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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 s ... [...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' ... [...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 Har ... [...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 ... [...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, on ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hermann Schlichting Hermann Schlichting (22 September 1907 – 15 June 1982) was a German fluid dynamics engin |
