viscosities can also be calculated in simplified units of 'dial reading/rpm', which are proportional to normal viscosity units.

Figure 2 -- Yield stress calculation using the 10 and 20 minute
gelation measurement values.

Dynamic viscosities in mPa·s are easy to calculate from Brookfield measurements, but yield stresses and Bingham viscosities are more difficult to define and calculate. The units 'dial reading/rpm' are definitely a simplification, but since it is difficult to calculate the actual applied shear rates for Brookfield measurements, these units are handy and easy to use. The yield stress and Bingham viscosity calculations benefit from these simplified units.

Characterization Parameters

Nine rheological parameters can then either be directly measured or calculated from the measurements. The equations for these parameters are shown below. In these equations, m is viscosity, t is shear stress, and g' (gamma dot) is shear rate.

m_RH,10 (1)

m_RL,20 (2)

BBU = m_RL,20 - m_RH,10 (3)

RBU = (m_RL,12 - m_RH,10) / (m_RL,20 - m_RH,10) (4)

m_B = (t_RH,10 - t_RL,20) / (g'_RH - g'_RL) (5a)

= (t_RH,10 - t_RL,20) / (RH - RL) (5b)

where m_B has units mPa·s, or 'Dial Reading/rpm'.

t_y = t_RH,10 - m_Bg'_RH = t_RH,10 - m_B RH (6)

or t_y = t_RL,20 - m_B RL (7)

where t_y has units Pa, or 'Dial Reading'.

Plasticity Index = t_y / m_B (8)

m = (log m_RL,20 - log m_RH,10 ) / (log RL - log RH) (9)

                where m_B = Bingham plastic viscosity,
                            t_y =   yield stress,
                       t_RH,10 =    t_100,10 or t_60,10 = shear stress at high rpm (at 100 rpm or at 60 rpm) after 10 minutes,
                       t_RL,20 =     t_10,20 or   t_6,20 = shear stress at low rpm (at 10 rpm or at 6 rpm)
                                                                      after 10 additional minutes (after 20 minutes total)
                      m_RH,10 =    m_100,10 or m_60,10 = viscosity at high rpm (at 100 rpm or at 60 rpm) after 10 minutes,
                      m_RL,20 =     m_10,20 or   m_6,20 = viscosity at low rpm (at 10 rpm or at 6 rpm)
                                                                      after 10 additional minutes (after 20 minutes total)
                         PI     =   Plasticity Index,
                         m      =   pseudoplastic index,
                        RH    =    high rpm, such as 100 or 60 rpm, and
                        RL     =    low rpm, such as 10 or 6 rpm.

The High-RPM and Low-RPM Viscosities

These high-rpm and low-rpm viscosities come directly from the 20 minute gelation test measurements. The viscosities are the 10 minute (high shear rate) and 20 minute (low shear rate) viscosity readings:

m_RH,10 (1)

m_RL,20 (2)

Instead of plotting the data as dial reading vs time (as shown in Figure 1), it can also be plotted as viscosity vs time. When the data is plotted as viscosity vs time, the curves will be similar in shape, but the viscosities will generally be higher for the low rpm measurements (the second half of the 20 minute test) than for the high rpm measurements (the first half of the test.) In suspensions with shear-thinning rheologies (which applies to most ceramic suspensions), high rpm viscosites will be lower than the low rpm viscosities. In viscosity vs time plots, the step at 10 minutes will be up to a higher viscosity, while in shear stress vs time plots, the step after 10 minutes will be down to a lower shear stress.

Bingham BuildUp (BBU)

The Bingham BuildUp shows the change in viscosity between the 20 and 10 minute readings. This corresponds to the increase in viscosity as the viscometer rpm changes from its high to its low values. Larger BBU values are indicative of stronger gelation behaviors.

BBU = m_RL,20 - m_RH,10 (3)

Rate of BuildUp (RBU)

The Rate of BuildUp (RBU) is the change over the first two minutes at the low rpm relative to the total change over the full 10 minutes at the low rpm. This can be calculated as a fraction as shown in Equation 4, or the fraction can be converted to a percentage. An excellent gelation behavior will produce values of 0.6-0.7 for RBU. Values that are too much higher that that may be indicative of syneresis (one must check the full shape of the 10-20 minute segment of the gel curve measurement to be sure). Values that are very low are indicative of really poor gelation behavior.

RBU = (m_RL,12 - m_RH,10) / (m_RL,20 - m_RH,10) (4)

Bingham Viscosity

The Bingham viscosity is a necessary part of the calculation to determine the yield stress value. It is also an indication of the minimum viscosity that should be achievable as high shear rates in Bingham (shear thinning) suspensions. Since all particulate suspensions become dilatant at high shear rates, the Bingham viscosity has little practical value other than its mathematical simplicity and its usefulness to help calculate the yield stress.

m_B = (t_RL,10 - t_RL,20) / (g'_RH - g'_RL)

= (t_RL,10 - t_RL,20) / (RH - RL) (5)

Units for Bingham viscosities can be normal viscosity units (mPa·s) or the simplified units (Dial Reading/rpm). Which ever you choose to use, just be consistent and use the same units routinely so the operators can develop a feel for the type of behaviors to expect at the various viscosity numbers.

Yield Stress

The Yield Stress is an indication of the strength of the gel structure in a quiescent, non-sheared suspension. The yield stress can be calculated, as shown in Figure 2, by calculating the Bingham viscosity for the straight line connecting the high (100 or 60) and low (10 or 6) rpm shear stress values, and using that slope to extrapolate back to 0 rpm to determine the stress intercept. This parameter gives an indication of yield stress variations from sample to sample. As one builds a data base of these measurements, it will be possible to determine how your suspensions routinely behave under normal conditions. With that information in hand, it is possible to quickly determine how the current suspension will behave relative to all previous suspensions.

t_y = t_RH,10 - m_Bg'_RH = t_RH,10 - m_B RH (6)

or t_y = t_RL,20 - m_B RL (7)

Plasticity Index

A very plastic suspension is one that has a high yield stress and a low Bingham viscosity. With a low Bingham viscosity, a suspension will flow easily after flow has begun, and with a high yield stress, the ware will hold its shape well after shear has ceased. The ratio of the yield stress to the Bingham viscosity is an excellent indication of the level of plasticity of a slip or body. Both high yield stresses and low Bingham viscosities increase the value of the plasticity index. A poor (low) yield stress and/or a high Bingham viscosity will produce a low plasticity index. Such suspensions or bodies can be expected to perform poorly.

Plasticity Index = t_y / m_B (8)

Although the plasticity index has units of shear rate, we normally ignore the units and pay attention simply to the magnitude of the value. This requires that the yield stress and Bingham viscosity are always calculated with the same units. Most companies that use this index have standardized their daily procedures, so the two parameters and the Plasticity Index all have consistent units from day to day.

Pseudoplastic Index

The Pseudoplastic Index is indicative of the level of flocculation/deflocculation of a suspension. Maximum plasticity usually occurs at a pseudoplastic index of about -0.9. Maximum values of pseudoplastic index for clay-based suspensions usually occur between -0.85 to -0.95. One wants to set the level of flocculation/deflocculation so the pseudoplastic index is at its maximum value. When systems are too flocculated, or too deflocculated, pseudoplastic indices will be reduced to lower negative values (<-0.7). When pseudoplastic indices become positive, they are indicative of severe problems (dilatancy).

m = (log m_RL,20 - log m_RH,10 ) / (log RL - log RH) (9)

Data Bases

Today's automatic viscometers make it rather simple to define and measure 20 minute gel tests. Since many new viscometers are under computer control and many older models can be connected to and monitored by computers, and when all else fails, the data from all other instruments can always be entered by hand into spreadsheet programs, all of these parameters can be calculated routinely and quickly for all suspensions on which the gel tests are performed.

One needs to set up, build, and maintain a data base of all parameters associated with this gelation test. When this test is routinely performed, one can usually take a quick look at the set of measured parameters to see how a particular suspension is behaving. But before this can occur, the data base of these parameters must be set up and data must be added to it routinely (daily). When these tests become routine and automatic, and engineers become familiar with the values, they are very handy. This information is obviously very useful to those who are responsible for tuning process suspensions.

Another reason for maintaining a data base is to help, over time, to learn whether various problem occurrences during processing correlate with any of these parameters. Each of these parameters can be related to various processing characteristics. When problems come and go, for no apparent reason, an appropriate data base of characterization parameters is always useful. All problems are caused by fundamental properties of suspensions and forming bodies. The difficult part is to determine which properties correlate with each of those problems. Since gelation properties directly affect forming properties and behaviors, they are especially useful in this regard.

Applicable to All Slips and Slurries

Examples above may have mentioned clay-based slips and slurries, but all suspensions can be characterized using this 20 minute measurement. Clay and kaolin minerals are the ingredients that usually contribute the plastic properties to traditional ceramic slips. But when slips and slurries contain no clays or kaolins, they still need plasticity and gelation to allow forming to take place. Even when polymeric additives are used in such systems to provide the plastic properties, the gelation test is a useful suspension characterization tool.

This measurement technique, which uses commonly available rotational viscometers, is applicable to all ceramic slips and slurries to characterize gelation behaviors. If you are working with slips and slurries in your process, give it a try.

Miscellany

Short Courses:

Remember, 15 May 2003 is the last day for early payment discounts for the short courses. Registration, of course, will remain open right up to the start of each of the courses. If you are planning to attend, please register as early as possible so I can produce the appropriate number of handouts for each course. If you are planning to pay by check on the day of the course, that's fine, but please send a registration form in advance. The only means I have to accept credit cards is through PayPal over the internet, so I cannot accept credit cards on the day of the course. If you want to (need to) use a credit card, send a registration form as soon as possible, and submit your payment at my web payment page using PayPal a few days before the course.

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