By definition, fluid materials are systems which flow when subjected to stress. Analyzing how they respond to an input stress is the main objective of rheological testing and may be a complicated issue.
Fluid materials are classified broadly as simple and structured fluids. Simple fluids are materials consisting of a homogenous phase such as a pure substance or a solution. Materials consisting of multiple phases such as an emulsion of immiscible liquids, gas particles in foam, solid particles dispersed in a liquid, and semisolids consisting of a multiphase structure and exhibiting a complex flow behavior are called structured fluids. This is because the interactions of their constituents generally dominate their rheological behavior.
The stability of structured fluids is affected by various factors. The flow properties of dispersions are greatly influenced by the viscosity of the liquid phase in them. Factors such as particle shape, size, and concentration and any attraction with the continuous phase wherein dispersions are suspended also affect the performance of dispersions.
Particles in suspension form a network structure in the existence of a repulsive electrostatic or steric force between them, making the suspension stable when undisturbed. This delicate structure can be destroyed by shearing or even Brownian motion and consequently the viscosity of the fluids is affected. Figure 1 shows the complex flow behavior (Newtonian fluid behavior) of a structured fluid.
Figure 1. Viscosity of a structured fluid as a function of shear rate and particle concentration
The viscosity of most of these materials decreases at higher rates of shear velocity resp, stress. This phenomenon is called shear thinning, which gradually becomes larger with increasing volume concentration of solid particles. The material becomes yielding due to the disappearance of the low shear rate viscosity region at high concentration of solid content.
The viscosity of some materials increases with an increasing rate or stress after the shear thinning region, typically a result of structure rearrangements caused by the applied shear. This behavior is called flow induced shear thickening.
Characteristic Flow Parameters and Functions
According to Eugene Bingham, it is necessary to attain a critical level of stress to make most real fluids flow. The material acts like a solid below this critical stress (τy), absorbing the stress energy without flowing. The material yields to flow after reaching the threshold of critical stress, which is called the yield stress. Bingham Fluids are materials exhibiting Newtonian flow above the yield stress.
Many materials do not show Newtonian flow after the yield, but experience a drop in viscosity until a plateau is reached. Toothpastes, drilling muds, lipsticks are such shear thinning non-Newtonian materials with a yield stress.
Pseudoplasticity and Dilatancy
Pseudoplastic materials such as paints and cosmetics exhibit a nonlinear behavior, but do not have a yield stress. Upon application of stress, they tend to flow immediately. They also exhibit shear thinning behavior. Figure 2 depicts a plot of viscosity versus shear rate for various materials.
Figure 2. Viscosity versus shear rate for different types of material
The viscosity of some materials such as quicksand and moist beach sand increases upon stirring or shearing. This phenomenon is called dilatancy or shear thickening. Material instability and phase separation or structure rearrangements are the causes of shear thickening.
The steady state of most fluid materials relies on the stabilization of internal network structures, which can be destroyed upon application of shearing and take time to rebuild. The viscosity reaches a plateau following the establishment of equilibrium between structure breakdown and rebuilding. The material rebuilds its internal network and consequently its viscosity upon removal of the stress (Figure 3). This phenomenon is called Thixotropy.
Figure 3. Structure build up after previous shear monitored with small strain amplitude oscillatory testing
The viscosity of a thixotropic fluid declines over time upon application of a constant shear rate. Conversely, the viscosity of a rheopectic fluid such as a dense suspension of latex particals or plastisols increases upon applying shear force. A hysteresis loop is formed by the viscosity-shear rate curve and there is possibility for hysteresis to be repeated indefinitely.
This is a way of distinguishing true and apparent rheopectic behavior. The viscosity of fluids that modify physically or chemically (solvent evaporation and gelling) upon application of a shear also increases. However, these changes are irreversible and therefore do not represent true rheopexy.
Time Dependency- Creep and Creep Recovery
Hookean and Newtonian materials respond instantaneously under an imposed input stress or strain rate. Viscoelastic materials do not respond instantaneously with constant flow even if the applied stress is higher than the critical stress or yield point. They return to their original state when the stress is removed, but gradually and generally incompletely. This phenomenon is called creep.
The yield stress of materials can be determined using creep studies (Figure 4). The material acts like a solid and experiences complete recovery when the stress is less than the yield stress. Incomplete recovery indicates that the material has attained its yield stress.
Figure 4. Series of creep tests to determine the yield point
Rheological Test Methods
Yield Stress and Stress Ramp
The Yield stress is a key parameter in production, determining the force required to fill a product into its container or start pumping via a pipeline. The yield stress is often measured by the stress ramp test (Figure 5). The stress at the viscosity maximum, which can be readily measured for most structured fluids, is a measure for the yield stress.
Figure 5. Yield stress measurement of a cosmetic cream based on the viscosity maximum method in a stress ramp
Critical Strain and Strain Sweep
A viscoelastic material exhibits linear rheological properties below a critical strain level gc, beyond which it shows a non-linear behavior and the storage modulus drops. Therefore, the measurement of the amplitude dependence of the storage and loss moduli (G’, G”) is a first step in the characterization of visco-elastic behavior. The extent of linearity of a material is established by a strain sweep (Figure 6). The strength of the colloidal forces is represented by tan d = (G”/G’). An intermediate tan d is preferred for a stable system.
Figure 6. Strain sweep for a water-based acrylic coating
Structure and Frequency Sweep
After defining the linear viscoelastic region of a fluid by a strain sweep, a frequency sweep at a strain less than the critical strain (γc) can be used to characterize the structure of the fluid to gain insights into the effect of colloidal forces, and the interactions among droplets or particles. Measurements in a frequency sweep are performed over a range of oscillation frequencies at a stable oscillation amplitude and temperature.
Below the critical strain, the frequency often does not have an effect on the elastic modulus G’ as would be anticipated from a structured or solid-like material. The materials behave more fluid-like when the elastic modulus is more frequency dependent (Figure 7).
Figure 7. Frequency sweep on a simulated rocket propellant material: shows a more fluid-like behavior at high strain amplitudes (G”>G’), more solid-like at low strains (G’>G”)
Yield Stress and Creep Recovery
The time-dependent characteristics of a sample can be analyzed using a creep test, which provides key parameters such as equilibrium compliance (Jeo) and zero shear viscosity (ηo) to measure the elastic recoil of the material (Figure 8). After allowing a sample to creep under load, its extent of recovery is measured subsequent to the removal of the imposed stress in order to obtain its elastic behavior.
Figure 8. Creep recovery of cookie dough
Structure Changes and Thixotropic Loop
The structure of a thixotropic material breaks down under an imposed shear and recovers on standing. This characteristic is crucial for products such as cosmetics and paints. A time lag is necessary to level the paint and after which the paint must be able to rebuild its viscosity to avoid drips and sagging. This behavior is also crucial in food products such as mayonnaise. The thixotropy of three hand lotions is presented in Figure 9, wherein the area between the curves represents the extent of the thixotropy.
Figure 9. Thixotropy of hand lotions - Stress ramps at 25 °C
Flow Curve and Step Shear Rate
The processing and performance data of a material can be obtained from its viscosity in accordance with the rate at which it is sheared. Materials exhibit low shear rate behavior in storage conditions. Materials that may have the same behavior at one end of the flow curve may behave differently at the other end due to structural differences (Figure 10).
Figure 10. Flow curve of two adhesive dispersions. The products differ significantly at high shear rates.
Temperature Dependence in Oscillatory Temperature Ramp
Figure 11 shows a dynamic temperature ramp study involved cooling carrageenan from 70 to 20°C at a rate of 1.5°C/min and keeping the sample at the lower temperature for 1h. The material experienced high strain (10%) during the cooling period, but a very low strain (0.1%) during the isothermal period to avoid disrupting the structure being created at that low temperature.
Figure 11. Carrageenan temperature ramp is used to reproduce production cycles, storage or use conditions
With dynamic temperature ramp studies, production, storage and use conditions can be simulated or long-term stability of products such as cosmetic creams can be evaluated. Using rheological testing, material behavior can be predicted without expensive batch studies.
Stress relaxation experiments observe the stress decay experienced by a sample over time when it is under an imposed strain created by the application of step strain deformation. The profile of stress relaxation is crucial for materials experiencing repetitive strain to determine the possibility of dissipation of the stress over a time scale of a typical use. Figure 12 shows the stress relaxation of a human cartilage subsequent to subjecting the material to 1% strain at 23°C.
Figure 12. Stress relaxation behavior of human cartilage
Decorative and Protective Coatings
The performance- critical rheological changes taking place during the life cycle of decorative and protective coatings can be measured with rheological tests. Brushability, spatter resistance, leveling, and sagging are among the major performance aspects of coatings that are affected by rheology. The ability to flow laterally and reduce differences in thickness of adjacent areas of the coating is referred to as leveling. Leveling affects color, gloss, smoothness, and mechanical behavior. The subjective ranking of leveling behavior of six latex paint versus their complex viscosity at 25% strain is compared in Table 1.
Table 1. Comparison of leveling behavior versus complex viscosity of Latex paint
||Viscosity (Pa s) @25% strain
The undesirable flow of a coating down a vertical surface is called sagging, which relies on the thickness and viscosity of the coating at low shear rates. Spatter resistance in spraying refers the elasticity of a coating and relies largely on the fluid’s elongational viscosity. Elastic modulus (G’) measurements at high strains help predicting spatter resistance. Brushability is related to the effect of shear rate on viscosity. It is easier to brush pseudoplastic coatings than Newtonian fluids.
Two major classes of inks are those used for screen printing in the graphics arts and electronics industry, and those used for printing newspaper. While their compositions differ, they share a characteristic: rheological complexity. Screen printing is possible becasue inks are thixotropic. Dynamic tests such as thixotropic analysis and strain, temperature and frequency sweeps, and transient stress ramp tests for yield stress measurements are used to support the development of graphic inks.
These dynamic tests are also helpful in the advancement of thick film resistor, solder, electrode, capacitor, and thermoset conductor pastes applied by high speed screen printing onto electronic circuit components and boards. Tests such as steady and transient shear studies and measurement of normal stresses and elongational viscosity need to be performed for the characterization of newspaper inks for better performance. This is because they experience high shear rates and abrupt shear rate and shear direction changes while being passed through the nips of the printing press (Figure 13).
Figure 13. Viscosity and shear stress vs. shear rate for three model inks. The plateau value of the stress at low rate is the yield stress.
Soft solids such as peanut butter, toothpaste and cements have a relatively low modulus, but exhibit solid properties due to a highly elastic response and internal structure upon the application of very small deformations. However, they show a complex flow behavior upon application of larger deformations. They often have a yield stress and are difficult to process due to their solid-like behavior at low strains. After initiating the flow, the velocity profile may show properties of both laminar and plug flow, especially in the presence of a yield stress and phenomena such as wall slip.
However, modern rheometers are capable of measuring the viscoelastic responses of soft solids under conditions similar to processing conditions, providing information to help process design. Rotational shear measurements yield the viscosity versus shear rate response of soft solids, providing data about the transient behavior at the onset of flow or variations in flow rate. The structure of soft solids can be determined by performing dynamic mechanical testing at low strains. Soft solids can be characterized at stress levels above and below the yield point using controlled stress tests (creep, stress ramp) (Figure 14).
Figure 14. Strain dependence of the storage modulus G’ of process cheese spreads differing in pumping ease
Polymers dissolved in solvents are employed widely as adhesives and coatings. And, with added surfactants, polymer solutions provide the basis for paints, cosmetics, detergents, and other recovery fluids. Both steady and dynamic rheological tests can be used to evaluate these materials. Polymers solutions can be evaluated using both steady and dynamic rheological tests. High polymer solutions employed for improved oil recovery lose their efficiency after prolonged use due to a permanent viscosity reduction caused by shear degradation of the polymer at the high shear rates induced by the rotating bit in the well bore. Complexes immune to shear degradation can be formed by developing high viscosities through the combination of a high molecular weight polymer and a surfactant (Figure 15). Rheological tests, especially dynamic time tests, are widely employed in the analysis of solutions of reactive systems to measure the viscoelastic changes experienced by them during their reaction and the formation of products into their desired final form.
Figure 15. Zero Shear Viscosity versus CTAB and TTAB concentration for 0.5% aqueous hmHEC sample at a shear rate below 1–1001/s
A mixture of acicular iron oxide particles dispersed in a polymer solution is used to make magnetic coatings used in products such as hard and floppy computer disks, and audio, video, and digital recording media. For these applications, knowing the behavior of magnetic coatings at low stresses and high shear rates is crucial.
The high shear rate viscosity helps in estimating pumping pressures and coating roll separating forces and torques. The yield stress is crucial for leveling, thickness homogeneity in spin coating, and pick-out in rotogravure coating. Drying behavior and flow stability are also affected by the yield stress. The magnetic forces between particles, their topology, and the extent they are orientable by an external magnetic field can be measured from the shear modulus (Figures16 and 17).
Figure 16. Creep and creep recovery for a model magnetic suspension after imposing a stress of 2 Pa, below its yield stress
Figure 17. Creep and creep recovery for a model magnetic suspension after imposing its yield stress (20 Pa) and a stress substantially higher
Rheological testing is helpful to gain new insights into the human and animal body fluids in different phases of research and development of pharmaceutical, medical and personal hygienic products. For instance, using steady, dynamic, and transient tests, synthetic polypeptides are characterized and evaluated to observe protein network formation in biological fluids; explore the role of some side groups in naturally occurring proteins; study the mechanism of blood clotting; and develop synthetic body fluids for bandage and sanitary napkin evaluations (Figure 18).
Figure 18. Effects of tetrameric concanavalin A on the clot rigidity (G’) and contractile force of platelet-fibrin clots
Rheology of Fluids—Case Studies
Predict the Texture of Food Products
Low fat foods have a great market potential due to increasing health conscious of shoppers. However, their mouth appeal is a major concern. The rheological profile of a food with low fat content is different (Figure 19). The variations in viscosity can have negative impact on customer view for spreading and mouth feel during consumption. A lower G’ (storage energy) represents issues with long term settling of the product, which will also have a negative impact on consumer preference.
Figure 19. Peanut butter frequency sweep for low and high fat content
Many different types of materials are utilized in conditions of immersion. Dry and in situ testing show significantly different behavior profiles. It is necessary to monitor the ability to dissipate stress and the extent of frequency dependence of a material in the conditions it will encounter in its application. Figure 20 illustrates the behavior of a Fibrin Gel immersed in water over a wide frequency range. It is not possible to determine product applicability without such in-situ testing.
Figure 20. Frequency sweep of an immersed fibrin gel
Sol-Gel Transition of PVC Gels
A polymeric gel is a 3D network generating from flexible chains through physical or chemical interactions. Sol-gel transition represents the transformation from liquid state (sol) to the solid state (gel) and the gel point is the critical transition point. It is possible to determine the gel point rheologically if the loss tangent becomes frequency independent, as a function of the concentration.
The concentration dependence of tan δ for a series of frequencies from 0.1 to 100 rad/s for poly vinyl chloride in bi(2-ethylhexyl) phthalate (PVC in DOP) is presented in Figure 21. From the common point in the multi-frequency plot of tan δ (at constant frequency) versus concentration, the gel point can be easily derived.
Figure 21. Sol-gel transition of PVC gels
This information has been sourced, reviewed and adapted from materials provided by TA Instruments.
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