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Generalized Newtonian Fluid
A generalized Newtonian fluid is an idealized fluid for which the shear stress is a function of shear rate at the particular time, but not dependent upon the history of deformation. Although this type of fluid is non-Newtonian (i.e. non-linear) in nature, its constitutive equation is a generalised form of the Newtonian fluid. Generalised Newtonian fluids satisfy the following rheological equation: :\tau = \mu_( \dot ) \dot where \tau is the shear stress, and \dot is the shear rate. The quantity \mu_ represents an '' apparent viscosity'' or '' effective viscosity'' as a function of the shear rate. The most commonly used types of generalized Newtonian fluids are: *Power-law fluid * Cross fluid * Carreau fluid * Bingham fluid It has been shown that lubrication theory may be applied to all generalized Newtonian fluids in both two and three dimensions. See also *Navier–Stokes equations The Navier–Stokes equations ( ) are partial differential equations which describe the motio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fluid
In physics, a fluid is a liquid, gas, or other material that may continuously motion, move and Deformation (physics), deform (''flow'') under an applied shear stress, or external force. They have zero shear modulus, or, in simpler terms, are Matter, substances which cannot resist any shear force applied to them. Although the term ''fluid'' generally includes both the liquid and gas phases, its definition varies among branches of science. Definitions of ''solid'' vary as well, and depending on field, some substances can have both fluid and solid properties. Non-Newtonian fluids like Silly Putty appear to behave similar to a solid when a sudden force is applied. Substances with a very high viscosity such as Pitch (resin), pitch appear to behave like a solid (see pitch drop experiment) as well. In particle physics, the concept is extended to include fluidic matters other than liquids or gases. A fluid in medicine or biology refers to any liquid constituent of the body (body fluid ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Shear Stress
Shear stress (often denoted by , Greek alphabet, Greek: tau) is the component of stress (physics), stress coplanar with a material cross section. It arises from the shear force, the component of force vector parallel to the material cross section. ''Normal stress'', on the other hand, arises from the force vector component perpendicular to the material cross section on which it acts. General shear stress The formula to calculate average shear stress or force per unit area is: \tau = ,where is the force applied and is the cross-sectional area. The area involved corresponds to the material face (geometry), face parallel to the applied force vector, i.e., with surface normal vector perpendicular to the force. Other forms Wall shear stress Wall shear stress expresses the retarding force (per unit area) from a wall in the layers of a fluid flowing next to the wall. It is defined as:\tau_w := \mu\left.\frac\_,where is the dynamic viscosity, is the flow velocity, and is the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Shear Rate
In physics, mechanics and other areas of science, shear rate is the rate at which a progressive shear strain is applied to some material, causing shearing to the material. Shear rate is a measure of how the velocity changes with distance. Simple shear The shear rate for a fluid flowing between two parallel plates, one moving at a constant speed and the other one stationary ( Couette flow), is defined by :\dot\gamma = \frac, where: *\dot\gamma is the shear rate, measured in reciprocal seconds; * is the velocity of the moving plate, measured in meters per second; * is the distance between the two parallel plates, measured in meters. Or: : \dot\gamma_ = \frac + \frac. For the simple shear case, it is just a gradient of velocity in a flowing material. The SI unit of measurement for shear rate is s−1, expressed as "reciprocal seconds" or " inverse seconds". However, when modelling fluids in 3D, it is common to consider a scalar value for the shear rate by calculating the s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Constitutive Equation
In physics and engineering, a constitutive equation or constitutive relation is a relation between two or more physical quantities (especially kinetic quantities as related to kinematic quantities) that is specific to a material or substance or field, and approximates its response to external stimuli, usually as applied fields or forces. They are combined with other equations governing physical laws to solve physical problems; for example in fluid mechanics the flow of a fluid in a pipe, in solid state physics the response of a crystal to an electric field, or in structural analysis, the connection between applied stresses or loads to strains or deformations. Some constitutive equations are simply phenomenological; others are derived from first principles. A common approximate constitutive equation frequently is expressed as a simple proportionality using a parameter taken to be a property of the material, such as electrical conductivity or a spring constant. Howe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Newtonian Fluid
A Newtonian fluid is a fluid in which the viscous stresses arising from its flow are at every point linearly correlated to the local strain rate — the rate of change of its deformation over time. Stresses are proportional to the rate of change of the fluid's velocity vector. A fluid is Newtonian only if the tensors that describe the viscous stress and the strain rate are related by a constant viscosity tensor that does not depend on the stress state and velocity of the flow. If the fluid is also isotropic (i.e., its mechanical properties are the same along any direction), the viscosity tensor reduces to two real coefficients, describing the fluid's resistance to continuous shear deformation and continuous compression or expansion, respectively. Newtonian fluids are the easiest mathematical models of fluids that account for viscosity. While no real fluid fits the definition perfectly, many common liquids and gases, such as water and air, can be assumed to be Newtonian fo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rheological
Rheology (; ) is the study of the flow of matter, primarily in a fluid (liquid or gas) 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 forcRheology is the branch of physics that deals with the deformation and flow of materials, both solids and liquids.W. R. Schowalter (1978) Mechanics of Non-Newtonian Fluids Pergamon 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 Deborah Number The term was inspired by the of |
Apparent Viscosity
In fluid mechanics, apparent viscosity (sometimes denoted ) is the shear stress applied to a fluid divided by the shear rate: :\eta = \frac For a Newtonian fluid, the apparent viscosity is constant, and equal to the Newtonian viscosity of the fluid, but for non-Newtonian fluids, the apparent viscosity depends on the shear rate. Apparent viscosity has the SI derived unit Pa·s ( Pascal-second), but the centipoise is frequently used in practice: (1 mPa·s = 1 cP). Application A single viscosity measurement at a constant speed in a typical viscometer is a measurement of the instrument viscosity of a fluid (not the apparent viscosity). In the case of non-Newtonian fluids, measurement of apparent viscosity without knowledge of the shear rate is of limited value: the measurement cannot be compared to other measurements if the speed and geometry of the two instruments is not identical. An apparent viscosity that is reported without the shear rate or information about the instrument ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Power-law Fluid
In continuum mechanics, a power-law fluid, or the Ostwald–de Waele relationship, is a type of generalized Newtonian fluid. This mathematical relationship is useful because of its simplicity, but only approximately describes the behaviour of a real non-Newtonian fluid. Power-law fluids can be subdivided into three different types of fluids based on the value of their flow behaviour index: pseudoplastic, Newtonian fluid, and dilatant. A first-order fluid is another name for a power-law fluid with exponential dependence of viscosity on temperature. As a Newtonian fluid in a circular pipe give a quadratic velocity profile, a power-law fluid will result in a power-law velocity profile. Description In continuum mechanics, a power-law fluid, or the Ostwald–de Waele relationship, is a type of generalized Newtonian fluid (time-independent non-Newtonian fluid) for which the shear stress, , is given by :\tau = K \left( \frac \right)^n where: * is the ''flow consistency index'' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cross Fluid
In fluid dynamics, a Cross fluid is a type of generalized Newtonian fluid whose viscosity depends upon shear rate according to the Cross Power Law equation: :\mu_\mathrm(\dot \gamma) = \mu_\infty + \frac where \mu_\mathrm(\dot \gamma) is viscosity as a function of shear rate, \mu_\infty is the infinite-shear-rate viscosity, \mu_0 is the zero-shear-rate viscosity, m is the time constant, and n is the shear-thinning index. The zero-shear viscosity \mu_0 is approached at very low shear rates, while the infinite shear viscosity \mu_\infty is approached at very high shear rates. When \mu_0 > \mu_\infty , the fluid exhibits shear thinning (pseudoplastic) behavior where viscosity decreases with increasing shear rate; when \mu_0 < , the fluid displays (dilatant) behavior where viscosity increases wi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Carreau Fluid
In fluid dynamics, a Carreau fluid is a type of generalized Newtonian fluid (named after Pierre Carreau) where viscosity, \mu_, depends upon the shear rate, \dot \gamma, by the following equation: : \mu_(\dot \gamma) = \mu_ + (\mu_0 - \mu_) \left(1+\left(\lambda \dot \gamma\right) ^2 \right) ^ Where: \mu_0, \mu_, \lambda and n are material coefficients: \mu_0 is the viscosity at zero shear rate (Pa.s), \mu_ is the viscosity at infinite shear rate (Pa.s), \lambda is the characteristic time (s) and n power index. The dynamics of fluid motions is an important area of physics, with many important and commercially significant applications. Computers are often used to calculate the motions of fluids, especially when the applications are of a safety critical nature. Shear rates * At low shear rate ( \dot \gamma \ll 1/\lambda ) a Carreau fluid behaves as a Newtonian fluid with viscosity \mu_0 . * At intermediate shear rates ( \dot \gamma \gtrsim 1/\lambda ), a Carreau fluid behav ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
