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Hele–Shaw Flow
Hele-Shaw flow is defined as flow taking place between two parallel flat plates separated by a narrow gap satisfying certain conditions, 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 conditions that needs to be satisfied are :\frac \ll 1, \qquad \frac \frac \ll 1 where h is the gap width between the plates, U is the characteristic velocity scale, l is the characteristic length scale in directions parallel to the plate and \nu is the kinematic viscosity. Specifically, the Reynolds number \mathrm=Uh/\nu need not always be small, but can be order unity or greater as long as it satisfies the condition \mathrm(h/l) \ll 1. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Henry Selby Hele-Shaw
Henry Selby Hele-Shaw Fellow of the Royal Society, FRS (1854–1941) was an English mechanical and automobile engineer. He was the inventor of the Variable-pitch propeller (aeronautics), 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 (bishop), 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 The Whitworth Society, Whitworth Scholar. In 188 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Boundary Layer
In physics and fluid mechanics, a boundary layer is the thin layer of fluid in the immediate vicinity of a Boundary (thermodynamic), bounding surface formed by the fluid flowing along the surface. The fluid's interaction with the wall induces a No-slip condition, no-slip boundary condition (zero velocity at the wall). The flow velocity then monotonically increases above the surface until it returns to the bulk flow velocity. The thin layer consisting of fluid whose velocity has not yet returned to the bulk flow velocity is called the velocity boundary layer. The air next to a human is heated, resulting in gravity-induced convective airflow, which results in both a velocity and thermal boundary layer. A breeze disrupts the boundary layer, and hair and clothing protect it, making the human feel cooler or warmer. On an aircraft wing, the velocity boundary layer is the part of the flow close to the wing, where viscosity, viscous forces distort the surrounding non-viscous flow. In ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hele-Shaw Clutch
The Hele-Shaw clutch was an early form of multi-plate wet clutch, in use around 1900. It was named after its inventor, Professor Henry Selby Hele-Shaw, who was noted for his work in viscosity and flows through small gaps between parallel plates. The clutch was innovative in not relying upon friction, as other clutches did. Description The clutch appears outwardly similar to most other multi-plate clutches. A stack of plates is enclosed in a housing with a divided central shaft. Alternate plates are keyed to either the input or output shafts, through either the inner or outer housings. A pressure plate is arranged at one end of the stack so that an axial force may be applied, compressing the stack and causing it to transmit the drive. Releasing the pressure releases the clutch. In the Hele-Shaw clutch, the many plates are lightweight pressings from thin sheets of steel. Each plate has a ring pressed into it, V-shaped in section and forming a frustum of a cone with each side. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Thin-film Equation
In fluid mechanics, the thin-film equation is a partial differential equation that approximately predicts the time evolution of the thickness of a liquid film that lies on a surface. The equation is derived via lubrication theory which is based on the assumption that the length-scales in the surface directions are significantly larger than in the direction Normal (geometry), normal to the surface. In the non-dimensional form of the Navier–Stokes equations, Navier-Stokes equation the requirement is that terms of order and are negligible, where is the aspect ratio and is the Reynolds number. This significantly simplifies the governing equations. However, lubrication theory, as the name suggests, is typically derived for flow between two solid surfaces, hence the liquid forms a lubricating layer. The thin-film equation holds when there is a single free surface. With two free surfaces, the flow must be treated as a viscous sheet. Definition The basic form of a 2-dimensional t ... [...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] |
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] |
Circulation (physics)
In physics, circulation is the line integral of a vector field around a closed curve embedded in the field. In fluid dynamics, the field is the fluid velocity field. In electrodynamics, it can be the electric or the magnetic field. In aerodynamics, it finds applications in the calculation of lift, for which circulation was first used independently by Frederick Lanchester, Ludwig Prandtl, Martin Kutta and Nikolay Zhukovsky. It is usually denoted (uppercase gamma). Definition and properties If is a vector field and is a vector representing the differential length of a small element of a defined curve, the contribution of that differential length to circulation is : \mathrm\Gamma = \mathbf \cdot \mathrm\mathbf = \left, \mathbf\ \left, \mathrm\mathbf\ \cos \theta. Here, is the angle between the vectors and . The circulation of a vector field around a closed curve is the line integral: \Gamma = \oint_\mathbf \cdot \mathrm d \mathbf. In a conservative vector field ... [...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 in 1786. 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 simp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Viscosity
Viscosity is a measure of a fluid's rate-dependent drag (physics), resistance to a change in shape or to movement of its neighboring portions relative to one another. For liquids, it corresponds to the informal concept of ''thickness''; for example, syrup has a higher viscosity than water. Viscosity is defined scientifically as a force multiplied by a time divided by an area. Thus its SI units are newton-seconds per metre squared, or pascal-seconds. Viscosity quantifies the internal friction, 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 center line than near its walls. Experiments show that some stress (physics), 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reynolds Number
In fluid dynamics, the Reynolds number () is a dimensionless quantity that helps predict fluid flow patterns in different situations by measuring the ratio between Inertia, inertial and viscous forces. At low Reynolds numbers, flows tend to be dominated by laminar flow, laminar (sheet-like) flow, while at high Reynolds numbers, flows tend to be turbulence, 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 (fluid dynamics), 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–turbulent transition, laminar to turbulent flow and is used in the scaling of similar but different-sized fl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Navier–Stokes Equations
The Navier–Stokes equations ( ) are partial differential equations which describe the motion of viscous fluid substances. They were named after French engineer and physicist Claude-Louis Navier and the Irish physicist and mathematician George Gabriel Stokes. They were developed over several decades of progressively building the theories, from 1822 (Navier) to 1842–1850 (Stokes). The Navier–Stokes equations mathematically express momentum balance for Newtonian fluids and make use of conservation of mass. They are sometimes accompanied by an equation of state relating pressure, temperature and density. They arise from applying Isaac Newton's second law to fluid motion, together with the assumption that the stress in the fluid is the sum of a diffusing viscous term (proportional to the gradient of velocity) and a pressure term—hence describing ''viscous flow''. The difference between them and the closely related Euler equations is that Navier–Stokes equat ... [...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) ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
