Applied Rheology Richard R. Eley, Ph.D. Senior Scientist ICI Paints 16651 Sprague Road Strongsville, OH 44136 The science of Rheology by definition is the study of the deformation and flow behavior of materials. Rheological science seeks to understand the relationship between applied stress and the resulting deformation or flow, particularly for materials showing non-simple responses. Applied rheology endeavors to connect fundamental properties and industrial performance for complex fluids or viscoelastic solids. Successful performance in a wide range of commercial products and industrial processes depends on meeting specific flow requirements. Paints and industrial coatings, molded plastics, adhesives, personal care products and cosmetics, inks, cement, drilling muds, ceramic slips, solder pastes, foodstuffs and medicines are examples of the range of industrial materials whose commercial viability depends on having the right rheology. For each of these materials, the necessary rheological properties must be defined with due regard to the flow conditions which prevail during processing and application. However, it is often difficult to link fundamental properties with real-world performance. Grounding in the principles and practices of rheology is essential to industrial scientists, engineers, chemists, and formulators who need to design products or processes involving non-newtonian materials. Introduction The discussion in this brief article is about protective and decorative coatings, but applies as well to adhesives, sealants, inks, and a host of commercial fluids of complex rheology. Many of these products share a common task: they must be applied to substrates and function as a thin layer. Industrial importance of thin-film fluid flow is illustrated by a few examples: Deposition of films of controlled thickness and uniformity by blade coating, slot-die coating, direct/reverse rollcoating, spray Uniform coating of diffusive layer on controlled-release delivery systems Controlled, precise application of solder pastes and adhesives on microcircuitry boards Liquid permeation of porous materials Foam stability The application, film formation, and defect remediation of thin, fluid layers is an important issue affecting a variety of industrial processes and products. In this presentation, we give a brief survey of some newer aspects of coatings rheology characterization. Emphasis is on interpretation of flow curve data in the analysis of coating flows associated with key application and film formation processes. We will also touch on the value of viscoelastic properties to the foregoing, viscoelastic characterization by creep analysis, and the potential for more detailed understanding offered by computer modeling of coating flows.
Relevance of Rheology to Coatings Formulation To a degree matched by few other materials, rheology determines success for coatings. Though all other properties be acceptable, a coating will usually not meet with success if the rheology is not. Experienced formulators say that more than half the cost of new product development is consumed in getting the rheology right. Moreover, apparently minor changes in a raw material or process can cause significant and unexpected variability in product rheology, a problem that will obviously require urgent resolution. For all these reasons, rheological analysis is a vital and cost-effective tool for the coatings industry. In the times when the majority of paints and industrial coatings were solvent-borne, the array of solvents from which to choose was large, and provided great latitude in formulating for performance. Control of rheology, pigment dispersion stability, substrate wetting, open time, and film formation were relatively straightforward to achieve by solvent selection and blending. The large-scale move toward environmentally compliant coatings (waterborne, higher solids, reduced- or zero-voc) has in general resulted in more complex rheology, while reducing the number of formulating options and at the same time generating a host of performance/application problems. In fact, the achievement of solventborne-like flow and appearance in a waterborne system has remained an elusive target. Reduced-VOC aqueous coatings have consequent higher surface tension and stronger Marangoni effects, which make it more difficult to coat substrates of lower quality (lower or less uniform in surface energy), or substrates having sharp edges or small radii of curvature (holes or sharp corners). Difficult pigment wetting and stable foam are other consequences of reduced solvent content. Rheology and Performance Generally, a prime success criterion is the achievement of a uniform coating layer during the film formation and solidification process. A final film of uniform thickness implies good flow and leveling and the avoidance of defect development in the course of film formation. Achievement of this goal is complicated by complex rheology, complexities of substrate geometry, geometric and rate factors of the application process, surface tension gradients, and environmental factors. For coatings, the process of application and film formation obviously requires not only a large total deformation, but also a high degree of control of flow, in order to achieve success. Flow cannot be controlled unless it can be properly measured. The objective for the applied rheologist, therefore, is to develop methods of rheological characterization that (a) yield accurate data for complex fluids, and (b) are relatable to the critical processes that paints must undergo. To meet the latter objective requires characterization methods that cover a wide range of stresses and time scales. Modern rheological instrumentation is helping to achieve that goal. The understanding of coating performance in terms of rheology is still far from complete, for certain reasons. Among these reasons are (a) the sheer complexity of coatings processes, which complicates the understanding of the role of rheology in process outcomes, and (b) difficulty in linking measured fundamental properties with real-world performance. One answer to the dilemma is computer simulation of coating processes, which utilizes the fundamental rheological data as the required input. A sophisticated fluid dynamics model should take account not only of
coating rheological and physicochemical properties but also of process details, irregular substrate geometry, environmental factors, body forces (gravity and centrifugal force) and changes in properties with evaporation and temperature. However, while computer modeling is perhaps the ideal approach, it is not readily accessible. Fortunately, many coating problems can be understood and solved from shear viscosity and viscoelastic data alone, provided the experiments performed are well designed and the results properly interpreted. The following sections will elaborate on these points, with emphasis on the understanding and interpretation of steady-shear flow curve data. Non-Newtonian Behavior Commercial fluid products comprise a wide variety of materials, with a wide range of consistencies. In general, polymer solutions and melts (above M c ), emulsions, colloidal dispersions, and other suspensions of particulate solids at useful concentrations will be non- Newtonian. For non-newtonian materials, the viscosity is no longer a material constant, but a material function in this case, a function of the shear rate (or shear stress). For non- Newtonian fluids, a viscosity measured at a single shear rate is not an adequate representation of the rheology of the system. For this reason, and because of other more fundamental shortcomings. 1,2 the rugged but simple single-point viscometers commonly used in the industrial laboratory are generally not well suited for the characterization of non-newtonian fluids. Research-quality rheometers measure some rheological property, or material function, such as the viscosity as a function of shear rate or shear stress. Normally, a curve will be produced representing the functional dependence of the measured property. A plot of viscosity against shear rate or shear stress (normally log-log) may be termed a flow curve, and may be generated using equilibrium or non-equilibrium flow measurement methods. 2 We will neglect here the subjects of rheological models, mechanisms of shear thinning and shear thickening, and yield behavior. Detailed discussions of these important topics, as well as definitions of rheological terms can be found in [1] and [2] and references therein. Controlled Stress and Controlled Rate One has a choice of working principles in modern rotational rheometers: either controlled strain (or controlled strain rate) or controlled stress. The difference is in whether the torque or the angular displacement is the controlled variable. In a controlled-strain instrument the angular displacement (or the angular velocity) is the independent (controlled) variable and the viscous drag-torque the dependent (measured) variable. Controlled-stress instruments in actuality control the torque, and measure the resulting angular displacement. Instruments of the controlled-strain type include, for example, the TA Instruments Weissenberg Rheogoniometer, Haake CV, Rheometrics ARES, and Bohlin CVO. Instruments of the 1. Eley, R. R., Rheology and viscometry, ASTM Paint and Coatings Testing Manual, 14 th ed., ASTM, Philadelphia, 1995, Chap. 33, 333-368. 2. Eley, R. R., Principles and methods of rheology in coatings, in Encyclopedia of Analytical Chemistry: Instrumentation and Applications, R. A. Meyers, Ed., J. Wiley & Sons, Ltd., (2000).
controlled-stress type include the TA Instruments AR-1000, Rheometrics SR5, Bohlin CSR, Haake RS, and Physica MC rheometers. Each of the two main instrument types has characteristic advantages and limitations. The choice between them depends on the material under test and the intended experiments. In terms of performance, controlled-stress (CS) instruments can measure much lower angular velocities than can controlled-strain-rate (CR) instruments, but CS instruments tend to be more limited at the high angular velocity and oscillation frequency end. CS is better suited to measure long relaxation times, an advantage of its typically stable torque capability and high angular resolution. CR instruments impose a shear-rate sweep while measuring the drag-torque response of materials. Structured fluids tend to be shear-sensitive (more precisely, strain-sensitive). Consequently, as strain increases exponentially under a linear strain-rate sweep protocol, fluid structure tends to collapse rapidly, with the result that relatively few data points are obtained to provide information on structure. In contrast, CS devices use linear (and logarithmic) rates of stress increase, a test mode which allows materials to obey their own rules of stress-strain response. CS instruments are especially useful for characterizing structured fluids and granular dispersions such as paint, printing ink, adhesives, ceramic slips, coal slurries, cement, pigment and colorant dispersions, drilling muds, medicines, foodstuffs, personal care products and cosmetics, solder pastes, etc. This is particularly true where materials exhibit apparent yield behavior. CS instruments can, in principle, directly measure the stress at the onset of yield, avoiding errors associated with extrapolation or curve-fitting methods. Taking coating flows as a case in point, it is important to realize that the proper variable for correlating coating rheology to real-world coating processes is the shear stress, not the shear rate. First of all, coating flows are the outcome of the sum of forces acting on a fluid coating layer. That is, the rheological response to those forces determines the resulting coating flow. Therefore, coating flows are not driven at a characteristic shear rate, but rather the observed shear rate is the resultant of the stress driving the process and the corresponding viscosity at that stress. Using stress as the controlled or independent variable is, in this sense, the more natural way to characterize coatings and other complex fluids. Rheology of Coating Application and Film Formation In graphing the viscosity flow curve, the usual practice is to plot with shear rate as the independent variable. We prefer to use the shear stress as the abscissa for several reasons: i) the torque (shear stress) is the independent variable for the rheometer used, ii) many industrial flows are governed by the available shear stress, with the shear rate a rheology-dependent variable, iii) separation between flow curves is always better as a function of shear stress (more sensitive variable), and iv) the collapse of particle flocs or gel networks is more obvious. There is an important point to be made in regard to the role of rheology in coating flow during application and leveling, as well as in undesirable flows which may lead to film defects (e.g., sagging, cratering, crawling, edge withdrawal). It is that these flows are driven by specific shear stresses, which can be calculated from the forces acting (e.g., gravity and surface tension) and
the geometry of the film [1,2]. However, these processes can occur over a wide range of shear rates, depending on the coating s viscosity at the acting shear stress. The shear stress acting on a coating layer (for a given process) is independent of the rheology. In contrast, the shear rate will be dependent on paint rheology. For this reason it is preferable to represent flow data as viscosity vs. shear stress plots, as opposed to viscosity vs. shear rate, which is the more common practice. The shear rate is a dependent variable, for real processes. The appropriate independent variable to use to differentiate the performance of paints in terms of their rheology is the shear stress. Not to do so is wrong in principle and will result in incorrect comparisons of paints with respect to their relative rates of, e.g., sagging, leveling, pigment settling, or ease of application. This issue is key to using flow curve data correctly to understand coating performance. Plotting with shear stress as the independent variable, as in Fig. 1, allows straightforward and correct comparison of paints A and B at the specific shear stress for a particular process. The process stresses illustrated in the Figure are for (i) gravity-driven sagging of a 3-mil wet film, (ii) surface tension-driven leveling of surface roughness, and (iii) application by brush or roller. The point is that, no matter what the rheology of a paint, the shear stress acting on a coating layer for a given process is the same (for a given geometry, density, surface tension). The shear rates for these processes, however, are not the same, as illustrated in Fig. 2. Fig. 2 shows the same two paints as in Fig. 1, this time with the viscosity plotted as a function of shear rate. Note that process shear rates are shifted to the left for the higher viscosity paint. Sagging is driven by gravitational shear stress σ g whose magnitude depends solely on the wet film thickness h and density ρ (g is gravitational acceleration): σ g =ρgh cosθ (1) (cos θ =1 for a vertical substrate). Predictions of sagging from comparison of viscosities measured at an arbitrary shear rate will be misleading because paints sag at different shear rates, depending on their rheology. The proper way to predict relative sagging tendency is to first select the governing viscosity from a plot of viscosity vs. shear stress, rather than shear rate. The sagging shear stress calculated from Eq. (1) determines the viscosity controlling sagging (η sag ) from the flow curve. Fig. 1 compares two paints in this manner, with gravitational shear stress levels corresponding to 3 mils wet film thickness indicated. Fig. 2 shows flow curves for the same two paints plotted as a function of shear rate, with the calculated sagging shear rates at 3 mils indicated ( γ & sag =σ sag / η sag ). The solid vertical line in Fig. 2 approximates the shear rate of the Stormer viscometer. The viscosities of the two paints at the Stormer shear rate are about the same (Paint B actually slightly higher). At an arbitrary shear rate of 1 s -1, paint A is about 50% higher than B, whereas at the actual sagging shear stress or shear rates paint A is 600% higher in viscosity. Clearly, comparison of viscosities measured at arbitrary shear rates can lead to incorrect predictions of relative sagging behavior, particularly when flow curves cross over. Comparison of coating rheology as a function of shear stress both simplifies the process and is more correct in principle. In a typical paint development laboratory, rheology is characterized by a two-point method, using the Stormer viscometer and the so-called ICI Cone and Plate Viscometer. The key question to ask is whether such a two-point method adequately represents paint rheology. Fig. 2
shows flow curves for two paints, one mildly shear thinning, while the other shows evidence of a sudden structural collapse at a shear stress of around 250 dyne/cm 2. Superimposed on the curves are points indicating the corresponding measurements from the Stormer and ICI viscometers. It is apparent that the Stormer and ICI data points are located in the sheared-out region of the paint rheology curves. Also shown in Fig. 2 are vertical dashed lines indicating shear stresses driving several important film formation processes, namely, leveling of surface waviness, and gravitational sag at 3, 6, and 12 wet mils film thickness. Clearly, the two-point characterization method would give no information about the leveling/sagging/pigment settling regimes at all. The two-point method also misses the region of high structural viscosity due to flocculation. Presence of the latter will have profound effects on sag, leveling, pigment settling, color, opacity, etc. 1000 A viscosity (poise) 100.0 10.00 1.000 B 3-mil sagging stress Leveling stress Brushing/rolling stress 0.1000 1.000 10.00 100.0 1000 shear stress (dyne/cm^2) 10000 Figure 1. Viscosity vs. shear stress plot for two paints A () and B (). Vertical dashed lines indicate (i) gravitational shear stress driving sagging for 3-wet-mil paint layer; (ii) surface-tension-driven leveling stress; (iii) brushing/rolling application.
viscosity (poise) 1000 100.0 10.00 1.000 Sagging shear rates Leveling shear rates Stormer shear rate 0.1000 0.01000 1.000 100.0 shear rate (1/sec) Application shear rates B A 100000 Figure 2. Viscosity vs. shear rate plot for paints A () and B (). Shear rates for sagging, leveling, application are different for A and B, shifted to left for higher-viscosity paint. Vertical dashed lines indicate shear rates for each paint and process. Vertical solid line is the approximate shear rate for the Stormer Viscometer.