The determination of the yield value of ink using a falling bar viscometer.

In ink performance evaluation, the yield value is a key rheological parameter that characterizes the minimum shear stress required for the ink to begin flowing. Accurate measurement of this value is essential for predicting the transfer behavior, dot reproducibility and stability of the ink during the printing process. As a classic rheological measurement instrument, the drop rod viscometer provides an intuitive and effective method for determining ink yield value by simulating the flow initiation process under low shear conditions. The principle is based on Stokes' law and plastic fluid mechanics, which estimates the stress threshold for the initial flow of ink by measuring the time or velocity at which a particular rod falls freely in the ink sample.

Principle of determination

The core measurement principle of a drop rod viscometer is a cylindrical rod of known mass and size, which falls vertically under gravity into a sample tube filled with the ink to be tested. As a non-Newtonian fluid, the flow behavior of ink is often described by the Bingham plastic model, which is expressed as:

τ = τ₀ + η_p · γ̇

where τ is the shear stress, τ₀That is, the yield value, η_pis the plastic viscosity, and γ̇ is the shear rate. When the rod falls, the shear stress it generates must overcome the yield value τ of the ink₀Only then can the flow be started. By measuring the uniform falling time or velocity of the rod after reaching the equilibrium velocity, combined with the geometric parameters of the annular gap between the rod and the sample tube, the shear stress and shear rate can be calculated, and then the yield value can be obtained by extrapolation method or calculation model. The relevant calculations can be derived from standard rheological formulas.

Test steps

A standard drop rod viscometer consists of several components: a precision-machined vertical sample tube, a set of calibrated drop rods of different masses and diameters, a thermostatic control, a timing system, and a support frame. Sample tubes are usually made of transparent material for easy observation. Before testing, ensure that the instrument is in a horizontal state and adjust the thermostatic system to a standard test temperature, such as 25°C.

The test procedure is as follows: First, a well-pre-treated and bubble-free ink sample is injected into the sample tube to the specified scale. The drop rod is then selected to match the expected rheological range of the sample and carefully centered on the ink surface. Release the drop stick so that it falls freely, using a timer to accurately record the time it takes for the drop rod to pass through the two predetermined marked intervals on the sample tube. To improve accuracy, it is often necessary to repeat the test multiple times and replace the drop rods of different qualities to obtain data points under a range of shear conditions.

Yield value calculation

Once the raw time data is obtained, it needs to be converted into rheological parameters. The basic calculations involve falling velocity, shear stress and shear rate. For the flow in the annular gap, the shear stress τ can be calculated by the ratio of the net gravity to the side surface area of the falling rod. The shear rate γ̇ is related to the falling velocity and gap size. The stable falling velocity (corresponding to the shear rate) measured under different falling rod masses (corresponding to different shear stresses) is plotted, and the data points are often linear. Extrapolating the fitting line to the shear rate of zero, its intercept on the stress axis is the yield value τ of the ink₀。 The following is a schematic table of key parameter relationships:

This method is suitable for determining the yield value of paste inks and offset printing inks with medium and high viscosity. Its advantage is that the instrument structure is relatively simple, can effectively simulate the low-shear start-up process, and is sensitive to yield values. In practical application, several key points need to be noted: the temperature must be strictly controlled, because the temperature has a significant impact on the rheology of the ink; The sample should be uniform and free of thixotropic failure to reflect the performance of the real structure after recovery. The clearance between the drop rod and the pipe wall should be appropriate, too small may cause wall slippage, and too large may be insensitive to measurement. In addition, for fluids with very low yield values, the method can have increased errors. The test results can be used to guide ink formulation adjustments, optimizing its roll-to-roll transfer performance and anti-settling stability on the press.

Summary

Determining ink yield value using a drop rod viscometer is a classic and practical rheological method. It provides a quantitative basis for understanding the flow initiation characteristics of inks through direct mechanical measurements. Although modern rotary rheometers have more comprehensive functions, the drop rod method still has its application value in specific industrial quality control and R&D scenarios due to its intuitive principle and low equipment requirements. Accurate implementation of this method requires operators to understand the principles and strictly control all aspects of sample preparation, testing conditions, and data processing.