Rheology (/riːˈɒlədʒi/; from Greek ῥέω rhéō, "flow" and -λoγία, -logia, "study of") is the study of the flow of matter, primarily in a liquid state, but also as "soft solids" or solids under conditions in which they respond with plastic flow rather than deforming elastically in response to an applied force. Rheology is the science of deformation and flow within a material. It is a branch of physics which deals with the deformation and flow of materials, both solids and liquids.
The term rheology was coined by Eugene C. Bingham, a professor at Lafayette College, in 1920, from a suggestion by a colleague, Markus Reiner. The term was inspired by the aphorism of Simplicius (often attributed to Heraclitus), panta rhei, "everything flows", and was first used to describe the flow of liquids and the deformation of solids. It applies to substances that have a complex microstructure, such as muds, sludges, suspensions, polymers and other glass formers (e.g., silicates), as well as many foods and additives, bodily fluids (e.g., blood) and other biological materials, and other materials that belong to the class of soft matter such as food.
Newtonian fluids can be characterized by a single coefficient of viscosity for a specific temperature. Although this viscosity will change with temperature, it does not change with the strain rate. Only a small group of fluids exhibit such constant viscosity. The large class of fluids whose viscosity changes with the strain rate (the relative flow velocity) are called non-Newtonian fluids.
Rheology generally accounts for the behavior of non-Newtonian fluids, by characterizing the minimum number of functions that are needed to relate stresses with rate of change of strain or strain rates. For example, ketchup can have its viscosity reduced by shaking (or other forms of mechanical agitation, where the relative movement of different layers in the material actually causes the reduction in viscosity) but water cannot. Ketchup is a shear-thinning material, like yogurt and emulsion paint (US terminology latex paint or acrylic paint), exhibiting thixotropy, where an increase in relative flow velocity will cause a reduction in viscosity, for example, by stirring. Some other non-Newtonian materials show the opposite behavior, rheopecty: viscosity increasing with relative deformation, and are called shear-thickening or dilatant materials. Since Sir Isaac Newton originated the concept of viscosity, the study of liquids with strain-rate-dependent viscosity is also often called Non-Newtonian fluid mechanics.
The experimental characterisation of a material's rheological behaviour is known as rheometry, although the term rheology is frequently used synonymously with rheometry, particularly by experimentalists. Theoretical aspects of rheology are the relation of the flow/deformation behaviour of material and its internal structure (e.g., the orientation and elongation of polymer molecules), and the flow/deformation behaviour of materials that cannot be described by classical fluid mechanics or elasticity.
In practice, rheology is principally concerned with extending continuum mechanics to characterize flow of materials, that exhibits a combination of elastic, viscous and plastic behavior by properly combining elasticity and (Newtonian) fluid mechanics. It is also concerned with establishing predictions for mechanical behavior (on the continuum mechanical scale) based on the micro- or nanostructure of the material, e.g. the molecular size and architecture of polymers in solution or the particle size distribution in a solid suspension. Materials with the characteristics of a fluid will flow when subjected to a stress which is defined as the force per area. There are different sorts of stress (e.g. shear, torsional, etc.) and materials can respond differently under different stresses. Much of theoretical rheology is concerned with associating external forces and torques with internal stresses and internal strain gradients and flow velocities.
The study of the physics of continuous materials
The study of the physics of continuous materials with a defined rest shape.
Describes materials that return to their rest shape after applied stresses are removed.
Describes materials that permanently deform after a sufficient applied stress.
The study of materials with both solid and fluid characteristics.
The study of the physics of continuous materials which deform when subjected to a force.
|Non-Newtonian fluids do not undergo strain rates proportional to the applied shear stress.|
|Newtonian fluids undergo strain rates proportional to the applied shear stress.|
Rheology unites the seemingly unrelated fields of plasticity and non-Newtonian fluid dynamics by recognizing that materials undergoing these types of deformation are unable to support a stress (particularly a shear stress, since it is easier to analyze shear deformation) in static equilibrium. In this sense, a solid undergoing plastic deformation is a fluid, although no viscosity coefficient is associated with this flow. Granular rheology refers to the continuum mechanical description of granular materials.
One of the major tasks of rheology is to empirically establish the relationships between strains (or rates of strain) and stresses, by adequate measurements, although a number of theoretical developments (such as assuring frame invariants) are also required before using the empirical data. These experimental techniques are known as rheometry and are concerned with the determination with well-defined rheological material functions. Such relationships are then amenable to mathematical treatment by the established methods of continuum mechanics.
The characterization of flow or deformation originating from a simple shear stress field is called shear rheometry (or shear rheology). The study of extensional flows is called extensional rheology. Shear flows are much easier to study and thus much more experimental data are available for shear flows than for extensional flows.
On one end of the spectrum we have an inviscid or a simple Newtonian fluid and on the other end, a rigid solid; thus the behaviour of all materials fall somewhere in between these two ends. The difference in material behaviour is characterized by the level and nature of elasticity present in the material when it deforms, which takes the material behaviour to the non-Newtonian regime. The non-dimensional Deborah number is designed to account for the degree of non-Newtonian behaviour in a flow. The Deborah number is defined as the ratio of the characteristic time of relaxation (which purely depends on the material and other conditions like the temperature) to the characteristic time of experiment or observation. Small Deborah numbers represent Newtonian flow, while non-Newtonian (with both viscous and elastic effects present) behaviour occurs for intermediate range Deborah numbers, and high Deborah numbers indicate an elastic/rigid solid. Since Deborah number is a relative quantity, the numerator or the denominator can alter the number. A very small Deborah number can be obtained for a fluid with extremely small relaxation time or a very large experimental time, for example.
In fluid mechanics, the Reynolds number is a measure of the ratio of inertial forces (vsρ) to viscous forces (μ/) and consequently it quantifies the relative importance of these two types of effect for given flow conditions. Under low Reynolds numbers viscous effects dominate and the flow is laminar, whereas at high Reynolds numbers inertia predominates and the flow may be turbulent. However, since rheology is concerned with fluids which do not have a fixed viscosity, but one which can vary with flow and time, calculation of the Reynolds number can be complicated.
It is one of the most important dimensionless numbers in fluid dynamics and is used, usually along with other dimensionless numbers, to provide a criterion for determining dynamic similitude. When two geometrically similar flow patterns, in perhaps different fluids with possibly different flow rates, have the same values for the relevant dimensionless numbers, they are said to be dynamically similar.
Typically it is given as follows:
Rheometers are instruments used to characterize the rheological properties of materials, typically fluids that are melts or solution. These instruments impose a specific stress field or deformation to the fluid, and monitor the resultant deformation or stress. Instruments can be run in steady flow or oscillatory flow, in both shear and extension.
Rheology has applications in materials science, engineering, geophysics, physiology, human biology and pharmaceutics. Materials science is utilized in the production of many industrially important substances, such as cement, paint, and chocolate, which have complex flow characteristics. In addition, plasticity theory has been similarly important for the design of metal forming processes. The science of rheology and the characterization of viscoelastic properties in the production and use of polymeric materials has been critical for the production of many products for use in both the industrial and military sectors. Study of flow properties of liquids is important for pharmacists working in the manufacture of several dosage forms, such as simple liquids, ointments, creams, pastes etc. The flow behavior of liquids under applied stress is of great relevance in the field of pharmacy. Flow properties are used as important quality control tools to maintain the superiority of the product and reduce batch to batch variations.
Examples may be given to illustrate the potential applications of these principles to practical problems in the processing and use of rubbers, plastics, and fibers. Polymers constitute the basic materials of the rubber and plastic industries and are of vital importance to the textile, petroleum, automobile, paper, and pharmaceutical industries. Their viscoelastic properties determine the mechanical performance of the final products of these industries, and also the success of processing methods at intermediate stages of production.
In viscoelastic materials, such as most polymers and plastics, the presence of liquid-like behaviour depends on the properties of and so varies with rate of applied load, i.e., how quickly a force is applied. The silicone toy 'Silly Putty' behaves quite differently depending on the time rate of applying a force. Pull on it slowly and it exhibits continuous flow, similar to that evidenced in a highly viscous liquid. Alternatively, when hit hard and directly, it shatters like a silicate glass.
In addition, conventional rubber undergoes a glass transition (often called a rubber-glass transition). E.g. The Space Shuttle Challenger disaster was caused by rubber O-rings that were being used well below their glass transition temperature on an unusually cold Florida morning, and thus could not flex adequately to form proper seals between sections of the two solid-fuel rocket boosters.
With the viscosity of a sol adjusted into a proper range, both optical quality glass fiber and refractory ceramic fiber can be drawn which are used for fiber optic sensors and thermal insulation, respectively. The mechanisms of hydrolysis and condensation, and the rheological factors that bias the structure toward linear or branched structures are the most critical issues of sol-gel science and technology.
The scientific discipline of geophysics includes study of the flow of molten lava and study of debris flows (fluid mudslides). This disciplinary branch also deals with solid Earth materials which only exhibit flow over extended time-scales. Those that display viscous behaviour are known as rheids. For example, granite can flow plastically with a negligible yield stress at room temperatures (i.e. a viscous flow). Long-term creep experiments (~10 years) indicate that the viscosity of granite and glass under ambient conditions are on the order of 1020 poises.
Physiology includes the study of many bodily fluids that have complex structure and composition, and thus exhibit a wide range of viscoelastic flow characteristics. In particular there is a specialist study of blood flow called hemorheology. This is the study of flow properties of blood and its elements (plasma and formed elements, including red blood cells, white blood cells and platelets). Blood viscosity is determined by plasma viscosity, hematocrit (volume fraction of red blood cell, which constitute 99.9% of the cellular elements) and mechanical behaviour of red blood cells. Therefore, red blood cell mechanics is the major determinant of flow properties of blood.
Thickening agents, or thickeners, are substances which, when added to an aqueous mixture, increase its viscosity without substantially modifying its other properties, such as taste. They provide body, increase stability, and improve suspension of added ingredients. Thickening agents are often used as food additives and in cosmetics and personal hygiene products. Some thickening agents are gelling agents, forming a gel. The agents are materials used to thicken and stabilize liquid solutions, emulsions, and suspensions. They dissolve in the liquid phase as a colloid mixture that forms a weakly cohesive internal structure. Food thickeners frequently are based on either polysaccharides (starches, vegetable gums, and pectin), or proteins.
Concrete's and mortar's workability is related to the rheological properties of the fresh cement paste. The mechanical properties of hardened concrete increase if less water is used in the concrete mix design, however reducing the water-to-cement ratio may decrease the ease of mixing and application. To avoid these undesired effects, superplasticizers are typically added to decrease the apparent yield stress and the viscosity of the fresh paste. Their addition highly improves concrete and mortar properties.
The incorporation of various types of fillers into polymers is a common means of reducing cost and to impart certain desirable mechanical, thermal, electrical and magnetic properties to the resulting material. The advantages that filled polymer systems have to offer come with an increased complexity in the rheological behavior.
Usually when the use of fillers is considered, a compromise has to be made between the improved mechanical properties in the solid state on one side and the increased difficulty in melt processing, the problem of achieving uniform dispersion of the filler in the polymer matrix and the economics of the process due to the added step of compounding on the other. The rheological properties of filled polymers are determined not only by the type and amount of filler, but also by the shape, size and size distribution of its particles. The viscosity of filled systems generally increases with increasing filler fraction. This can be partially ameliorated via broad particle size distributions via the Farris effect. An additional factor is the stress transfer at the filler-polymer interface. The interfacial adhesion can be substantially enhanced via a coupling agent that adheres well to both the polymer and the filler particles. The type and amount of surface treatment on the filler are thus additional parameters affecting the rheological and material properties of filled polymeric systems.
It is important to take into consideration wall slip when performing the rheological characterization of highly filled materials, as there can be a large difference between the actual strain and the measured strain.
A rheologist is an interdisciplinary scientist or engineer who studies the flow of complex liquids or the deformation of soft solids. It is not a primary degree subject; there is no qualification of rheologist as such. Most rheologists have a qualification in mathematics, the physical sciences (e.g. chemistry, physics, biology), engineering (e.g. mechanical, chemical, materials science, plastics engineering and engineering or civil engineering), medicine, or certain technologies, notably materials or food. Typically, a small amount of rheology may be studied when obtaining a degree, but a person working in rheology will extend this knowledge during postgraduate research or by attending short courses and by joining a professional association (see below).
The asthenosphere (from Greek ἀσθενής asthenḗs 'weak' + "sphere") is the highly viscous, mechanically weak and ductilely deforming region of the upper mantle of the Earth. It lies below the lithosphere, at depths between approximately 80 and 200 km (50 and 120 miles) below the surface. The Lithosphere–asthenosphere boundary is usually referred to as LAB. The asthenosphere is almost solid, although some of its regions could be molten (e.g., below mid-ocean ridges). The lower boundary of the asthenosphere is not well defined. The thickness of the asthenosphere depends mainly on the temperature. However, the rheology of the asthenosphere also depends on the rate of deformation, which suggests that the asthenosphere could be also formed as a result of a high rate of deformation. In some regions the asthenosphere could extend as deep as 700 km (430 mi). It is considered the source region of mid-ocean ridge basalt (MORB).Bingham Medal
The Bingham Medal is an annual award for outstanding contributions to the field of rheology awarded at the Annual Meeting of The Society of Rheology. It was instituted in 1948 by the society to commemorate Eugene C. Bingham (1878-1945).British Society of Rheology
A British society for those interested in all aspects of rheology.
Formed in 1940 by G. W. Scott Blair (Secretary), V. G. W. Harrison, and H. R. Lang as the British Rheologist's Club and changed to its present name in 1950. The inaugural meeting was on 16 November 1940 at the University of Reading, at which Sir Geoffrey Taylor was elected President, and its first major conference was at St Hilda's College, Oxford in 1944. A news journal, The Bulletin of the British Rheologist's Club began in 1941. This included some abstracts of papers, which in 1958 became a separate publication Rheology Abstracts which ceased as a printed publication in 2013.Scott Blair went on to become the first President of the renamed society in 1950.It awards a Gold Medal for outstanding contributions to the field as well as other awards and scholarships. It was a founder member of the International Society of Rheology and the European Society of Rheology.Publishes:
Rheology Reviews: peer-refereed academic journal
Rheology Bulletin: news of interest to membersByerlee's law
In rheology, Byerlee's law, also known as Byerlee's friction law concerns the shear stress (τ) required to slide one rock over another. The rocks have macroscopically flat surfaces, but the surfaces have small asperities that make them "rough." For a given experiment and at normal stresses (σn) below about 2000 bars (200 MPa) the shear stress increases approximately linearly with the normal stress (τ = 0.85 σn) and is highly dependent on rock type and the character (roughness) of the surfaces, see Mohr-Coulomb friction law. Byerlee's law states that with increased normal stress the required shear stress continues to increase, but the rate of increase decreases (τ = 0.5 + 0.6σn), and becomes nearly independent of rock type.The law describes an important property of crustal rock, and can be used to determine when slip along a geological fault takes place.Deborah number
The Deborah number (De) is a dimensionless number, often used in rheology to characterize the fluidity of materials under specific flow conditions. It quantifies the observation that given enough time even a solid-like material might flow, or a fluid-like material can act solid when it is deformed rapidly enough. Materials that have low relaxation times flow easily and as such show relatively rapid stress decay.Food rheology
Food rheology is the study of the rheological properties of food, that is, the consistency and flow of food under tightly specified conditions. The consistency, degree of fluidity, and other mechanical properties are important in understanding how long food can be stored, how stable it will remain, and in determining food texture. The acceptability of food products to the consumer is often determined by food texture, such as how spreadable and creamy a food product is. Food rheology is important in quality control during food manufacture and processing. Food rheology terms have been noted since ancient times. In ancient Egypt, bakers judged the consistency of dough by rolling it in their hands.Hemorheology
Hemorheology, also spelled haemorheology (from the Greek ‘αἷμα, haima "blood" and rheology [from Greek ῥέω rhéō, "flow" and -λoγία, -logia, "study of"]), or blood rheology, is the study of flow properties of blood and its elements of plasma and cells. Proper tissue perfusion can occur only when blood's rheological properties are within certain levels. Alterations of these properties play significant roles in disease processes. Blood viscosity is determined by plasma viscosity, hematocrit (volume fraction of red blood cell, which constitute 99.9% of the cellular elements) and mechanical properties of red blood cells. Red blood cells have unique mechanical behavior, which can be discussed under the terms erythrocyte deformability and erythrocyte aggregation. Because of that, blood behaves as a non-Newtonian fluid. As such, the viscosity of blood varies with shear rate. Blood becomes less viscous at high shear rates like those experienced with increased flow such as during exercise or in peak-systole. Therefore, blood is a shear-thinning fluid. Contrarily, blood viscosity increases when shear rate goes down with increased vessel diameters or with low flow, such as downstream from an obstruction or in diastole. Blood viscosity also increases with increases in red cell aggregability (see below).Journal of Rheology
Journal of Rheology is a peer-reviewed scientific journal publishing original (primary) research on all aspects of rheology, the study of those properties of materials which determine their response to mechanical force. It is published bi-monthly by the Society of Rheology through the American Institute of Physics.
The editor-in-chief of Journal of Rheology is Ralph Colby.Manfred Wagner
Manfred Hermann Wagner (born 1948) is the author of Wagner model and the molecular stress function theory for polymer rheology.
He is a Professor for Polymer engineering and Polymer physics at the Technical University of Berlin.
Manfred was born in Stuttgart, Germany in 1948. He obtained his PhD in Chemical engineering at the Institute for Polymer Processing of Stuttgart University. He worked as a post-doc in Polymer Physics under Joachim Meissner at the Eidgenössische Technische Hochschule in Zurich, and in the Plastic industry, then he returned to Stuttgart University in 1988 as Professor for Fluid Dynamics and Rheology. In 1998-1999, he was Dean of the Faculty of Chemical Engineering and Engineering Cybernetics of Stuttgart University. In 1999, he moved to Technical University of Berlin.
His works include the constitutive equations for polymer melts, the application of rheology to the processing of polymers, and structure-property relationships for polymers. The focus of his work on rheology is the field of non-linear shear and elongational behavior of polymer melts and effects of polydispersity, branching and blending on melt behavior. The outstanding point associated with Wagner's work is the relative simplicity of the structural picture of the polymer chain and its respective mathematical formulation.
His latest contribution to the constitutive modeling, the MSF (Molecular Stress Function) theory, assumes a microstructure-based damping function (developed by himself in the late 1970s) that modifies the tube model of Doi and Edwards by considering the tube diameter to change with deformation. This assumption overcomes the most important disadvantage of the DE theory and produces excellent predictions consistent with the picture of the polymer chain.
He has published to date over 100 scientific papers. In 1981, he received the annual award of the British Society of Rheology . The Institute of Materials, London, awarded him the Swinburne Award 2002.
Wagner was the President of the German Society of Rheology 1991-2003, and he is Secretary of the European Society of Rheology since 1996.
Until 2008 Wagner and Rolon-Garrido are studying the constitutive equations model to improve the rheology model at Polymertechnik/Polymerphysik at the TU-Berlin.
Other rheological projects as polymer/additive interactions are being studied by Wagner and Marco Müller.Mouthfeel
Mouthfeel refers to the physical sensations in the mouth caused by food or drink, as distinct from taste. It is a fundamental sensory attribute which, along with taste and smell, determines the overall flavor of a food item. Mouthfeel is also sometimes referred to as texture.It is used in many areas related to the testing and evaluating of foodstuffs, such as wine-tasting and food rheology. It is evaluated from initial perception on the palate, to first bite, through chewing to swallowing and aftertaste. In wine-tasting, for example, mouthfeel is usually used with a modifier (big, sweet, tannic, chewy, etc.) to the general sensation of the wine in the mouth.Mouthfeel is often related to a product's water activity—hard or crisp products having lower water activities and soft products having intermediate to high water activities.Paste (rheology)
In physics, a paste is a substance that behaves as a solid until a sufficiently large load or stress is applied, at which point it flows like a fluid. In rheological terms, a paste is an example of a Bingham plastic fluid.
Pastes typically consist of a suspension of granular material in a background fluid. The individual grains are jammed together like sand on a beach, forming a disordered, glassy or amorphous structure, and giving pastes their solid-like character. It is this "jamming together" that gives pastes some of their most unusual properties; this causes paste to demonstrate properties of fragile matter.
In pharmacology, paste is basic pharmaceutical form. It consists of fatty base (e.g., petroleum jelly) and at least 25% solid substance (e.g., zinc oxide).
Pastes are the semisolid preparations intended for external application to the skin. Usually they are thick and do not melt at normal temperature. Remain on the area for longer duration.
Examples include starch pastes, toothpaste, mustard, and putty.Rheometer
A rheometer is a laboratory device used to measure the way in which a liquid, suspension or slurry flows in response to applied forces. It is used for those fluids which cannot be defined by a single value of viscosity and therefore require more parameters to be set and measured than is the case for a viscometer. It measures the rheology of the fluid.
There are two distinctively different types of rheometers. Rheometers that control the applied shear stress or shear strain are called rotational or shear rheometers, whereas rheometers that apply extensional stress or extensional strain are extensional rheometers.
Rotational or shear type rheometers are usually designed as either a native strain-controlled instrument (control and apply a user-defined shear strain which can then measure the resulting shear stress) or a native stress-controlled instrument (control and apply a user-defined shear stress and measure the resulting shear strain).Rheometry
Rheometry (from the Greek ῥέος – rheos, n, meaning "stream") generically refers to the experimental techniques used to determine the rheological properties of materials, that is the qualitative and quantitative relationships between stresses and strains and their derivatives. The techniques used are experimental. Rheometry investigates materials in relatively simple flows like steady shear flow, small amplitude oscillatory shear, and extensional flow.The choice of the adequate experimental technique depends on the rheological property which has to be determined. This can be the steady shear viscosity, the linear viscoelastic properties (complex viscosity respectively elastic modulus), the elongational properties, etc.
For all real materials, the measured property will be a function of the flow conditions during which it is being measured (shear rate, frequency, etc.) even if for some materials this dependence is vanishingly low under given conditions (see Newtonian fluids).
Rheometry is a specific concern for smart fluids such as electrorheological fluids and magnetorheological fluids, as it is the primary method to quantify the useful properties of these materials.
Rheometry is considered useful in the fields of quality control, process control, and industrial process modelling, among others. For some, the techniques, particularly the qualitative rheological trends, can yield the classification of materials based on the main interactions between different possible elementary components and how they qualitatively affect the rheological behavior of the materials.Robert Byron Bird
Robert Byron Bird (born February 5, 1924 in Bryan, Texas) is a chemical engineer and professor emeritus in the Department of Chemical Engineering at the University of Wisconsin-Madison. He is known for his research in transport phenomena of non-Newtonian fluids, including fluid dynamics of polymers, polymer kinetic theory, and rheology. He, along with Warren E. Stewart and Edwin N. Lightfoot, is an author of the classic textbook Transport Phenomena. Bird was a recipient of the National Medal of Science in 1987.Shear thinning
In rheology, shear thinning is the non-Newtonian behavior of fluids whose viscosity decreases under shear strain. It is sometimes considered synonymous for pseudoplastic behaviour, and is usually defined as excluding time-dependent effects, such as thixotropy. Shear-thinning behaviour is generally not seen in pure liquids with low molecular mass, or ideal solutions of small molecules like sucrose or sodium chloride, but is often seen in polymer solutions and molten polymers, and complex fluids and suspensions like ketchup, whipped cream, blood, paint, and nail polish.Society of Rheology
The Society of Rheology is an American professional society formed in December, 1929 to represent scientists and technologists working in the field of rheology, the science of the deformation and flow of matter. Current membership is of the order of 1700 and meetings are held at leat annually to discuss topics of common interest. The Society publishes scientific and technical papers in the field of rheology in its own Journal of Rheology and presents a number of annual awards to acknowledge and encourage successful research.
The society was one of the founding members of the American Institute of Physics and is also a member of the International Committee on Rheology, which organizes an international congress on the subject every four years.Stiffness
Stiffness is the extent to which an object resists deformation in response to an applied force.The complementary concept is flexibility or pliability: the more flexible an object is, the less stiff it is.Viscosity
The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water.Viscosity can be conceptualized as quantifying the frictional force that arises between adjacent layers of fluid that are in relative motion. For instance, when a fluid is forced through a tube, it flows more quickly near the tube's axis than near its walls. In such a case, experiments show that some stress (such as a pressure difference between the two ends of the tube) is needed to sustain the flow through the tube. This is because a force is required to overcome the friction between the layers of the fluid which are in relative motion: the strength of this force is proportional to the viscosity.
A fluid that has no resistance to shear stress is known as an ideal or inviscid fluid. Zero viscosity is observed only at very low temperatures in superfluids. Otherwise, the second law of thermodynamics requires all fluids to have positive viscosity; such fluids are technically said to be viscous or viscid. A fluid with a high viscosity, such as pitch, may appear to be a solid.Weissenberg number
The Weissenberg number (Wi) is a dimensionless number used in the study of viscoelastic flows. It is named after Karl Weissenberg. The dimensionless number compares the elastic forces to the viscous forces. It can be variously defined, but it is usually given by the relation of stress relaxation time of the fluid and a specific process time. For instance, in simple steady shear, the Weissenberg number, often abbreviated as Wi or We, is defined as the shear rate times the relaxation time . Using the Maxwell Model and the Oldroyd Model, the elastic forces can be written as the first Normal force (N1).
Since this number is obtained from scaling the evolution of the stress, it contains choices for the shear or elongation rate, and the length-scale. Therefore the exact definition of all non dimensional numbers should be given as well as the number itself.
While Wi is similar to the Deborah number and is often confused with it in technical literature, they have different physical interpretations. The Weissenberg number indicates the degree of anisotropy or orientation generated by the deformation, and is appropriate to describe flows with a constant stretch history, such as simple shear. In contrast, the Deborah number should be used to describe flows with a non-constant stretch history, and physically represents the rate at which elastic energy is stored or released.