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2. Theoretical Approach

Most rotational rheometers are based on the principle that the material is stirred at a controlled speed and the resulting torque is measured. In the case of a Newtonian fluid, the viscosity is defined as the ratio between the stress and the shear rate [7]. Concrete and mortar are generally accepted to be Bingham fluids [6]. In such materials, the plastic viscosity is defined as the slope of the stress versus shear rate in the high shear rate limit. Most rheometers measure torque versus rotational speed. Therefore to obtain the true or absolute plastic viscosity, the slope of the curve should be corrected by a function, f, that depends on the rheometer geometry and experimental conditions. So the following equation could be used:

where ∆T/∆V = Slope of the torque (T) versus rotational speed (V)
ηT = True or absolute plastic viscosity
f(G,C) = function depending on the rheometer geometry (G) and experimental conditions (C).

The function f is not fully known for most of the concrete rheometers due to their complex geometry and the lack of a standard material that could be used for calibration. Oils are often used as standard materials but they are too expensive and have a viscosity too low to be used in a large concrete rheometer. These oils are designed for small rheometers such as the one used for cement paste. The parameters, G and C, of the function, take into account not only the type of rheometer (parallel plate or coaxial) but also the type of coupling between the fluid and the rheometer, the type of fluid tested, environmental conditions and the limits of the instrument (the limits of measurable torque or rotational speed). It could be imagined that the parameters, G and C, vary with the type of fluid used in the same rheometer. However, as will be shown below by the experimental results, the factor f (G,C) depends more on the type of rheometer than on the type of fluid tested. This observation should be further confirmed by more testing. Due to the lack of knowledge of the function f, the true or absolute plastic viscosity cannot be known with low uncertainty. This could explain why it was not possible to compare the absolute values of the plastic viscosity obtained with the concrete rheometer during the round robin test [1,2].

A method should be developed to either determine this function f or to eliminate it. Suppose that two measurements are performed with the same rheometer on two different mixtures (1) and (2). The following equation could be written:

where the indices (1) and (2) stand for the two mixtures tested in the same rheometer. For instance, material could be the concrete while material 2 could the mortar with the same composition of the concrete without the coarse aggregates. This ratio, ηT1/ ηT2, is defined as the relative plastic viscosity. From Eq. (2), we could say that the relative plastic viscosity does not depend on the rheometer used. This implies that plots of the relative plastic viscosity, measured with different rheometers, versus a mixture factor, such as the coarse aggregate concentration, should all be on one curve. It also implies that the relative plastic viscosity is independent of the physical units used to represent plastic viscosity. This hypothesis was tested using a wide variety of mixtures, although more types of rheometers should be included to confirm this finding.

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