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Hele-Shaw Flow
Hele-Shaw flow is defined as Stokes flow between two parallel flat plates separated by an infinitesimally small gap, named after Henry Selby Hele-Shaw, who studied the problem in 1898. Various problems in fluid mechanics can be approximated to Hele-Shaw flows and thus the research of these flows is of importance. Approximation to Hele-Shaw flow is specifically important to micro-flows. This is due to manufacturing techniques, which creates shallow planar configurations, and the typically low Reynolds numbers of micro-flows. The governing equation of Hele-Shaw flows is identical to that of the inviscid potential flow and to the flow of fluid through a porous medium (Darcy's law). It thus permits visualization of this kind of flow in two dimensions. Mathematical formulation of Hele-Shaw flows Let x, y be the directions parallel to the flat plates, and z the perpendicular direction, with H being the gap between the plates (at z=0, H). When the gap between plates is asymptotically sm ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 advective inertial forces are small compared with 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, sperm and the flow of lava. In technology, it occurs in paint, 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 differential equations. The primary Green's ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Henry Selby Hele-Shaw
Henry Selby Hele-Shaw FRS (1854–1941) was an English mechanical and automobile engineer. He was the inventor of the variable-pitch propeller, which contributed to British success in the Battle of Britain in 1940, and he experimented with flows through thin cells. Flows through such configurations are named in his honour ( Hele-Shaw flows). He was also a co-founder of Victaulic. Life Born on 29 July 1854 at Billericay, he was the eldest son of Henry Shaw (1825 – 1880), a lawyer who went bankrupt, and his wife Marion Selby Hele (1834 – 1891), daughter of the Reverend Henry Selby Hele, vicar of Grays Thurrock and grandson of the Reverend George Horne. He was first articled at the age of 17 to Messrs Rouch and Leaker, at the Mardyke Engineering Works, Bristol and served an engineering apprenticeship until 1876. Hele-Shaw was also elected a Whitworth Scholar. He was the first Professor of Engineering at University College, Bristol, and in 1885 became the first to hold the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reynolds Number
In fluid mechanics, the Reynolds number () is a dimensionless quantity that helps predict fluid flow patterns in different situations by measuring the ratio between inertial and viscous forces. At low Reynolds numbers, flows tend to be dominated by laminar (sheet-like) flow, while at high Reynolds numbers flows tend to be turbulent. The turbulence results from differences in the fluid's speed and direction, which may sometimes intersect or even move counter to the overall direction of the flow (eddy currents). These eddy currents begin to churn the flow, using up energy in the process, which for liquids increases the chances of cavitation. The Reynolds number has wide applications, ranging from liquid flow in a pipe to the passage of air over an aircraft wing. It is used to predict the transition from laminar to turbulent flow and is used in the scaling of similar but different-sized flow situations, such as between an aircraft model in a wind tunnel and the full-size v ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Potential Flow
In fluid dynamics, potential flow (or ideal flow) describes the velocity field as the gradient of a scalar function: the velocity potential. As a result, a potential flow is characterized by an irrotational velocity field, which is a valid approximation for several applications. The irrotationality of a potential flow is due to the curl of the gradient of a scalar always being equal to zero. In the case of an incompressible flow the velocity potential satisfies Laplace's equation, and potential theory is applicable. However, potential flows also have been used to describe compressible flows. The potential flow approach occurs in the modeling of both stationary as well as nonstationary flows. Applications of potential flow are for instance: the outer flow field for aerofoils, water waves, electroosmotic flow, and groundwater flow. For flows (or parts thereof) with strong vorticity effects, the potential flow approximation is not applicable. Characteristics and applications ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Darcy's Law
Darcy's law is an equation that describes the flow of a fluid through a porous medium. The law was formulated by Henry Darcy based on results of experiments on the flow of water through beds of sand, forming the basis of hydrogeology, a branch of earth sciences. It is analogous to Ohm's law in electrostatics, linearly relating the volume flow rate of the fluid to the hydraulic head difference (which is often just proportional to the pressure difference) via the hydraulic conductivity. Background Darcy's law was first determined experimentally by Darcy, but has since been derived from the Navier–Stokes equations via homogenization methods. It is analogous to Fourier's law in the field of heat conduction, Ohm's law in the field of electrical networks, and Fick's law in diffusion theory. One application of Darcy's law is in the analysis of water flow through an aquifer; Darcy's law along with the equation of conservation of mass simplifies to the groundwater flow equation, one ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hermann Schlichting
Hermann Schlichting (22 September 1907 – 15 June 1982) was a German fluid dynamics engineer. Life and work Hermann Schlichting studied from 1926 till 1930 mathematics, physics and applied mechanics at the University of Jena, Vienne and Göttingen. In 1930 he wrote his PhD in Göttingen titled ''Über das ebene Windschattenproblem'' and also in the same year passed the state examination as teacher for higher mathematics and physics. His meeting with Ludwig Prandtl had a long-lasting effect on him. He worked from 1931 till 1935 at the Kaiser Wilhelm Institute for Flow Research in Göttingen. His main research area was fluid flows with viscous effects. Simultaneously he also started working on airfoil aerodynamics. In 1935 Schlichting went to Dornier in Friedrichshafen. There he did the planning for the new wind tunnel and after short construction time took charge over it. With it he gained useful experience in the field of aerodynamics. At the age of 30 in 1937 he joined T ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Horace Lamb
Sir Horace Lamb (27 November 1849 – 4 December 1934)R. B. Potts,, ''Australian Dictionary of Biography'', Volume 5, MUP, 1974, pp 54–55. Retrieved 5 Sep 2009 was a British applied mathematician and author of several influential texts on classical physics, among them ''Hydrodynamics'' (1895) and ''Dynamical Theory of Sound'' (1910). Both of these books remain in print. The word vorticity was coined by Lamb in 1916. Biography Early life and education Lamb was born in Stockport, Cheshire, the son of John Lamb and his wife Elizabeth, ''née'' Rangeley. John Lamb was a foreman in a cotton mill who had gained some distinction by the invention of an improvement to spinning machines, he died when his son was a child. Lamb's mother married again, and shortly afterwards Horace went to live with his strict but maternal aunt, Mrs. Holland. He studied at Stockport Grammar School, where he made the acquaintance of a wise and kindly headmaster in the Rev. Charles Hamilton, and a grad ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hele Shaw Geometry
Hele, Hélé'', or ''Hèle may refer to: Places ;in England :in Cornwall *Hele, Cornwall, a village near Bude, Cornwall :in Devon *Hele, Devon, a village near Bradninch in Mid Devon * Hele, North Devon, a village near Ilfracombe **Hele Bay * Hele, Teignbridge, a hamlet near Ashburton * Hele, Torquay, an area of the town of Torquay * Hele, Torridge, a hamlet in the far west of Devon *South Hele, Devon, a hamlet near South Brent *Croker's Hele, Meeth, an historic estate :in Somerset * Hele, Somerset, a village near Taunton ;in China * Hele, Hainan, a township-level division in Hainan :* Hele Railway Station, on the Hainan Eastern Ring Railway in Hainan ;in Greece * Hele (Laconia), a town of ancient Laconia People ;as a first name * Hele Everaus (born 1953), Estonian medical scientist, physician and politician * Hele Kõrve (born 1980), Estonian actress and singer * Hele-Mall Pajumägi (born 1938), Estonian badminton player and coach ;as a surname * Andrew Hele (born 1967), En ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Circulation (physics)
In physics, circulation is the line integral of a vector field around a closed curve. In fluid dynamics, the field is the fluid velocity field. In electrodynamics, it can be the electric or the magnetic field. Circulation was first used independently by Frederick Lanchester, Martin Kutta and Nikolay Zhukovsky. It is usually denoted Γ (Greek uppercase gamma). Definition and properties If V is a vector field and dl is a vector representing the differential length of a small element of a defined curve, the contribution of that differential length to circulation is dΓ: :\mathrm\Gamma=\mathbf\cdot \mathrm\mathbf=, \mathbf, , \mathrm\mathbf, \cos \theta. Here, ''θ'' is the angle between the vectors V and dl. The circulation Γ of a vector field V around a closed curve ''C'' is the line integral: :\Gamma=\oint_\mathbf\cdot \mathrm d \mathbf. In a conservative vector field this integral evaluates to zero for every closed curve. That means that a line integral between any two ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Laplace's Equation
In mathematics and physics, Laplace's equation is a second-order partial differential equation named after Pierre-Simon Laplace, who first studied its properties. This is often written as \nabla^2\! f = 0 or \Delta f = 0, where \Delta = \nabla \cdot \nabla = \nabla^2 is the Laplace operator,The delta symbol, Δ, is also commonly used to represent a finite change in some quantity, for example, \Delta x = x_1 - x_2. Its use to represent the Laplacian should not be confused with this use. \nabla \cdot is the divergence operator (also symbolized "div"), \nabla is the gradient operator (also symbolized "grad"), and f (x, y, z) is a twice-differentiable real-valued function. The Laplace operator therefore maps a scalar function to another scalar function. If the right-hand side is specified as a given function, h(x, y, z), we have \Delta f = h. This is called Poisson's equation, a generalization of Laplace's equation. Laplace's equation and Poisson's equation are the simplest exa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Diffusion-limited Aggregation
Diffusion-limited aggregation (DLA) is the process whereby particles undergoing a random walk due to Brownian motion cluster together to form aggregates of such particles. This theory, proposed by T.A. Witten Jr. and L.M. Sander in 1981, is applicable to aggregation in any system where diffusion is the primary means of transport in the system. DLA can be observed in many systems such as electrodeposition, Hele-Shaw flow, mineral deposits, and dielectric breakdown. The clusters formed in DLA processes are referred to as Brownian trees. These clusters are an example of a fractal. In 2D these fractals exhibit a dimension of approximately 1.71 for free particles that are unrestricted by a lattice, however computer simulation of DLA on a lattice will change the fractal dimension slightly for a DLA in the same embedding dimension. Some variations are also observed depending on the geometry of the growth, whether it be from a single point radially outward or from a plane or line ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lubrication Theory
In fluid dynamics, lubrication theory describes the flow of fluids (liquids or gases) in a geometry in which one dimension is significantly smaller than the others. An example is the flow above air hockey tables, where the thickness of the air layer beneath the puck is much smaller than the dimensions of the puck itself. Internal flows are those where the fluid is fully bounded. Internal flow lubrication theory has many industrial applications because of its role in the design of fluid bearings. Here a key goal of lubrication theory is to determine the pressure distribution in the fluid volume, and hence the forces on the bearing components. The working fluid in this case is often termed a lubricant. Free film lubrication theory is concerned with the case in which one of the surfaces containing the fluid is a free surface. In that case the position of the free surface is itself unknown, and one goal of lubrication theory is then to determine this. Examples include the flow ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
