THE PARTICLE FLOW INTERACTION THEORY – THIXOTROPIC
BEHAVIOR AND STRUCTURAL BREAKDOWN
J. E. Wallevik, Innovation Center Iceland, Iceland
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36 Conference on Our World in Concrete & Structures
Singapore, August 14-16, 2011
THE PARTICLE FLOW INTERACTION THEORY – THIXOTROPIC
BEHAVIOR AND STRUCTURAL BREAKDOWN
J. E. Wallevik
ICI Rheocenter, Innovation Center Iceland
Keldnaholti, IS-112 Reykjavik, Iceland
Tel: +354 8490355 Fax: +354 522 9111
E-Mail: [email protected]
Keywords: Cement paste; Rheology; Thixotropy; Structural Breakdown
Abstract. In this work, the so-called Particle Flow Interaction theory (or the PFI –
theory) is presented. It is used to simulate rheological behavior of cement paste.
This material model is among others based on combined concepts by Hattori and
Izumi and by Tattersall and Banfill. More precisely, coagulation, dispersion and re–
coagulation of the cement particles (giving a true thixotropic behavior) in combination
with the breaking of certain chemically formed linkages between the particles (giving
a so-called structural breakdown behavior) are assumed to play an important role in
generating the overall time-dependent behavior of the cement paste. The model
evaluation is done by comparing experimental data with model prediction.
1. INTRODUCTION
The Particle Flow Interaction theory (PFI – theory) consists of several coupled partial differential
equations (PDEs) and is well explained in [1]. These equations describe the process of coagulation,
dispersion and re-coagulation of the cement particles (giving a true thixotropic behavior), as well as
describing the breaking of certain chemically formed linkages between the particles (giving a socalled structural breakdown behavior). These concepts were proposed by Hattori and Izumi [2,3] and
by Tattersall and Banfill [4,5,6], respectively. The primary objective with the PFI – theory is to be an
analysis tool where the attained parameters give additional information about the material properties
of the fresh cement paste, beyond what is for example gained by the Bingham model alone.
2. THIXOTROPIC BEHAVIOR
The interest in thixotropic phenomena is nearly as old as modern rheology [7]. An increasing
number of real materials have been found to show thixotropic effects. Also, they have been applied in
various industrial applications, the cement paste being one example. The term thixotropy was
originally coined to describe an isothermal reversible gel–sol (i.e. solid–liquid) transition due to
mechanical agitation [7].
In the PFI – theory, the thixotropic behavior of cement paste is related to coagulation, dispersion and
re–coagulation of the cement particles. This is in accordance with the original idea presented by
Hattori and Izumi [2]. Here, the term “coagulation” describes the occurrence when two (or more)
cement particles come into a contact with each other for some duration of time; i.e. when the cement
particles become “glued” to each other and work is required to separate them. The particles become
glued together as a result of the total potential energy interaction VT that exists between them. This is
J. E. Wallevik
illustrated in Figure 1 (the term Ds. is the solid-surface-to-solid-surface distance between the cement
particles; see [8]). The total potential energy interaction VT originates from combined forces of van der
Waals attraction, electrostatic repulsion and steric hindrance [6,9] (detailed description is also
available in [8]). The polymers (i.e. HRWRA and so forth) will generally adsorb on the surface of the
cement particles. Their function is to change the above mentioned total potential energy in such
manner that coagulation is more difficultly obtained and dispersion more easily achieved.
Figure 1: Total potential energy interaction VT between cement particles.
3. STRUCTURAL BREAKDOWN
In most time dependent models for cement based materials, only thixotropic behavior is
assumed. The structural breakdown phenomenon seems to be less known and less used and is
unfortunately often confused with thixotropy. The term structural breakdown was made by Tattersall
in 1954 – 1955 [4,5]. Because no recovery in torque was measured in the corresponding experiment,
structural breakdown was considered to be a phenomenon different from thixotropic behavior
[6,4,5,10,11,12]. More precisely, structural breakdown is not the same as thixotropic breakdown
[4,5]. As mentioned in previous section, the latter is related to behavior generated by the total
potential energy VT that exists between cement particles (i.e. van der Waals attraction, electrostatic
repulsion and steric hindrance), while the former is not. A proposed mechanism of structural
breakdown was given in 1983 in a textbook by Tattersall and Banfill [6]. There, it was attributed to the
process of breaking certain linkages (i.e. connections) between the cement particles formed by the
hydration process. That is, the idea was that when a pair or more of cement particles came into
contact with water, hydration products (in the form of membrane) formed around both of them,
making the cement particles link together. With agitation of the cement paste (i.e. shearing), such
formed linkages would then break, meaning that the bridging membrane is ruptured and the cement
particles separate (see Figure 3.13 in [6]).
In addition to the above explanation, other similar related phenomenon could also contribute to the
behavior of structural breakdown. For example in [13], it is hypothesized that a certain needle shaped
chemical product formed in the pre–dormant and dormant period could make connections between
the cement particles (in this case, the needles are syngenite, slightly above several microns in
length). More precisely during the early growth, such needles can form bridges between free cement
particles as shown in Figure 2a, which could make initial deformation of the corresponding system of
cement particles more difficult. Although the cement particles are strictly speaking free, they are in
effect linked (or immobilized) together by the needles and thus should not be considered as free.
During agitation and depending on strength, such needles can break, making the “linked” cement
particles free as shown in Figure 2b.
J. E. Wallevik
Figure 2: Hypothesis about the mechanism of structural breakdown.
Another hypothesis about the mechanism of structural breakdown is shown in Figure 2c. There, the
idea is that the growing crystals (e.g. ettringite, syngenite and/or whatever that can grow on, and/or
stick to, the surface of a cement particle) manage to interlock to each other and thus create a
successful link between two (or more) cement particles. During agitation and depending on strength,
such interlocking crystals can break, making the linked cement particles free as shown in Figure 2d.
The point is that the structural breakdown is related to the breaking of chemical products (i.e. early CS-H, syngenite, ettringite or whatever) that in some form or another manage to generate some sort of
breakable connections (i.e. reversible linkages) between the cement particles. At least relative to a
single rheological experiment (50 seconds), this process is highly irreversible and thus nonthixotropic. This is so, because the growth rate of the hydration products, or “buildup of structure due
to hydration of cement minerals” [10], is slow during the dormant period. That is, it takes much longer
time than the duration of single rheological test (lasting several minutes, or so) to generate new
linkages of any type.
In the PFI – theory, both concepts thixotropic behavior as well as structural breakdown are assumed
to be occurring simultaneously in the cement paste during a rheological test.
4. PARTICLE SIZE NUMBERS 3 AND 4
Cement particles are poly-dispersed in size. Some 7 - 9% of the material (by weight) is typically
finer than 2 µm in diameter and 0 - 4% coarser than 90 µm [14]. Traditionally, the particles that are
influenced by the total potential energy effects are considered to be colloid particles. General
definition of such particle is that at least one dimension is in the size range from 1 nm to 1 µm [9,15].
However, there is no clear distinction between the behavior of particles with somewhat larger
dimensions than those of the traditional colloidal particle [9]. In [8] (Section 2.5.2), it is demonstrated
that cement particles as large as 40 µm in diameter seem to be able to “behave”, at least to some
degree, as a colloid particle, somewhat controlled by the action of the total potential energy VT. All
cement particles (i.e. the domain of particle sizes) that can significantly be influenced by the total
potential energy effects are classified in the PFI – theory as “particle size number 3” (meaning that
the diameter of these particles is less than the above mentioned 40 µm).
J. E. Wallevik
When considering a pair of cement particles larger than of “particle size number 3”, their kinetic
energy (or inertia) starts to be sufficiently large to overcome their mutual energy barrier against
coagulation and dispersion. When this condition applies, coagulation does not occur and the cement
particles rather interact with each other by a pure hard sphere collision factor. Such cement particles
that are not (or only slightly) influenced by the total potential energy effects VT, are classified in the
PFI – theory as “particle size number 4”. As cement particles of this size domain do not coagulate, the
corresponding (reversible) junction number (i.e. number of connections by VT) is always zero (see
[1]). Although the size 4 cement particles do not participate in coagulation and dispersion (through
VT), it is fair to assume that these cement particles do participate in chemical reactions, meaning that
chemically formed linkages can still form between the size 4 cement particles as suggested with
Figures 2e and 2f.
In [2], the numbers “1” and “2” are reserved for water molecules and water adsorption. It is therefore
for historical reason that it is started with the subscript “3” for the smaller cement particles in the PFI –
theory (as in “particle size number 3”), and thereafter with “4” for the larger cement particles (as in
“particle size number 4”).
In the PFI – theory, both cement size domains 3 and 4 are treated.
5. THE NEED FOR AN IMPROVED MODEL
Rheological data are usually attained through measurement with viscometers/rheometers of
various types and sizes. One example being the coaxial cylinders viscometer (see for example [16]).
To test the PFI – theory, such instrument has been used, namely the ConTec Viscometer 4, shown in
Figure 3a (an example of simulated velocity flow is shown in Figure 3b). One example of rheological
test result attained with this instrument is shown in Figure 4, in which the test sample is cement paste
with w/c=0.3 mixed with SNF polymer (for further information, see [1]). As shown in Figure 4, the time
duration of single rheological test is 50 seconds in this example.
In the case of Figure 3, the inner cylinder (of the viscometer), measures torque as a function of time.
The outer cylinder rotates in a step wise manner as shown in Figure 4b. This stepwise change in
angular velocity is done to increase the complexity of the shear rate during the rheological test, to
gain better information about performance of HRWRA (the aim was to quantify the performance of
each HRWRA type; see [1] for further information).
Figure 3: The ConTec Viscometer 4 (left) and its flow simulation using MHI (right).
Using classical models like that of the modified vom Berg (Figure 4a), the Hattori–Izumi theory
(Figure 4c), or of the modified Shangraw (Figure 4d) to fit experimental data has shown to be
unattainable [8,17,1]. In particular, the problem rests in that by setting the material parameters to
such that it simulates (or reproduces) part the experimental data, the rest of the experimental data
cannot be simulated. A wide variety of different parametric values were tested by trial and error,
without any success [8,17,1].
The successor of the original Hattori–Izumi theory is the modified Hattori–Izumi theory (or the MHI –
theory) [8,18]. This model has shown to be more successful than the standardized models mentioned
above. Still, the MHI – theory has shown to have problems, especially in reproducing experimental
J. E. Wallevik
results for stiffer cement pastes. The problem is apparently present in its failure to reproduce the
large recovery in the measured torque. Accordingly, the MHI – theory has its limitations. For further
information about the MHI – theory, and the corresponding test results, see [18].
Figure 4: Comparison of a rheological test result with the outcome of different material models.
In contrast to the models of modified vom Berg, Hattori–Izumi, modified Shangraw, or MHI, the PFI –
theory includes both the effect of thixotropic behavior as well as structural breakdown. With these two
effects simultaneously present, it has the potential to reproduce the measured behavior of cement
paste much better than the other models. An example of this is shown in Figure 4e.
With the inclusion of thixotropic behavior and structural breakdown, as well as using two different
cement particles size domains, the PFI – theory is mathematically complicated. Although it can be
somewhat hard to use, this model does provide some fundamental explanation of rheological
behavior. Describing the mathematics of the PFI – theory is beyond the scope of this article, but is
available in [1] for the interested reader.
CONCLUSION
With both the thixotropic behavior as well as structural breakdown effects simultaneously present, the
PFI – theory has the potential to produce the rheological response of cement paste under more
complex shear rate condition. The three concepts “thixotropic behavior”, “thixotropic breakdown” and
“structural breakdown” should not be confused.
REFERENCES
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J. E. Wallevik
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