# Modelling the Relations of Rheological Characteristics with Composition of Plaster Mortar

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

^{−1}) and the thixotropy of the mixes were determined with rotational viscometer for 18 compositions (according to the design of the experiment). Each of the 18 viscosity curves were described with the Ostwald–de-Waele equation. The Experimental–Statistical models describing the dependencies of the parameters of the rheological model and of mix thixotropy on the composition factors were built on the obtained data. ES-models have allowed the individual and synergetic effects of mix components on the rheological characteristics to be evaluated. The expanded perlite powder can increase the viscosity by two times, probably due to its pozzolanic effect increasing the content of the CSH phase during cement hydration. The thixotropy can be increased by the quantity of limestone. The computational experiments with ES-models have made it possible for the information set, without a noticeable interrelation between rheological characteristics, to be stratified into subsets, in which such interrelations differ significantly.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Characteristics of Materials and Design of Experiment

_{1}), perlite sand (X

_{2}), cellulose methyl ether, 2-hydroxyethyl ether-Tylose MH60010 (X

_{3}), and copolymer powder of vinyl acetate and ethylene Vinnapas 5034N (X

_{4}). The contents of other components remained constant. The values of Y were determined for 18 compositions according to 18-points of 4-factor design of experiment [28]. The points of the design in coordinates of composition factors normalized to dimensionless −1 ≤ x

_{i}≤ +1 (instead of dimensional X

_{i}, X

_{i.min}≤ X

_{i}≤ X

_{i.max}) are shown in Figure 1 and given with corresponding compositions (natural factor levels X

_{i}) in Table 2.

- x—vector of normalized factors,
- x
_{i}= (X_{i}− X_{0i})/ΔX_{i}, X_{0i}= (X_{i.min}+ X_{i.max})/2, ΔX_{i}= (X_{i.max}− X_{i.min})/2 - X
_{i}= x_{i}· ΔX_{i}+ X_{0i.}

- Predesign of the experiment, i.e., selection of the factors to be varied, limits of varying them, properties, the level of which should be determined, considering physico-chemical, technological, and other a priori knowledge.
- Design of the experiment, with regard to the rational form of the polynomial model and possible existence of present experimental points and “forbidden” areas in the factor domain.
- Building the regression model adequate for experimental data, with insignificant estimates eliminated.
- Solving a variety of scientific and industrial problems, making decisions on the basis of individual ES-model (for separate criteria) and their complexity, extracting as much as possible scientific and industrial information from the models.

#### 2.2. Testing Method

^{−1}), from the lowest γ′ = 0.045 to the highest 5.705 s

^{−1}and back. The effective viscosity η (Pa·s) of each of the 18 mixes was measured sequentially 3 times by turning the rotor on and off. The average value of these measurements was taken as the measurement result. The duration of the measurement for each sample was 8 h. The temperature of the mortar was 19 ± 1 °C during the measurement and was kept at a pre-set level by the thermostatic chamber. The liquid in the annular gap is propelled to flow by the driven inner cylinder. It is possible to minimize errors during testing by making the gap size between cylinders smaller, linearizing the velocity gradient across radius of the cup and rotor [37]. So, we used type T2-B100 cylinders (manufacturer “Himpribor-1”, Tula, Russia). The inner diameter of the outer cylinder is 24 mm. The outer diameter of the inner cylinder is 17.479 mm. To define the annular gap size, we used the ratio of the radii, δ = 0.73. The DIN 53,018 standard [36] allows the use of devices, in which δ lies in the range 1 < δ < 1.10. The annular gap is of constant width: the test may be run with samples that contain particles of a particle size less than 1/3 of the gap size. The outcome of the resistance of the liquid being sheared between the stationary and rotating boundaries of the sensor system is a viscosity-related torque operating on the inner cylinder, counteracting the torque produced by the drive motor. Due to the torque applied by a spring twist, this torque detector is put between the drive motor and the shaft of the inner cylinder. The twist slope of the torque spring then serves as a direct measure of the viscosity of the sample.

#### 2.3. Method of Measuring Theological Parameters

_{1}, Pa∙s, at shear rate γ′ = 1 s

^{−1}, and the exponent m < 0 characterizes the rate destruction of fluid structure during shear deformations-the higher |m|, the less stable the fluid structure during flow [37].

^{−1}and maximum speed γ’ = 5.705 s

^{−1}. For further analysis, we discarded these points in the calculations, since at the initial velocity the flow of the sample cement mixtures has not yet begun and the resulting deformations cannot be interpreted as an indication of yielding [38,39]. On the other hand, at high speeds, the behaviour of the sample is close to the viscosity of simple liquids with an extremely destroyed structure, where the critical deformation is the end of the linear elastic regime [40]. All rheological models obtained have the high coefficient of determination, R

^{2}= 0.989 − 0.999.

## 3. Results

#### 3.1. Effects of Varied Components on Rheological Properties

_{1}(with significant effects at experimental error of 4%), written in structured form.

_{0}= 406.2 presents the level of η

_{1}at medium values of all x, equal to zero, at the center of the experiment. The first block evaluates the effects of limestone and expanded perlite (so-called, effects of disperse phase) at central values of the factors from another group (quantity of polymer modifiers). The effects of those from another group at central values of the first group factors are presented in the second block. The third block evaluates the synergism or antagonism of the factors from two groups. The viscosity η

_{1}described by Equation (4) has a minimum level η

_{1}.

_{min}= 18.24 Pa·s (at lower values of all 4 factors, x

_{1}= x

_{2}= x

_{3}= x

_{4}= −1) and maximum η

_{1.max}= 511.45 Pa·s (at x

_{1}= −0.19, x

_{2}= 0.65, x

_{3}= 0.4, x

_{4}= 1). The influence of the additives on the viscosity may be analyzed from the graphs shown in Figure 4.

_{1}is nonlinear: in concentration from 1 to 1.2 w.p., methyl hydroxyethyl cellulose increases the viscosity, but in higher amounts Tylose decreases the viscosity. Similar data of cellulose admixture in modified mortars were observed by other authors [41,42]. Such behaviour of Tylose can be attributed to the fact that cellulose might lubricate the particles of solid phase that lead to decreasing viscosity. However, the increase in viscosity can be associated with the ability of cellulose coming into contact with water, it begins an adsorption process, adhering to the periphery of the water molecules, imbibing and fixing part of the water in the mixture, thus increasing the viscosity of the material, as the authors of [43] note.

_{4}) has the most substantial effect on the viscosity at the unit shear rate, when the mix is rather viscous. This indicates the possible strong bonds created by Vinnapas. It can be seen that the addition of expanded perlite powder to the mixes in quantities from 30 to 60 w.p. (by dry mix), increases the viscosity by two times in the zone of maximum. Similar results were obtained by the authors of [44], using 15–20% of expanded vermiculite in self-compacting mortars led to high viscosity at low rotational speed. The increase of viscosity can be ascribed to the pozzolanic effect of perlite, increasing the content of the CSH phase during cement hydration [45]. However, if the amount of other modifiers in mixes is low, this property of perlite weakens. The influence of limestone on the viscosity is less insignificant.

_{1}≤ 157 Pa·s) at the same time could have a high rate of destruction (|m| > 1). This is a quite expected effect, which demonstrates that the created bonds are easily broken while mixing and at high values of |m| the mixtures lose their stability. In spite of this, some samples demonstrate stability of structure: No. 4, 15, and 12 have on average |m|

_{mid}≈ 0.87 while η

_{1mid}≈ 230 Pa·s. As can be seen in Figure 5, increasing the amount of Pelrite (x

_{2}) and Vinnapas (x

_{4}) from minimum to maximum will decrease the rate of structure destruction. The above analysis indicates that it is important to take the compatibility of the mixes’ components into consideration, since this can affect the conditions of processing the mortars and the stability of the structure.

_{2}, x

_{3}, and x

_{4}. However, the content of limestone, x

_{1}, has a higher effect in the zone of minimum. When the minimum and medium amounts of limestone are added in mixes, the thixotropy doubles from 150 to 300 Wt/m

^{3}. With further increase of x

_{1,}thixotropy decreases. The decrease of thixotropy can be observed in the maximum zone as well, A

_{th}drops from 550 to 350 Wt/m

^{3}. Limestone is well known as an inert additive [46] which influences the flow properties of mixtures related with its different particle size. No relevant effects of limestone on rheological properties are confirmed by [47]: zeolite and silica fume have more effect on the rheological properties of fresh cement pastes than limestone, as it is indicated in his work. Not showing strong effect on viscosity, as mentioned above in our work, the limestone particles, however, can act as intercalated grains with strong nucleating properties and they enhance the thixotropy during the mixing process. In the study [48], also indicated the high thixotropy of the mortars with limestone and author associated this increase with a reduction in maximum packing density which, at a constant solid volume fraction in the suspension, leads to an increase in the contact interactions. Therefore, one of the efficient ways to create thixotropic mixes is to introduce hydration accelerating products, like limestone. The thixotropy increases with the contents of other modifiers only in the zone of its maximum, by 2–2.5 times. The effect described above can be related to the decrease of free water in mixes that leads to formation of the bigger microflocculation units complicating the movement.

#### 3.2. Correlation between Rheological Characteristics

_{th}) correlate to the rate of its structure destruction (|m|)?

_{th}and |m| widens the possibilities for express controlling the quality of finishing mixes.

_{th}, |m|} = −0.53. However, this should not be accepted formally, since these data could present essentially different structures of the mortar in various zones of formulation region (at this or that fixed dosages of mineral or organic components).

_{th}in various formulation zones to be revealed and characterized can be obtained in computational experiments, in which the statistical trials (with Monte Carlo method [50,51]) are carried out [30,52]. The paired samples of any size (n) necessary for the analysis and for building possible prediction equations can be simulated with the help of the ES-models obtained. In each realization of the trial, the sufficiently great number of compositions (x) uniformly distributed in the whole formulation region under study or in its subregion are generated. For each x the generated normally distributed experimental error is added to the level of the property (Y) calculated by corresponding ES-model. By n pairs of these values the point estimate of coefficient r (or other measure of correlation) is obtained. Multiple realization of such trials makes it possible to get the distribution and interval estimate of r.

_{th}), for 100 generated compositions: uniformly distributed quantities of limestone aggregate (within the range 60 ≤ L ≤ 100 w.p., −1 ≤ x

_{1}≤ +1) and of dispersible polymer (within the range 1 ≤ V ≤ 2 w.p., −1 ≤ x

_{4}≤ +1), at maximal contents of perlite and methylcellulose (x

_{2}= x

_{3}= +1, Figure 8), and at the lowest values of these factors (x

_{2}= x

_{3}= −1, Figure 9).

_{th}, |m|} = −0.91) practically disappears with low content of these components (average r{A

_{th}, |m|} = −0.20, at right estimate +0.07). Thus, when one controls the structure of technological mix by varying the quantity of dispersible polymer in the matrix and the content of the aggregate the increase of |m| does imply the lowering of the thixotropy if the mixes contain “much” perlite and methylcellulose.

_{th}in the lesser degree, the certain other effects weaken the relation. The hypothesis of linear statistical relationship of K and |m| (evident in Figure 8) remains significant over most of factors subregions considered. In some cases, the non-linear hypothesis could be also admitted (as determination coefficients R

^{2}in Figure 8 show).

## 4. Conclusions

^{−1}to 5.705 s

^{−1}and back) obtained for each of the 18 plaster compositions in the designed experiment have been described with the Ostwald–de–Waele equation. The influence of the contents of limestone aggregate, perlite filler, Tylose, and Vinnapas in the compositions on the parameters of the power law model and on thixotropy has been evaluated with the help of ES-models.

^{−1}within the range from 18.24 to 511.45 Pa·s. The changes are related to the amount of physically bound water and the bonds created by the components of the mixture.

- -
- Estimating the viscosity of technological mix of any composition at any shear rate in the studied region;
- -
- Inverse problems, of determining the shear rate that would provide the necessary viscosity of the mix, or of finding acceptable, optimal, and compromise compositions by rheological criteria together with operational properties of hardened composites.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Conflicts of Interest

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**Figure 2.**Logarithmic dependences of the viscosity on shear rate for compositions with minimum and maximum viscosity.

**Figure 7.**Scatter diagrams of viscosity at shear rate equal unity (K in Ostvald-de-Waele model), of thixotropy, and destruction rate of the 18 compositions (results of natural experiment).

**Figure 8.**Scatter diagrams of the estimates of rheological characteristics at upper content of perlite and methylcellulose (x

_{2}= x

_{3}= +1) obtained in computational experiments with the help of ES-models (results of one trial).

**Figure 9.**Scatter diagrams obtained in computational experiments at the lowest content of perlite and methylcellulose (x

_{2}= x

_{3}= –1).

Mixture Components | Basic Characteristics |
---|---|

Portland cement | Additive-free cement produced by “Baltsem” M500 mark (PC I-500-N D0) (European quality certificate EN-197-1, CEM I 42.5 N). Specific surface is 300 m^{2}/kg and fineness is 11.3% |

Calcium hydroxide | Contention of CaO + MgO—73% by weight, water demand is 70%, bulk density is 0.5 kg/dm^{3} |

Limestone shell rock | Shell rock, with specific surface Ss.d. = 400 m^{2}/kg, sifted through a sieve of 0.63 mm. |

Quartz sand | Quartz sand from the Volnogorsk Mining and Metallurgical Combine. Density of quartz is 2.04 g/cm^{3}, the particle size modulus is 1.1, the content of dust and clay particles is 0.3%, the clay content in the lumps is 0%, and the moisture content is 3.6%. The work used sand sifted through a sieve of 0.63. |

Perlite sand | Perlite sand from the Beregovsky quarry of the Transcarpathian region. Expanded perlite fraction 0.16–1.05, grade in terms of bulk density 100, bulk density is 80 kg/m^{3}, heat conductance at 25 ± 5 °C no more 0.052 Wt/m °C |

Tylose MH60010 | Water-retaining additive, methyl hydroxyethyl cellulose. Tylose is a water-soluble non-ionic cellulose ether, which is a derivative of the natural cellulose material. |

Vinnapas RE5034 N | Adhesion improving additive, copolymer of vinyl chloride, ethylene, and vinyl laurate |

Hostapur OSB | Air-entraining additive. Humidity—2%, sodium sulfate content of not more than 5.5%, potassium carbonate content of not more than 4%, bulk density—0.3 t/m^{3} |

Vinnapas 8031H | Water repellent, a triple copolymer of ethylene, vinyl laurate, and vinyl chloride. Bulk weight–450 ± 50 g/L, preferred particle size 0.3–9 microns, minimum glass transition temperature about 0 °C. |

Number of Composition | Normalised Levels | Dosages (w.p. in 1000 w.p. of Dry Mix) | ||||||
---|---|---|---|---|---|---|---|---|

x_{1} | x_{2} | x_{3} | x_{4} | Limestone | Perlite | Tylose | Vinnapas | |

1 | 0 | 0 | 0 | 0 | 80 | 40 | 1.15 | 1.5 |

2 | 1 | −1 | −1 | −1 | 100 | 30 | 1 | 1 |

3 | 1 | 1 | 1 | 1 | 100 | 50 | 1.3 | 2 |

4 | −1 | −1 | 1 | 1 | 60 | 30 | 1.3 | 2 |

5 | −1 | 1 | −1 | 1 | 60 | 50 | 1 | 2 |

6 | −1 | 1 | 1 | −1 | 60 | 50 | 1.3 | 1 |

7 | 0 | 1 | −1 | −1 | 80 | 50 | 1 | 1 |

8 | 0 | −1 | 1 | −1 | 80 | 30 | 1.3 | 1 |

9 | 0 | −1 | −1 | 1 | 80 | 30 | 1 | 2 |

10 | −1 | 0 | −1 | −1 | 60 | 40 | 1 | 1 |

11 | 1 | 0 | 1 | −1 | 100 | 40 | 1.3 | 1 |

12 | 1 | 0 | −1 | 1 | 100 | 40 | 1 | 2 |

13 | −1 | −1 | 0 | −1 | 60 | 30 | 1.15 | 1 |

14 | 1 | 1 | 0 | −1 | 100 | 50 | 1.15 | 1 |

15 | 1 | −1 | 0 | 1 | 100 | 30 | 1.15 | 2 |

16 | −1 | −1 | −1 | 0 | 60 | 30 | 1 | 1.5 |

17 | 1 | 1 | −1 | 0 | 100 | 50 | 1 | 1.5 |

18 | 1 | −1 | 1 | 0 | 100 | 30 | 1.15 | 1.5 |

**Table 3.**The obtained values of rheological characteristics of the polymer–cementitious compositions.

No | Viscosity η _{1} (Pa·s) | The Error of Ostwald–de–Waele Model | Destruction Rate |m| | Thixotropy A _{th} (Wt/m^{3}) |
---|---|---|---|---|

1 | 425 | 0.04 | 0.86 | 215 |

2 | 120 | 0.89 | 1.02 | 153 |

3 | 303 | 0.99 | 0.89 | 370 |

4 | 226 | 0.13 | 0.84 | 201 |

5 | 200.6 | 0.06 | 0.95 | 183 |

6 | 123.9 | 0.09 | 1.07 | 137 |

7 | 122.8 | 0.40 | 0.94 | 98 |

8 | 186.3 | 0.09 | 0.96 | 252 |

9 | 148.5 | 0.05 | 1.02 | 96 |

10 | 102.5 | 0.08 | 1.05 | 100 |

11 | 97.5 | 0.09 | 1.15 | 97 |

12 | 190.6 | 0.08 | 0.91 | 49 |

13 | 63.1 | 0.13 | 1.21 | 60 |

14 | 241.3 | 0.07 | 0.93 | 230 |

15 | 269.3 | 0.05 | 0.86 | 78 |

16 | 105.5 | 0.10 | 1.01 | 94 |

17 | 156.9 | 0.08 | 1.14 | 150 |

18 | 54.2 | 0.14 | 1.24 | 55 |

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**MDPI and ACS Style**

Moskalova, K.; Lyashenko, T.; Aniskin, A.
Modelling the Relations of Rheological Characteristics with Composition of Plaster Mortar. *Materials* **2022**, *15*, 371.
https://doi.org/10.3390/ma15010371

**AMA Style**

Moskalova K, Lyashenko T, Aniskin A.
Modelling the Relations of Rheological Characteristics with Composition of Plaster Mortar. *Materials*. 2022; 15(1):371.
https://doi.org/10.3390/ma15010371

**Chicago/Turabian Style**

Moskalova, Khrystyna, Tatiana Lyashenko, and Aleksej Aniskin.
2022. "Modelling the Relations of Rheological Characteristics with Composition of Plaster Mortar" *Materials* 15, no. 1: 371.
https://doi.org/10.3390/ma15010371