Principle and structure
The cone plate viscometer is a rotary instrument widely used in rheological measurements, and its core structure consists of a flat plate and a low-angle cone rotor. At the time of measurement, the sample is filled in a narrow gap between the cone and the plate. When the cone or plate rotates at a set angular velocity, the instrument calculates the shear stress on the sample by measuring the torque generated. Its core calculation formula is:
τ = (3M) / (2πR³)
where τ represents the shear stress, M is the measured torque, and R is the radius of the cone. The calculation of the shear rate γ̇ is related to the cone angle θ and the angular velocity Ω:
γ̇ = Ω / θ
This geometry ensures that the shear rate is uniform within the gap, which is crucial for obtaining accurate rheological data.
Adaptability
In ink R&D and quality control, only a small number of samples are often available. Cone plate viscometers are ideal due to the small sample volume required (typically 0.5 to 2 ml). Its narrow gap design not only reduces sample usage but also minimizes interference from solvent volatilization in the sample, ensuring the stability of the measurement process. Smaller gaps can be challenging for ink systems containing particles, but can be effectively measured by optimizing the cone angle (e.g., with a small angle cone of 1° to 4°) and surface treatment. Before measuring, it is necessary to ensure that the sample fills the entire gap evenly and without bubbles, which is a prerequisite for reliable data.
Rheological characteristic parameters
Measuring inks using a cone plate viscometer systematically reveals a variety of rheological behaviors that are directly related to printability and final results.
Viscosity Profile and Thixotropy:Flow curves can be plotted by performing steady-state flow scans, which gradually increase or decrease the shear rate and measure the corresponding viscosity. Many inks exhibit shear thinning behavior, where viscosity decreases with increasing shear rate. The thixotropic of the ink, the ability of its viscosity to recover over time, can be quantified by the hysteresis ring area formed by the upward and downward scanning curves, which is closely related to post-print leveling and dot sharpness.
Yield stress:Inks often have yield stress, which means that a minimal stress needs to be overcome before it can start flowing. This value can be determined by performing a stress scan or fitting the flow curve using the Herschel-Barkley model. Yield stress affects the transfer of ink on the anilox roller and the resistance to sagging on the substrate.
Viscoelastic characterization:With a small amplitude oscillation shear test, the linear viscoelastic region of the sample can be measured without damaging the structure. The curves of energy storage modulus (G') and loss modulus (G'') with frequency or strain can be obtained to evaluate the ratio of elasticity to viscous components of inks, which is of great significance for understanding the film-forming and mechanical stability of inks.
Data analysis
To ensure the accuracy and repeatability of measurement results on a small number of ink samples, the following operational points need to be paid attention to. First, the measured temperature must be precisely controlled, and it is recommended to use a viscometer equipped with a Peltier temperature control system. Second, the sample should be pre-sheared and resting before measurement to eliminate historical effects and obtain a consistent initial state. For data analysis, power law models, Carson models, etc. are often used to fit flow curves to obtain quantitative parameters. The following table lists some of the key rheological parameters that can be measured for inks and their implications:
| Measurement parameters | Physical significance and associated printing performance |
| Apparent viscosity (at specific shear rates) | It reflects the flow resistance of ink at the operating speed of the printing machine and affects the amount of transfer. |
| Yield to stress | The minimum stress required for the ink to start flowing is related to sagging resistance and dot sharpness. |
| Thixotropic index | Characterize the viscosity recovery rate, affect leveling and gloss. |
| The strain at the end of the linear viscoelastic zone | Indicates the limit of mechanical strength of the ink's internal structure. |
Conclusion
Cone plate viscometers provide an effective and accurate technical means for measuring the rheological properties of small quantities of ink samples. Through systematic steady-state and dynamic oscillation tests, key parameters such as viscosity curves, yield stress, thixotropy, and viscoelasticity of inks can be fully obtained. These data provide guiding value for understanding the ink's processing performance, storage stability, and final printing results. In practical applications, combined with standardized sample preparation and testing processes, and data analysis according to relevant industry standards, it can provide a solid scientific basis for ink formulation optimization and quality control.
References
1. Barnes, H. A., Hutton, J. F., & Walters, K. Introduction to Rheology.
2. Mewis, J., & Wagner, N. J. Rheology of colloidal dispersions.
3. ASTM D4287 - Standard Test Method for Determining Ink Viscosity at High Shear Rates Using a Cone Plate Viscometer.
4. ISO 2884-1 Colored Paints and Varnishes - Determination of Viscosity Using a Rotary Viscometer - Part 1: Cone Plate Viscometer Operated at High Shear Rates.