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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] |
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 quantifies the internal frictional force between adjacent layers of fluid that are in relative motion. For instance, when a viscous fluid is forced through a tube, it flows more quickly near the tube's axis than near its walls. Experiments show that some stress (such as a pressure difference between the two ends of the tube) is needed to sustain the flow. This is because a force is required to overcome the friction between the layers of the fluid which are in relative motion. For a tube with a constant rate of flow, the strength of the compensating force is proportional to the fluid's viscosity. In general, viscosity depends on a fluid's state, such as its temperature, pressure, and rate of deformation. However, the dependence on some of these properties is ... [...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] |
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] |
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] |
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] |
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] |
