Rheology is the science that studies the deformation and flow of matter. The ideal elastomer and the ideal viscous material do not actually exist, and many materials, such as paper, ink, etc., have their deformation laws complicated. The ink is pressed onto the ink roller on the printing press, transferred to the printing plate, transferred to the blanket, and finally transferred to the paper. In this process, there are various kinds of deformation and flow. When the ink is deformed by force, it will exhibit some characteristics of elastic deformation, and will show fluid viscosity. This phenomenon is called viscoelastic phenomenon. The force deformation of this viscoelastic object is not only related to the magnitude of the stress, but also related to the speed of development of these deformations. Obviously, the rheological properties of printing inks play an important role in printability.
I. Classification of modern fluids
Fluid is one of the objects of rheological research. Modern fluids are classified into Newtonian fluids and non-Newtonian fluids based on their properties under certain temperature and shear stress. Suppose a fluid is confined between two parallel plates with an area of ​​A parallel plates. Among them, the lower plate is stationary, and the upper plate is movable. The distance between them is x, so that the force F acts on the upper plate in a tangential direction. The sliding speed of the upper plate is v relative to the lower plate. The velocity of the upper layer of the fluid between the two plates is the largest, the middle layer has the medium velocity, and the lower layer has the smallest velocity.
For any part of the fluid, the velocity gradient is, because the velocity gradient is actually the rate of change of velocity between two layers of fluid after the fluid is stressed. Therefore, physically speaking, the velocity is called the shear rate and denoted by symbol D. That is, the shear stress is the pressure on a unit area and is represented by the symbol t, and the unit is dyn/cm.
Newtonian fluid
Newtonian fluids are characterized by a direct relationship between the shear stress r and the shear rate D in the laminar flow region. which is:
The viscosity of the fluid in the formula, expressed in Pa.s, is indicated by the symbol PaS. For each Newtonian fluid, the viscosity is an inherent property. When the temperature is constant, the viscosity is a constant.
2. Non-Newtonian fluid
All shear stress: relationship with the shear rate D does not obey the formula 1.3 of all fluids collectively referred to as non-Newtonian fluid. Non-Newtonian fluids in a broad sense include pseudoplastic fluids, plastic fluids, dilatant fluids, and the like. Pseudo-plastic fluids are characterized by a decrease in viscosity when the shear rate D increases. The characteristic of plastic fluids is that when the fluids are subjected to a small external force and the shear stress between the flow layers has not reached a certain value, the fluid is not. When relative flow occurs, only the external force increases. When the shear stress T between the fluid layers exceeds a certain limit, the fluid starts to generate relative flow. As the shear rate D increases, the viscosity decreases. The characteristics of the dilatant fluid are: As long as there is a shear stress T, no matter how small it is, under the effect of shear stress, the shear rate D of the fluid will be generated instantaneously. 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 formula (1.4):
Second, printing ink rheological parameters analysis
Viscosity
Viscosity refers to the degree of viscous fluid flow, is a measure of the relative motion of interfering molecules produced by the mutual absorption of fluid molecules, and is an indicator of the magnitude of resistance (or internal friction) of fluid flow. The viscosity of ink is important for all types of inks and it is one of the important indicators of ink rheology. The viscosity of a Newtonian fluid is a constant and does not depend on the shear rate.
The viscosity of non-Newtonian fluids depends on the shear rate. At very low shear rates, almost all viscous fluids exhibit Newtonian fluid properties, ie shear stress is linearly related to shear rate D. The viscosity of the fluid at this stage can be D (initial slope of the rheological curve). ) to represent zero shear viscosity
When the shear rate is high and the rD relationship is non-linear, the viscosity corresponding to a shear rate can be expressed in terms of apparent viscosity. The apparent viscosity is the slope of the cut OP that connects the origin O and the corresponding point P of the given shear rate on the D curve.
Yield value
The yield value is the minimum force required to force the ink to flow. It is used to characterize the viscous phenomenon and properties of the ink from the elastic deformation to the flow-deformation process. It is expressed by the symbol Ï„ and its unit is 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 mainly depends on the rheological properties of the used binder and its own viscosity.
The yield value was measured using a parallel plate viscometer. During the spreading of the ink, the shear stress between the plate and the ink and the weight P of the viscometer plate (self weight and its weight) and the spread of the ink column at a given time t were measured. The radius R is related; and the corresponding ink shear rate D is related to the rate of change dR/dt of the spreading diameters R and R of the ink column at a given moment t.
3. Thixotropy
Thixotropy refers to the difference in the rate of destruction of the internal structure of the fluid and the rate of recovery, thus showing that the shear stress or apparent viscosity has a dependence on the shear time under a constant shear rate. The thixotropy can be represented by a thixotropic ring method. The larger the thixotropy ring area, the greater the thixotropy of the fluid.
The thixotropic fluid has a time effect, showing that when the shear rate D is constant and remains constant, the relationship between the shear stress and the stress acting time t appears as the relationship between the stress increases first and then decreases.
Third, the viscoelastic fluid model
In most viscoelastic fluids, the relationship between the shear rate D and the shear stress r is non-linear, so a simple linear model is not sufficient to describe the relationship between the shear rate D and the shear stress of the plastic fluid. The simplest model for describing linear viscoelasticity is the Maxwen model, whereas the nonlinear viscoelasticity requires the use of a nonlinear viscoelastic model.
Maxwell linear viscoelastic model
The Maxwell model is a model derived from the study of the viscoelastic behavior of materials by Maxwel and Voigt prior to 1992. It is the simplest model for describing linear viscoelastic flows. Its mechanical analogy is equivalent to a damper in series with a spring.
2. Nonlinear viscoelastic model
The Maxwen linear viscoelastic model can neither predict the non-Newtonian viscosity nor the normal stress difference. Therefore, 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 application. There are more than a dozen variants of the oldro state model, of which the apparent viscosity of the three-parameter Oldroyd fluid model satisfies the following relationships:
With a viscoelastic fluid under a constant shear rate, the shear stress consists of elastic and viscous stresses. Before yielding, the elastic stress increases, and the structure is basically not destroyed. When the shear stress increases to a certain extent, the structure begins to be destroyed, the elastic stress decreases with increasing shear stress, and the viscous characteristic becomes more and more obvious.
I. Classification of modern fluids
Fluid is one of the objects of rheological research. Modern fluids are classified into Newtonian fluids and non-Newtonian fluids based on their properties under certain temperature and shear stress. Suppose a fluid is confined between two parallel plates with an area of ​​A parallel plates. Among them, the lower plate is stationary, and the upper plate is movable. The distance between them is x, so that the force F acts on the upper plate in a tangential direction. The sliding speed of the upper plate is v relative to the lower plate. The velocity of the upper layer of the fluid between the two plates is the largest, the middle layer has the medium velocity, and the lower layer has the smallest velocity.
For any part of the fluid, the velocity gradient is, because the velocity gradient is actually the rate of change of velocity between two layers of fluid after the fluid is stressed. Therefore, physically speaking, the velocity is called the shear rate and denoted by symbol D. That is, the shear stress is the pressure on a unit area and is represented by the symbol t, and the unit is dyn/cm.
Newtonian fluid
Newtonian fluids are characterized by a direct relationship between the shear stress r and the shear rate D in the laminar flow region. which is:
The viscosity of the fluid in the formula, expressed in Pa.s, is indicated by the symbol PaS. For each Newtonian fluid, the viscosity is an inherent property. When the temperature is constant, the viscosity is a constant.
2. Non-Newtonian fluid
All shear stress: relationship with the shear rate D does not obey the formula 1.3 of all fluids collectively referred to as non-Newtonian fluid. Non-Newtonian fluids in a broad sense include pseudoplastic fluids, plastic fluids, dilatant fluids, and the like. Pseudo-plastic fluids are characterized by a decrease in viscosity when the shear rate D increases. The characteristic of plastic fluids is that when the fluids are subjected to a small external force and the shear stress between the flow layers has not reached a certain value, the fluid is not. When relative flow occurs, only the external force increases. When the shear stress T between the fluid layers exceeds a certain limit, the fluid starts to generate relative flow. As the shear rate D increases, the viscosity decreases. The characteristics of the dilatant fluid are: As long as there is a shear stress T, no matter how small it is, under the effect of shear stress, the shear rate D of the fluid will be generated instantaneously. 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 formula (1.4):
Second, printing ink rheological parameters analysis
Viscosity
Viscosity refers to the degree of viscous fluid flow, is a measure of the relative motion of interfering molecules produced by the mutual absorption of fluid molecules, and is an indicator of the magnitude of resistance (or internal friction) of fluid flow. The viscosity of ink is important for all types of inks and it is one of the important indicators of ink rheology. The viscosity of a Newtonian fluid is a constant and does not depend on the shear rate.
The viscosity of non-Newtonian fluids depends on the shear rate. At very low shear rates, almost all viscous fluids exhibit Newtonian fluid properties, ie shear stress is linearly related to shear rate D. The viscosity of the fluid at this stage can be D (initial slope of the rheological curve). ) to represent zero shear viscosity
When the shear rate is high and the rD relationship is non-linear, the viscosity corresponding to a shear rate can be expressed in terms of apparent viscosity. The apparent viscosity is the slope of the cut OP that connects the origin O and the corresponding point P of the given shear rate on the D curve.
Yield value
The yield value is the minimum force required to force the ink to flow. It is used to characterize the viscous phenomenon and properties of the ink from the elastic deformation to the flow-deformation process. It is expressed by the symbol Ï„ and its unit is 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 mainly depends on the rheological properties of the used binder and its own viscosity.
The yield value was measured using a parallel plate viscometer. During the spreading of the ink, the shear stress between the plate and the ink and the weight P of the viscometer plate (self weight and its weight) and the spread of the ink column at a given time t were measured. The radius R is related; and the corresponding ink shear rate D is related to the rate of change dR/dt of the spreading diameters R and R of the ink column at a given moment t.
3. Thixotropy
Thixotropy refers to the difference in the rate of destruction of the internal structure of the fluid and the rate of recovery, thus showing that the shear stress or apparent viscosity has a dependence on the shear time under a constant shear rate. The thixotropy can be represented by a thixotropic ring method. The larger the thixotropy ring area, the greater the thixotropy of the fluid.
The thixotropic fluid has a time effect, showing that when the shear rate D is constant and remains constant, the relationship between the shear stress and the stress acting time t appears as the relationship between the stress increases first and then decreases.
Third, the viscoelastic fluid model
In most viscoelastic fluids, the relationship between the shear rate D and the shear stress r is non-linear, so a simple linear model is not sufficient to describe the relationship between the shear rate D and the shear stress of the plastic fluid. The simplest model for describing linear viscoelasticity is the Maxwen model, whereas the nonlinear viscoelasticity requires the use of a nonlinear viscoelastic model.
Maxwell linear viscoelastic model
The Maxwell model is a model derived from the study of the viscoelastic behavior of materials by Maxwel and Voigt prior to 1992. It is the simplest model for describing linear viscoelastic flows. Its mechanical analogy is equivalent to a damper in series with a spring.
2. Nonlinear viscoelastic model
The Maxwen linear viscoelastic model can neither predict the non-Newtonian viscosity nor the normal stress difference. Therefore, 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 application. There are more than a dozen variants of the oldro state model, of which the apparent viscosity of the three-parameter Oldroyd fluid model satisfies the following relationships:
With a viscoelastic fluid under a constant shear rate, the shear stress consists of elastic and viscous stresses. Before yielding, the elastic stress increases, and the structure is basically not destroyed. When the shear stress increases to a certain extent, the structure begins to be destroyed, the elastic stress decreases with increasing shear stress, and the viscous characteristic becomes more and more obvious.
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