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Carreau Fluid
Carreau fluid in physics is a type of generalized Newtonian fluid 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 = viscosity at zero shear rate (Pa.s) \mu_ = viscosity at infinite shear rate (Pa.s) \lambda = characteristic time (s) 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. Carreau Fluid 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 behaves as a Power-law fluid. * At high shear rat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Physics
Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular succession of events." Physics is one of the most fundamental scientific disciplines, with its main goal being to understand how the universe behaves. "Physics is one of the most fundamental of the sciences. Scientists of all disciplines use the ideas of physics, including chemists who study the structure of molecules, paleontologists who try to reconstruct how dinosaurs walked, and climatologists who study how human activities affect the atmosphere and oceans. Physics is also the foundation of all engineering and technology. No engineer could design a flat-screen TV, an interplanetary spacecraft, or even a better mousetrap without first understanding the basic laws of physic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 the shear rate. The quantity \mu_ represents an ''apparent'' 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 In physics, the Navier–Stokes equations ( ) are partial differential equations which describe the motion of vis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Shear Rate
In physics, shear rate is the rate at which a progressive shearing deformation is applied to some material. 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". The shear rate at the inner wall of a Newtonian fluid flowing within a pipe is :\dot\gamma = \frac, where: *\dot\gamma is the shear rate, measured in reciprocal seconds; * is the linear fluid velocity; * is the inside diameter of the pipe. The lin ... [...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 (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 simplest 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 for practical c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Power-law Fluid
__NOTOC__ 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'' ( SI units Pa s''n''), * is the shear rate or the velocity gradient perpendicular to the plane of shear (SI unit s−1), and * is the ''flow behavior index'' (dimensionless). The quantity :\mu_\mathrm = K \left( \frac \right)^ represents an ''apparent'' or ''effective viscosity'' as a function of the shear rate (SI unit Pa s). The value of and can be obtained from the graph of \log(\mu_\mathrm) and \log\left( \frac \right) . The slope line gives the value of , from which can be calculated. The intercept at \log\left( \frac \right) = 0 gives the value of . Also known as the Ostwald– de Waele power lawe.g. G. W. Scott Blair ''et al.'', ''J. Phys. Chem''., (1939) 43 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pierre Carreau
Pierre J. Carreau is a modern rheologist, the author of the model of Carreau fluid. He is currently a professor emeritus at École Polytechnique in Montreal Montreal ( ; officially Montréal, ) is the second-most populous city in Canada and most populous city in the Canadian province of Quebec. Founded in 1642 as '' Ville-Marie'', or "City of Mary", it is named after Mount Royal, the triple ... and the founding director of CREPEC (Center for Applied Research on Polymers and Composites presently named Center for Research on High Performance Polymer and Composite Systems). Pierre Carreau is internationally known for his research work on the rheology of polymers, an area in which he co-authored two books and published more than 160 scientific articles, most in leading scientific journals. His best known works on rheological equations and conformation models for polymer systems are considered benchmarks in polymer engineering. The so-called Carreau Viscosity Model is now ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fluid
In physics, a fluid is a liquid, gas, or other material that continuously deforms (''flows'') under an applied shear stress, or external force. They have zero shear modulus, or, in simpler terms, are 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 be both fluid and solid. Viscoelastic 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 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 any liquid constituent of the body (body fluid), whereas "liquid" is not used in this sense. Sometimes liquids given for flui ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cross Fluid
A Cross fluid is a type of generalized Newtonian fluid whose viscosity depends upon shear rate according to the following equation: :\mu_\mathrm(\dot \gamma) = \mu_\infty + \frac where \mu_\mathrm(\dot \gamma) is viscosity as a function of shear rate, \mu_\infty , \mu_0 , k and ''n'' are coefficients. 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. See also * Navier-Stokes equations *Fluid *Carreau fluid *Power-law fluid *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 n ... References *Kennedy, P. K., ''Flow Analysis of Injection Molds''. New York. Hanser. {{ISBN, 1-56990-181-3 Non-Newtonian fluids ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 the shear rate. The quantity \mu_ represents an ''apparent'' 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 In physics, the Navier–Stokes equations ( ) are partial differential equations which describe the motion of vis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
