Talking about the rheology of ink
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Rheology is the science of studying the deformation and flow of matter. The ideal elastomer and ideal viscous material are virtually non-existent. Many substances, such as paper, ink, etc., have complex deformation laws. The ink is pressed onto the ink roller on the press, transferred to the plate, transferred to the blanket, and finally transferred to the paper. In this process, there are various kinds of deformations and flows. When the ink is deformed by force, it will exhibit some characteristics of elastic deformation and exhibit the viscosity of the fluid. This phenomenon is called viscoelastic phenomenon. The deformation of the viscoelastic object is not only related to the magnitude of the stress, but also to the speed of development of these deformations. Obviously, the rheological properties of printing inks play an important role in printability.
First, the classification of modern fluids
Fluid is one of the objects of rheological research. Modern fluids are classified into Newtonian fluids and non-Newtonian fluids according to their characteristics under certain temperature and shear stress. Suppose a fluid is confined between two parallel plates with a parallel plate area of A. Wherein, the lower plate is stationary, the upper plate is movable, and the distance between them is x, so that the force F acts on the upper plate in a tangential direction, and the sliding speed of the upper plate is v with respect to the lower plate, the clip The velocity of the upper layer of the fluid between the two plates is the highest, the velocity of the intermediate layer is medium, and the velocity of the lower layer is the smallest, as shown in Fig. 1.
For any part of the fluid, the velocity gradient is, because the velocity gradient is actually the rate of change of velocity between the two layers of fluid after the fluid is forced, so in physics, the velocity is called the shear rate, denoted by the symbol D. , which is Shear stress is the pressure per unit area, expressed by the symbol t, in units of dyn/cm, ie
Newtonian fluid
The Newtonian fluid is characterized by a proportional relationship between the shear stress r and the shear rate D in the laminar flow zone. which is:
The viscosity of the fluid in the formula, expressed in Pa·s, is indicated by the symbol PaS. In other words, where the flow state obeys the formula 1.3, it is called Newtonian fluid. For each Newtonian fluid, viscosity is an inherent property, and viscosity is constant when the temperature is constant. The graphical curve of equation (1.3) is called the flow curve, as shown in Figure 2. It is not difficult to see that the flow curve of Newtonian fluid can be determined only by viscosity.
1-Newtonian fluid 2-pseudoplastic fluid 3-plastic fluid 4-expansion fluid
2. Non-Newtonian fluid
Any relationship between shear stress: and shear rate D is not in accordance with Equation 1.3. All fluids are collectively referred to as non-Newtonian fluids. Generalized non-Newtonian fluids include pseudoplastic fluids, plastic fluids, dilatant fluids, and the like. The pseudoplastic fluid is characterized by an increase in the shear rate D and a decrease in viscosity. The characteristic of the plastic fluid is that when the fluid is subjected to a small external force and the shear stress between the fluid layers has not reached a certain value, the fluid is not For the relative flow, only when the external force increases, and the shear stress T between the fluid layers exceeds a certain limit, the fluid begins to generate relative flow. As the shear rate D increases, the viscosity decreases. The characteristic of the dilatant fluid is that As long as there is a shear stress T, no matter how small it is, the shear rate D of the fluid will instantaneously occur under the action of shear stress. However, after the shear rate is generated, the shear rate D increases faster and faster as the shear stress increases. The mathematical model between the shear rate D of the plastic fluid and the shear stress r can be expressed by equation (1.4):
Second, the analysis of rheological parameters of printing ink
1. Viscosity
Viscosity refers to the degree of viscosity when a fluid flows, and is a measure of the ability of the fluid molecules to absorb each other to hinder the relative motion between molecules, and is an indicator of the magnitude of the resistance (or internal friction) of the fluid flow. The viscosity of the ink is important for all types of inks and is one of the important indicators of ink rheology. The viscosity of Newtonian fluid is a constant, independent of the shear rate, defined by equation (2.1):
The viscosity of non-Newtonian fluids is dependent on the shear rate. At very low shear rates, almost all viscous fluids exhibit the properties of Newtonian fluids, ie the shear stress is linear with the shear rate D. The viscosity of the fluid at this stage can be used D (the initial slope of the rheological curve) ), called zero shear viscosity, expressed in the symbol field, defined by equation (2.2):
When the shear rate is high and the r-D relationship is non-linear, the viscosity corresponding to a certain shear rate can be expressed as apparent viscosity. The apparent viscosity is the slope of the secant line OP connecting the origin O and the corresponding point P of the given shear rate on the D curve. Defined by equation (2.3):
The mathematical model between the plastic fluid shear rate and the apparent viscosity can be expressed by equation (2.4):
2. Yield value
The yield value is the minimum force required to force the ink to begin to flow. It is used to characterize the viscous phenomena and properties of the ink from elastic deformation to flow deformation, expressed as the symbol τ, in units of N/cm. The yield value affects the fluidity of the ink. The printing ink is mostly a plastic fluid. The magnitude of the yield value depends mainly on the rheological properties of the binder used, as well as the viscosity itself.
The yield value is measured by a parallel plate viscometer. During the spreading process, the shear stress between the plate and the ink and the weight P of the viscometer (self-weight and its weight) and the spread of the ink column at a given time t The radius R is correlated; and the shear rate D of the corresponding ink is related to the rate of change dR/dt of the spread diameter R and R of the ink column at a given time t. The yield value of the printing ink can be calculated according to Table 1.
3. Thixotropy
Thixotropy means that the shear stress or apparent viscosity has a dependence on shear time due to the rate of destruction of the internal structure of the fluid and the rate of recovery. The size of the thixotropic can be expressed by the thixotropic ring method. The larger the area of the thixotropic ring, the greater the thixotropy of the fluid.
The thixotropic fluid has a time effect, which shows that when the shear rate D is constant and constant, the relationship between the shear stress and the stress time t is expressed as the relationship between the stress first increasing and then decreasing. Let the law of change between the two be represented by the model (2.5)
Third, the model of viscoelastic fluid
Most viscoelastic fluids exhibit a nonlinear relationship between the shear rate D and the shear stress r, so a simple linear model is not sufficient to describe the relationship between the shear rate D of the plastic fluid and the shear stress. The simplest model describing linear viscoelasticity is the Maxwen model, and the nonlinear viscoelastic model is required to describe nonlinear viscoelasticity.
1.Maxwell linear viscoelastic model
The Maxwell model is a model that Maxwel and Voigt began to study the viscoelastic behavior of materials before 1992. It is the simplest model to describe the linear viscoelastic flow. Its mechanical equivalent is equivalent to a spring connected in series with a damper. Three are shown.
2. Nonlinear viscoelastic model
The Maxwen linear viscoelastic model neither predicts the non-Newtonian viscosity nor predicts the normal stress difference, so the Maxwen linear viscoelastic model cannot be used to describe nonlinear viscoelastic fluids. The oldroyd fluid model plays an important role in the constitutive theory and its applications. There are more than a dozen variants of the oldro state model, in which the apparent viscosity of the three-parameter Oldroyd fluid model satisfies the following relationship: The fluid with viscoelasticity consists of elastic stress and viscous stress under constant shear rate. Before yielding, the elastic stress increases, and the structure is not destroyed. When the shear stress increases to a certain extent, the structure begins to be destroyed, the elastic stress decreases with the increase of shear stress, and the viscosity characteristics become more and more obvious.