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Capillary Bridges
Usually, we understand the term capillary bridge as a minimized surface of liquid or membrane, created between two rigid bodies with an arbitrary shape. Capillary bridges also may form between two liquids. Plateau defined a sequence of capillary shapes known as (1) nodoid with 'neck', (2) catenoid, (3) unduloid with 'neck', (4) cylinder, (5) unduloid with 'haunch' (6) sphere and (7) nodoid with 'haunch'. The presence of capillary bridge, depending on their shapes, can lead to attraction or repulsion between the solid bodies. The simplest cases of them are the axisymmetric ones. We distinguished three important classes of bridging, depending on connected bodies surface shapes: * two planar surfaces (fig.1) * planar surface and spherical particle (fig. 2) * two spherical particles (in general, particles may not be of equal sizes, fig. 3) Capillary bridges and their properties may also be influenced by Earth gravity and by properties of the bridged surfaces. The bridging su ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Liquid
A liquid is a nearly incompressible fluid that conforms to the shape of its container but retains a (nearly) constant volume independent of pressure. As such, it is one of the four fundamental states of matter (the others being solid, gas, and plasma), and is the only state with a definite volume but no fixed shape. A liquid is made up of tiny vibrating particles of matter, such as atoms, held together by intermolecular bonds. Like a gas, a liquid is able to flow and take the shape of a container. Most liquids resist compression, although others can be compressed. Unlike a gas, a liquid does not disperse to fill every space of a container, and maintains a fairly constant density. A distinctive property of the liquid state is surface tension, leading to wetting phenomena. Water is by far the most common liquid on Earth. The density of a liquid is usually close to that of a solid, and much higher than that of a gas. Therefore, liquid and solid are both termed condensed matter. O ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Joseph Plateau
Joseph Antoine Ferdinand Plateau (14 October 1801 – 15 September 1883) was a Belgian physicist and mathematician. He was one of the first people to demonstrate the illusion of a moving image. To do this, he used counterrotating disks with repeating drawn images in small increments of motion on one and regularly spaced slits in the other. He called this device of 1832 the phenakistiscope. Biography Plateau was born in Brussels. His father, Antoine Plateau ( fr) born in Tournai, was a talented flower painter. At the age of six, the younger Plateau already could read, making him a child prodigy in those times. While attending primary school, he was particularly impressed by a lesson of physics; enchanted by the experiments he observed, he vowed to discover their secrets someday. Plateau spent his school holidays in Marche-les-Dames, with his uncle and his family; his cousin and playfellow was Auguste Payen, who later became an architect and the principal designer of the Belgia ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Plateau–Rayleigh Instability
The Plateau–Rayleigh instability, often just called the Rayleigh instability, explains why and how a falling stream of fluid breaks up into smaller packets with the same volume but less surface area. It is related to the Rayleigh–Taylor instability and is part of a greater branch of fluid dynamics concerned with fluid thread breakup. This fluid instability is exploited in the design of a particular type of ink jet technology whereby a jet of liquid is perturbed into a steady stream of droplets. The driving force of the Plateau–Rayleigh instability is that liquids, by virtue of their surface tensions, tend to minimize their surface area. A considerable amount of work has been done recently on the final pinching profile by attacking it with self-similar solutions. History The Plateau–Rayleigh instability is named for Joseph Plateau and Lord Rayleigh. In 1873, Plateau found experimentally that a vertically falling stream of water will break up into drops if its leng ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Relation Of Liquid Static Capillary Bridge Dimensionless Height And Dimensionless Radius In Cylindrical Coordinates
Relation or relations may refer to: General uses *International relations, the study of interconnection of politics, economics, and law on a global level *Interpersonal relationship, association or acquaintance between two or more people *Public relations, managing the spread of information to the public *Sexual relations, or human sexual activity *Social relation, in social science, any social interaction between two or more individuals Logic and philosophy *Relation (philosophy), links between properties of an object * Relational theory, framework to understand reality or a physical system Mathematics A finitary or ''n''-ary relation is a set of ''n''-tuples. Specific types of relations include: * Relation (mathematics) *Binary relation (or correspondence, dyadic relation, or 2-place relation) *Equivalence relation * Homogeneous relation * Reflexive relation * Serial relation *Ternary relation (or triadic, 3-adic, 3-ary, 3-dimensional, or 3-place relation) Relation may al ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Thin Layer (liquid Capillary Bridge)
Thin layers are concentrated aggregations of phytoplankton and zooplankton in coastal and offshore waters that are vertically compressed to thicknesses ranging from several centimeters up to a few meters and are horizontally extensive, sometimes for kilometers. Generally, thin layers have three basic criteria: 1) they must be horizontally and temporally persistent; 2) they must not exceed a critical threshold of vertical thickness; and 3) they must exceed a critical threshold of maximum concentration. The precise values for critical thresholds of thin layers has been debated for a long time due to the vast diversity of plankton, instrumentation, and environmental conditions. Thin layers have distinct biological, chemical, optical, and acoustical signatures which are difficult to measure with traditional sampling techniques such as nets and bottles. However, there has been a surge in studies of thin layers within the past two decades due to major advances in technology and instrum ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Catenoid Existence Domain
In geometry, a catenoid is a type of surface, arising by rotating a catenary curve about an axis (a surface of revolution). It is a minimal surface, meaning that it occupies the least area when bounded by a closed space. It was formally described in 1744 by the mathematician Leonhard Euler. Soap film attached to twin circular rings will take the shape of a catenoid. Because they are members of the same associate family of surfaces, a catenoid can be bent into a portion of a helicoid, and vice versa. Geometry The catenoid was the first non-trivial minimal surface in 3-dimensional Euclidean space to be discovered apart from the plane. The catenoid is obtained by rotating a catenary about its directrix. It was found and proved to be minimal by Leonhard Euler in 1744. Early work on the subject was published also by Jean Baptiste Meusnier. There are only two minimal surfaces of revolution ( surfaces of revolution which are also minimal surfaces): the plane and the catenoid. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Catenoid
In geometry, a catenoid is a type of surface, arising by rotating a catenary curve about an axis (a surface of revolution). It is a minimal surface, meaning that it occupies the least area when bounded by a closed space. It was formally described in 1744 by the mathematician Leonhard Euler. Soap film attached to twin circular rings will take the shape of a catenoid. Because they are members of the same associate family of surfaces, a catenoid can be bent into a portion of a helicoid, and vice versa. Geometry The catenoid was the first non-trivial minimal surface in 3-dimensional Euclidean space to be discovered apart from the plane. The catenoid is obtained by rotating a catenary about its directrix. It was found and proved to be minimal by Leonhard Euler in 1744. Early work on the subject was published also by Jean Baptiste Meusnier. There are only two minimal surfaces of revolution ( surfaces of revolution which are also minimal surfaces): the plane and the catenoid. Th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Elliptic Integral
In integral calculus, an elliptic integral is one of a number of related functions defined as the value of certain integrals, which were first studied by Giulio Fagnano and Leonhard Euler (). Their name originates from their originally arising in connection with the problem of finding the arc length of an ellipse. Modern mathematics defines an "elliptic integral" as any function which can be expressed in the form f(x) = \int_^ R \left(t, \sqrt \right) \, dt, where is a rational function of its two arguments, is a polynomial of degree 3 or 4 with no repeated roots, and is a constant. In general, integrals in this form cannot be expressed in terms of elementary functions. Exceptions to this general rule are when has repeated roots, or when contains no odd powers of or if the integral is pseudo-elliptic. However, with the appropriate reduction formula, every elliptic integral can be brought into a form that involves integrals over rational functions and the three Leg ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Young–Laplace Equation
In physics, the Young–Laplace equation () is an algebraic equation that describes the capillary pressure difference sustained across the interface between two static fluids, such as water and air, due to the phenomenon of surface tension or wall tension, although use of the latter is only applicable if assuming that the wall is very thin. The Young–Laplace equation relates the pressure difference to the shape of the surface or wall and it is fundamentally important in the study of static capillary surfaces. It's a statement of normal stress balance for static fluids meeting at an interface, where the interface is treated as a surface (zero thickness): \begin \Delta p &= -\gamma \nabla \cdot \hat n \\ &= -2\gamma H_f \\ &= -\gamma \left(\frac + \frac\right) \end where \Delta p is the Laplace pressure, the pressure difference across the fluid interface (the exterior pressure minus the interior pressure), \gamma is the surface tension (or wall tension), \hat n is the unit no ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Djehutihotep
Djehutihotep ("''Thoth is satisfied''") was an ancient Egyptian nomarch of the fifteenth '' nomos'' of Upper Egypt (''"the Hare"'') during the twelfth dynasty, c. 1900 BC. Biography Djehutihotep lived under the reigns of Amenemhat II, Senusret II, and Senusret III and was one of the most powerful nomarchs of the Middle Kingdom. His tomb—the only one among the necropolis of Deir el-Bersha that wasn't damaged by the explosives used in recent quarrying methods—is well known for the great quality of its decorations, a work carried out by an artist named Amenaankhu. For this reason, it is believed that Djehutihotep died prior to the strict measures reducing the power of the nomarchs that were established by Senusret III. Indeed, as their charge became hereditary at the end of the Old Kingdom, the nomarchs became local rulers effectively, although not nominally, independent of the pharaohs. This situation led to excesses in the exercise of power that worsened st ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Soldering
Soldering (; ) is a process in which two or more items are joined by melting and putting a filler metal ( solder) into the joint, the filler metal having a lower melting point than the adjoining metal. Unlike welding, soldering does not involve melting the work pieces. In brazing, the work piece metal also does not melt, but the filler metal is one that melts at a higher temperature than in soldering. In the past, nearly all solders contained lead, but environmental and health concerns have increasingly dictated use of lead-free alloys for electronics and plumbing purposes. Origins There is evidence that soldering was employed as early as 5,000 years ago in Mesopotamia. Soldering and brazing are thought to have originated very early in the history of metal-working, probably before 4000 BC. Sumerian swords from were assembled using hard soldering. Soldering was historically used to make jewelry, cookware and cooking tools, assembling stained glass, as well as other ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Atomic Force Microscopy
Atomic force microscopy (AFM) or scanning force microscopy (SFM) is a very-high-resolution type of scanning probe microscopy (SPM), with demonstrated resolution on the order of fractions of a nanometer, more than 1000 times better than the optical diffraction limit. Overview Atomic force microscopy (AFM) is a type of scanning probe microscopy (SPM), with demonstrated resolution on the order of fractions of a nanometer, more than 1000 times better than the optical diffraction limit. The information is gathered by "feeling" or "touching" the surface with a mechanical probe. Piezoelectric elements that facilitate tiny but accurate and precise movements on (electronic) command enable precise scanning. Despite the name, the Atomic Force Microscope does not use the Nuclear force. Abilities The AFM has three major abilities: force measurement, topographic imaging, and manipulation. In force measurement, AFMs can be used to measure the forces between the probe and the sample as ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
