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Stokes Flow
Stokes flow (named after George Gabriel Stokes), also named creeping flow or creeping motion,Kim, S. & Karrila, S. J. (2005) ''Microhydrodynamics: Principles and Selected Applications'', Dover. . is a type of fluid flow where advection, advective inertial forces are small compared with Viscosity, viscous forces. The Reynolds number is low, i.e. \mathrm \ll 1. This is a typical situation in flows where the fluid velocities are very slow, the viscosities are very large, or the length-scales of the flow are very small. Creeping flow was first studied to understand lubrication. In nature, this type of flow occurs in the swimming of microorganisms and sperm. In technology, it occurs in paint, Microelectromechanical systems, MEMS devices, and in the flow of viscous polymers generally. The equations of motion for Stokes flow, called the Stokes equations, are a linearization of the Navier–Stokes equations, and thus can be solved by a number of well-known methods for linear different ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stokes Sphere
The Stokes parameters are a set of values that describe the Polarization (waves), polarization state of electromagnetic radiation. They were defined by George Gabriel Stokes in 1851, as a mathematically convenient alternative to the more common description of coherence (physics), incoherent or partially polarized radiation in terms of its total Intensity (physics), intensity (''I''), (fractional) degree of polarization (''p''), and the shape parameters of the polarization ellipse. The effect of an optical system on the polarization of light can be determined by constructing the Stokes vector for the input light and applying Mueller calculus, to obtain the Stokes vector of the light leaving the system. They can be determined from directly observable phenomena. The original Stokes paper was discovered independently by Francis Perrin (physicist), Francis Perrin in 1942 and by Subrahamanyan Chandrasekhar in 1947, who named it as the Stokes parameters. Definitions The relationship of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Oseen Equations
In fluid dynamics, the Oseen equations (or Oseen flow) describe the flow of a viscous and incompressible fluid at small Reynolds numbers, as formulated by Carl Wilhelm Oseen in 1910. Oseen flow is an improved description of these flows, as compared to Stokes flow, with the (partial) inclusion of convective acceleration.Batchelor (2000), §4.10, pp. 240–246. Oseen's work is based on the experiments of G.G. Stokes, who had studied the falling of a sphere through a viscous fluid. He developed a correction term, which included inertial factors, for the flow velocity used in Stokes' calculations, to solve the problem known as Stokes' paradox. His approximation leads to an improvement to Stokes' calculations. Equations The Oseen equations are, in case of an object moving with a steady flow velocity U through the fluid—which is at rest far from the object—and in a frame of reference attached to the object: \begin -\rho\mathbf\cdot\nabla\mathbf &= -\nabla p\, +\, \mu \nabla ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Harry L
Harry may refer to: Television * ''Harry'' (American TV series), 1987 comedy series starring Alan Arkin * ''Harry'' (British TV series), 1993 BBC drama that ran for two seasons * ''Harry'' (New Zealand TV series), 2013 crime drama starring Oscar Kightley * ''Harry'' (talk show), 2016 American daytime talk show hosted by Harry Connick Jr. People and fictional characters *Harry (given name), a list of people and fictional characters with the given name, including **Prince Harry, Duke of Sussex Prince Harry, Duke of Sussex, (Henry Charles Albert David; born 15 September 1984) is a member of the British royal family. As the younger son of King Charles III and Diana, Princess of Wales, he is fifth in the line of succession to t ... (born 1984) * Harry (surname), a list of people with the surname Other uses *"Harry", the tunnel used in the Stalag Luft III escape ("The Great Escape") of World War II * ''Harry'' (album), a 1969 album by Harry Nilsson * Harry (derogatory te ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Taylor–Couette Flow
In fluid dynamics, the Taylor–Couette flow consists of a viscous fluid confined in the gap between two rotating cylinders. For low angular velocities, measured by the Reynolds number ''Re'', the flow is steady and purely azimuthal. This laminar flow, basic state is known as circular Couette flow, after Maurice Marie Alfred Couette, who used this experimental device as a means to measure viscosity. Sir Geoffrey Ingram Taylor investigated the stability of Couette flow in a ground-breaking paper. Taylor's paper became a cornerstone in the development of hydrodynamic stability theory and demonstrated that the no-slip condition, which was in dispute by the scientific community at the time, was the correct boundary condition for viscous flows at a solid boundary. Taylor showed that when the angular velocity of the inner cylinder is increased above a certain threshold, Couette flow becomes unstable and a secondary steady state characterized by axisymmetric toroidal vortices, known as T ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stokes' Paradox
In the science of fluid flow, Stokes' paradox is the phenomenon that there can be no creeping flow of a fluid around a disk in two dimensions; or, equivalently, the fact there is no non-trivial steady-state solution for the Stokes flow, Stokes equations around an infinitely long cylinder. This is opposed to the 3-dimensional case, where Stokes' method provides a solution to the problem of flow around a sphere. Stokes' paradox was resolved by Carl Wilhelm Oseen in 1910, by introducing the Oseen equations which improve upon the Stokes equations – by adding Navier–Stokes_equations#Convective_acceleration, convective acceleration. Derivation The velocity vector \mathbf of the fluid may be written in terms of the stream function \psi as : \mathbf = \left(\frac, - \frac\right). The stream function in a Stokes flow problem, \psi satisfies the biharmonic equation. By regarding the (x,y)-plane as the complex plane, the problem may be dealt with using methods of complex analysis. In ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Time Reversible Flow Demonstration In A Taylor-Couette System
Time is the continuous progression of existence that occurs in an apparently irreversible succession from the past, through the present, and into the future. It is a component quantity of various measurements used to sequence events, to compare the duration of events (or the intervals between them), and to quantify rates of change of quantities in material reality or in the conscious experience. Time is often referred to as a fourth dimension, along with three spatial dimensions. Time is one of the seven fundamental physical quantities in both the International System of Units (SI) and International System of Quantities. The SI base unit of time is the second, which is defined by measuring the electronic transition frequency of caesium atoms. General relativity is the primary framework for understanding how spacetime works. Through advances in both theoretical and experimental investigations of spacetime, it has been shown that time can be distorted and dilated, particular ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Boundary Condition
In the study of differential equations, a boundary-value problem is a differential equation subjected to constraints called boundary conditions. A solution to a boundary value problem is a solution to the differential equation which also satisfies the boundary conditions. Boundary value problems arise in several branches of physics as any physical differential equation will have them. Problems involving the wave equation, such as the determination of normal modes, are often stated as boundary value problems. A large class of important boundary value problems are the Sturm–Liouville problems. The analysis of these problems, in the linear case, involves the eigenfunctions of a differential operator. To be useful in applications, a boundary value problem should be well posed. This means that given the input to the problem there exists a unique solution, which depends continuously on the input. Much theoretical work in the field of partial differential equations is devote ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Distinguished Limit
In mathematics, a distinguished limit is an appropriately chosen scale factor used in the method of matched asymptotic expansions. External links Singular perturbation theory Scholarpedia ''Scholarpedia'' is an English-language wiki-based online encyclopedia with features commonly associated with Open access (publishing), open-access online academic journals, which aims to have quality content in science and medicine. ''Scholarpe ... Differential equations Asymptotic analysis {{Mathanalysis-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Leading-order
The leading-order terms (or leading-order corrections) within a mathematical equation, expression or model are the terms with the largest order of magnitude.J.K.Hunter, ''Asymptotic Analysis and Singular Perturbation Theory'', 2004. http://www.math.ucdavis.edu/~hunter/notes/asy.pdf The sizes of the different terms in the equation(s) will change as the variables change, and hence, which terms are leading-order may also change. A common and powerful way of simplifying and understanding a wide variety of complicated mathematical models is to investigate which terms are the largest (and therefore most important), for particular sizes of the variables and parameters, and analyse the behaviour produced by just these terms (regarding the other smaller terms as negligible). This gives the main behaviour – the true behaviour is only small deviations away from this. The main behaviour may be captured sufficiently well by just the strictly leading-order terms, or it may be decided that ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Incompressible Flow
In fluid mechanics, or more generally continuum mechanics, incompressible flow is a flow in which the material density does not vary over time. Equivalently, the divergence of an incompressible flow velocity is zero. Under certain conditions, the flow of compressible fluids can be modelled as incompressible flow to a good approximation. Derivation The fundamental requirement for incompressible flow is that the density, \rho , is constant within a small element volume, ''dV'', which moves at the flow velocity u. Mathematically, this constraint implies that the material derivative (discussed below) of the density must vanish to ensure incompressible flow. Before introducing this constraint, we must apply the conservation of mass to generate the necessary relations. The mass is calculated by a volume integral of the density, \rho : : = . The conservation of mass requires that the time derivative of the mass inside a control volume be equal to the mass flux, J, acro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Conservation Of Mass
In physics and chemistry, the law of conservation of mass or principle of mass conservation states that for any system closed to all transfers of matter the mass of the system must remain constant over time. The law implies that mass can neither be created nor destroyed, although it may be rearranged in space, or the entities associated with it may be changed in form. For example, in chemical reactions, the mass of the chemical components before the reaction is equal to the mass of the components after the reaction. Thus, during any chemical reaction and low-energy thermodynamic processes in an isolated system, the total mass of the reactants, or starting materials, must be equal to the mass of the products. The concept of mass conservation is widely used in many fields such as chemistry, mechanics, and fluid dynamics. Historically, mass conservation in chemical reactions was primarily demonstrated in the 17th century and finally confirmed by Antoine Lavoisier in the late 18 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
