There are two time-dependent (TD) non-Newtonian rheologies that characterize suspensions and fluids: thixotropy and rheopexy. Examples of these two rheologies are shown in Figure 5.1.
Increasing γ Rheopexy
µa
Newtonian (Apparent
Viscosity)
Thixotropy
Increasing γ Time
Figure 5.1 Time-Dependent Rheologies Measured at Constant Shear Rate Thixotropy
Apparent viscosities of thixotropic suspensions decrease and approach minimum, limiting viscosities as the suspensions are exposed to constant shear rates with time. The thixotropic rheograms are the two lower curves shown in Figure 5.1. As intensities of shear conditions increase, the measured, limiting apparent viscosities of thixotropic suspensions decrease. Beyond some upper shear rate,
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however, further increases in shear conditions no longer produce corresponding decreases in the limiting viscosity.
Rheopexy
The apparent viscosities of rheopectic suspensions increase with time under constant shear conditions. The rheopectic rheograms are the two upper curves in Figure 5.1. Higher shear rates produce increasingly viscous behavior with time, up to the limit of no flow at all.
Shear History
The apparent viscosities of time-dependent fluids and suspensions respond to the length of time of exposure and the rate of shear. The shear history is the imposed shear rate times the time of exposure. It can also be described as the area under a shear rate versus time curve. As such, it is a dimensionless number:
NSH = shear rate
⋅
time [=] s-1⋅
s = dimensionless (5-1) The greater the shear history, the more time the intensity of shear has to work on the structure of a suspension and raise or lower its apparent viscosity.Consider again the sample rheogram shown in Figure 4.5.
That figure depicts a rheogram measured as the suspension was exposed to constant acceleration from 0 to 1000s-1 in 10 minutes followed immediately by constant deceleration to 0s-1 over the next 10 minutes. Figure 5.2 shows the shear rate versus time program for that run.
When apparent viscosity is measured in a single acceleration/deceleration program as this, the shear history after the full 20 minute run is exactly double that of the shear history imposed over the first 10 minutes. The area under the curve for each 10 minutes of the run is the area of a triangle. The shear history for the constant acceleration part of the program is:
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0 200 400 600 800 1000
0 200 400 600 800 1000 1200
Time (seconds)
Shear Rate (1/seconds)
Figure 5.2 A Typical Rheometer Measurement Program:
10 minutes of constant acceleration to a maximum shear rate followed immediately by 10 minutes of constant deceleration back to 0 shear rate.
Shear HistoryAcceleration = ½bh = ½(600s)1000s-1 = 300,000 (5-2) The shear history during deceleration is the triangular area for the second half of the program which has the same value as that just calculated in Equation 5.2. The total shear history of the program is the sum of these two:
NSH Total = NSH Acceleration + NSH Deceleration =
= 300,000 + 300,000 = 600,000 (5-3) This calculation demonstrates that each half of this type of acceleration–deceleration measurement program contributes exactly the same shear history to the fluid or suspension being measured.
Consider, however, the shear histories at the two points in the program at which apparent viscosities are measured at 100s-1. One is measured after 60 seconds of acceleration and the other is measured after 1140 seconds (600 seconds of acceleration plus 540 seconds of deceleration).
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The shear history after one minute of acceleration when the shear rate reaches 100s-1 is:
NSH 1 @ 100s-1 = ½ (60s) 100s-1 = 3000 (5-4) After 10 minutes of constant acceleration from 0 to 1000s-1 and 9 more minutes of constant deceleration from 1000s-1 back to 100s-1, the shear history again at 100s-1 is:
NSH 2 @ 100s-1 = NSH Acceleration + NSH Deceleration =
(½ (600s) 1000s-1) + (½ (600s) 1000s-1 – ½ (60s) 100s-1) = (300,000) + (300,000 – 3000) = 597,000 (5-5) The difference between the 100s-1 shear history during acceleration (3,000) and the 100s-1 shear history during deceleration (597,000) is substantial. The shear history after 19 minutes when the shear rate decelerates to 100s-1 is 199 times the amount to which the suspension was exposed during the first minute of acceleration to 100s-1.
Time-dependent suspensions, which respond to the shear*time history, will exhibit very different apparent viscosities after such different shear histories, even when the apparent viscosities are both measured at the same shear rate.
Shear history is not usually quantified in this way, but these sample calculations show that shear histories can be substantially different, even within relatively common viscometer measurement programs.
Gelation and Thixotropy
Thixotropic rheologies are typical of flocculated, shear-thinning suspensions which exhibit gelation behavior. When shear is applied to a thixotropic suspension, gel structures break down and apparent viscosities decrease. When shear is discontinued and the suspension is allowed to sit undisturbed, gelation phenomena rebuild structures throughout the suspension and apparent viscosities increase again.
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When a gelled suspension is sheared, a dynamic balance occurs between the gelation which builds structure and increases viscosity, and the shear conditions which break the gel structure and decrease viscosity. Gelation proceeds at a rate that is controlled by the properties of the suspension components (additive type and concentration, flocculation/deflocculation state, interparticle spacing, etc.) Gel breakdown rate is a controlled by the rate of imposed shear.
As a gelling suspension is sheared, the rates of the two phenomena (gel buildup rate and gel breakdown rate) will find a balance point at each shear rate. When the rates of these two phenomena are equal, the TD rheograms will exhibit constant viscosity with time as shown by the relatively constant, limiting viscosities in Figure 5.1.
Higher shear rates will destroy more gel structure and suspensions will then exhibit lower apparent viscosities. When apparent viscosities no longer decrease with further increases in shear rate, this is an indication that all of the gel structure has been destroyed. Under such conditions, particles travel as individuals, rather than as small flocs that are remnants of the gel structure.
When shear conditions are reduced, gelation will again cause flocs and 3-D structures to form.
When gelation occurs in a suspension, the gel-building phenomena cannot be stopped simply by imposed shear, but gelation can be overpowered by high shear conditions. High shear conditions can break up gel structures faster than gelation phenomena can build them. When the intensity of shear decreases, the gelation phenomena will once again become apparent as apparent viscosities rise.
Rheopexy and Particle/Particle Collisions
In the introductory chapter, it was mentioned that corn starch in water is an example of a dilatant suspension. Apparent viscosities increase in dilatant suspensions as shear rates increase. Dilatancy is the independent (TI) shear-thickening rheology. Its time-dependent (TD) shear-thickening counterpart is rheopexy.
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Dilatancy and rheopexy in ceramic suspensions are the result of particle/particle collisions. As shear intensities increase, the magnitude of particle/particle interactions and collisions increase, and measured apparent viscosities increase. The TI dilatancy phenomena occurs independent of time as shear rates increase. The TD rheopexy phenomena occurs with time at constant shear rate.
Just as pseudoplasticity and thixotropy are related to gelation behavior, dilatancy and rheopexy are related to particle/particle interactions and collisions during shear.
Anything that increases the intensity of particle/particle interactions during flow can increase dilatant and rheopectic effects.
Deflocculated suspensions tend to exhibit dilatancy, and if it were easy to measure, most such suspensions would be found to be rheopectic as well.
Rheopexy is not easy to measure and it is rarely seen in viscometer measurements. Its TD rheograms, as shown in Figure 5.1, exhibit increasing apparent viscosities that build up to maximum levels at each set of applied shear conditions. Higher levels of applied shear produce greater measured apparent viscosities. The ultimate limit occurs when particles lock up into a dilatant structure and shear and flow come to an abrupt halt. Such blockages, known as dilatant blockages, will be discussed in more detail in a later chapter.
There are several reasons for the lack of measurements that confirm rheopexy in suspensions. Deflocculated suspensions that could show rheopectic properties tend to be unstable – i.e., particles settle quickly. If such suspensions are treated gently and with deliberation as measurements are being taken, the particles will settle before the measurements are completed.
Suspensions that could exhibit rheopexy will almost certainly also exhibit dilatancy. The process of taking rheological measurements on dilatant and rheopectic suspensions can easily damage viscometers. Blockages can clog narrow passageways, and the onset of such blockages can ruin viscometer measuring heads as well as control motors and gearing that are not sufficiently protected with appropriate clutch mechanisms.
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The magnitude of measured apparent viscosities in such suspensions can also quickly exceed the measurement capabilities of viscometers. If the target viscosity for a production body is well within the capabilities of a particular viscometer, the mere fact that measurements are headed out of range and will exceed the viscometer’s measurement limits are frequently sufficient to cause process engineers to stop the measurements and adjust the suspensions to lower apparent viscosities. These are good procedures to follow. Process corrections should be made well before hard viscometer limits are reached and viscometers are damaged.
Dilatant and rheopectic suspensions can also severely tax and ruin mixers and pumps. It will almost certainly be obvious, if a ceramist is paying attention, when dilatant suspension rheologies are causing problems. Adjustments should be made quickly when such properties appear.
Professor Funk frequently told the story8 about the student who ruined a set of ceramic ram press dies because the student wondered what would happen if he tried to press an extremely dilatant forming body. The student reasoned that if he first asked Professor Funk what would happen, he’d be told to “go try it.” So instead of asking first, he tried it first. He only reported his experiment after the die was broken into pieces.
Professor Funk also often jokingly suggested to students that if they were mixing extremely dilatant suspensions on a milkshake mixer, or if they were measuring viscosities on a viscometer, and they noticed the motors beginning to smoke ... that was a good indication they were dealing with dilatancy. He joked about it, but it is true.
Rheopexy and dilatancy can both reach extreme levels. It’s best not to subject a good viscometer to such suspensions if it’s known in advance that they will exhibit extreme properties. Precise measurements on dilatant and rheopectic suspensions are difficult to achieve unless the effects exhibited are relatively mild.
For all these reasons, measurements demonstrating rheopectic properties are difficult to acquire and are, therefore, rare. When rheopexy happens, however, it will be the result of particle/particle interactions and collisions within the suspension.
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Gelation Is Not Rheopexy
When apparent viscosities are monitored at low shear rates as gel structures form, the measured rheograms will look like the rheopectic curves in Figure 5.1. Gelation, however, is not rheopexy.
Such rheograms occur when measurement shear rates change (decrease) abruptly, for example, from 100s-1 to only 1s-1 and the viscometer continues to measure apparent viscosity versus time.
After such a change in shear rate, gelation causes structures to rebuild and measured apparent viscosities to increase until the new gel breakdown/buildup rate equilibrium has been achieved. This is an example of an increase in measured apparent viscosity that accompanies a decrease in shear intensity.
In rheopectic suspensions, increases in shear intensity cause increased rheopectic behavior and increased measured apparent viscosities. The effects of such behavior are opposite to the effects of high shear on gel structures. High shear intensities break gel structures and reduce apparent viscosities in thixotropic suspensions.
High shear intensities build structures and increase apparent viscosities in rheopectic suspensions.
Summary
The two time-dependent rheologies that ceramists must deal with are thixotropy and rheopexy. Thixotropy occurs as gel structures are broken down over a period of time by constant shear. As measured apparent viscosities of thixotropic fluids decrease with time, they approach limiting, minimum values. Rheopexy occurs as collision intensities increase over a period of time at constant shear.
Measured apparent viscosities of rheopectic fluids increase with time as they approach limiting, maximum values.
In thixotropic fluids under extremely high shear conditions, all particles flow as individuals. In rheopectic fluids under extremely high shear conditions, all particles can be mechanically bound together into a single compact which can cause flow to cease.
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Time-dependent rheologies respond to shear*time history. As the shear history increases, apparent viscosities of time-dependent fluids and suspensions can increase or decrease. When equilibrium has been achieved, apparent viscosities will remain constant as shear history continues to increase.
When the apparent viscosities of fluids are totally unaffected by shear history, those fluids are not time-dependent fluids.
Newtonian fluids, for example, are not time-dependent.
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