Preparation and stability of the samples
Sample nanofluids were prepared by dispersing a nanopowder in an aqueous electrolyte solution (the base solution). The TiO2 nanopowders (A1, A2, A3, R1, and R2) used in this study are specified in Table . The base solutions with adjusted pH values were prepared by adding HCl or NaOH to demineralized water with a possible content of dissolved gases.
Nanopowders used for the preparation of nanofluids
In preliminary experiments, 0.02 g of a nanopowder was added into 25 mL of each base solution. The flask with a suspension was treated for 30 min in a 40-kHz ultrasonic bath with a nominal acoustic power of 30 kW m-3. The samples were then tested using DLS technique (Zetasizer Nano ZS - Malvern Instruments) to determine the zeta potential, ξ. Actual values of pH, see Figure , slightly differ from idealized log-linear estimates (dotted line in Figure ) even for a series of the base solutions. This difference is caused by dissociation of water and hydrated TiO2, as well as by the presence of dissolved CO2 (around cNaOH = 10-5 mol/L). The resulting ξ-potentials dependent on the actual measured pH values are plotted in Figure .
Titration curves of the tested samples. Dotted line shows an idealized titration curve. Deviations for the individual samples are due to dissociation of hydrated TiO2 and dissolved CO2.
Acidobasic adjusting of ξ-potential. Individual nanopowders are specified in Table 1.
Assuming that the maximum stability of a TiO2
-water dispersion, i.e., the highest resistance against sedimentation, can be achieved at the extreme values of ξ
], further ten samples (A1±, A2±, A3±, R1±, and R2±), were prepared to examine their particle size distribution using again the DLS technique; see also Table . The preparation of these samples differs from the preliminary procedure only in the utilization of a larger primary amount of nanopowder (2.5 g in 100 g of dispersion) and a longer ultrasonication time (24 h). An external cooling system was employed to keep the sample at a constant temperature of 23°C during ultrasonic treatment. After keeping the sample aside for next 8 h, the sediment (ranging from 5 to 90% of the original content of nanopowder) was withdrawn and weighed to determine the final real particle concentration, shown in Table .
Parameters of the stable nanofluids
The resulting particle size distributions, Figure , show remarkable differences in the behaviors of anatase- and rutile-based dispersions. While the anatase dispersions display the maximum content of the finest particles in acid media (A1+, A2+, and A3+), the rutile dispersions in acid media (R1+ and R2+) are much more coarse. In alkaline media, on the contrary, the anatase dispersions (A1-, A2-, and A3-) display a remarkable shift toward coarse clusters, whereas the rutile dispersions (R1- and R2-) become finer. As a matter of fact, the coarser dispersions (A1-, A2-, A3-, R1+, and R2+) settle rather fast, while the finer dispersions (A1+, A2+, A3+, R1-, and R2-) are stable for a few days. Only the stable dispersions were further subjected to rheological examinations using the AWS rotational viscometry.
Figure 3 Particle size distributions via DLS method. Color and style of the curves identifies the samples, specified in Table 2. Note a large volumetric content of coarse particles in the anatase sample A1+ and in all the rutile samples. This is apparent in the (more ...)
AWS rotational viscometry
The concept of AWS effect from the viscometric viewpoint [17
] is illustrated in Figure for the simple shear flow between two mutually sliding parallel plates. A possible near-wall flow anomaly, resulting in a non-linear velocity profile under constant shear stress σ, is represented by the apparent slip velocity u
. The only experimentally available kinematic quantity, the sliding velocity U
, determines the apparent shear rate γapp U
for the Couette flow in a narrow gap h
between two coaxial cylinders), which is expressed as a sum of the bulk flow and wall slip contributions, as follows:
Figure 4 Scheme of a shear flow with the AWS effect. Dotted line - actual non-linear velocity profile observed at the constant shear stress σ due to the effect of a depletion layer of dispersion at the wall; Broken solid line - approximation of the actual (more ...)
Two material functions, the bulk fluidity
and the Navier slip coefficient χ
, are constant in many cases [17
]. The flow and slip effects can be distinguished through a series of viscometric experiments, in which the gap thickness h
is systematically varied whereas the shear stress σ
is kept constant. This is the essence of AWS viscometry.
Rotational viscometer with a KK sensor
The experimental realization of AWS viscometry needs a series of sensors of different and well-calibrated hydraulic radii (tube radius in the capillary viscometry, gap thickness between cup and bob in the rotational viscometry, etc.). The novel KK-type sensor for the rotational AWS viscometry [19
], shown in Figure complies with this need by means of an axial shift facility for adjusting Δz
and, subsequently, the gap thickness h
is given by
Figure 5 KK sensor for AWS viscometry operating under HAAKE RS 600 rotational viscometer. Common geometry parameters for all the KK sensors: H = 60 mm, R = 17.5 mm, cot(θ) = 10. The actual gap thickness h is adjustable through axial shift Δz, see (more ...)
where h0 corresponds to h at the starting position Δz = 0. Both the working surfaces of the sensor are the coaxial cones of the same cone angle θ, as in a Morse clutch. The gap thickness can be adjusted over a broad range of 100-2500 μm with substantially (ten times) higher accuracy than for the plate-plate (PP) sensor. At the same time, the KK sensor displays much lesser edge effects and better reproducibility. In many applications, it is important to note that the measurements with a varied gap thickness can be made without refilling samples.
The fully automated rotational rheometer HAAKE RS 600 has been used both for driving the KK sensors and for data acquisition. When operating the KK sensor under HAAKE software RheoWin
, it is appropriate to identify it with a PP-type sensor. Primary data in the text files, generated by the HAAKE RheoWin
software, were further treated using a home-made software AWSWork
, described in [19
Correction on centrifugal effects in AWS rotational viscometry
The original theory [19
] of the KK sensors ignores possible inertia effects at the edges of rotating spindle. An additional correction E
of the shear stress on inertia was until now considered only for the standard cylinder-cylinder Z40 DIN sensor [20
]. This result can be rearranged to a local edge correction for a single semi-infinite cylinder by radius R
rotating with a speed Ω in an infinite coaxial cylindrical vessel by radius R
+ h = R
(1 + κ), filled with a Newtonian liquid of kinematic viscosity υ = 1/(
where κ h
= 7.0 × 10-4
, and b
= 2.7 × 10-4
For a KK-type conical spindle, the local edge effects are related to different radii at the both fronts, R
, respectively, with a common h
and λ = 1 - tan(θ
, Figure . The final correction on centrifugal effects can be approximated for Newtonian liquids by the formula: