the property of a liquid that causes small drops to be spherical is called
surface tension
517863
The surface tension of the liquid causes the liquid to hang from the tube, forming a pendant. When the drop exceeds a certain size it is no longer stable and detaches itself. The falling liquid is also a drop held together by surface tension. Some substances that appear to be solid, can be shown to instead be extremely viscous liquids, because they form drops and display droplet behavior. In the famous pitch drop experiments, pitch - a substance somewhat like solid bitumen - is shown to be a liquid in this way. Pitch in a funnel slowly forms droplets, each
Drop (liquid)
517862
Drop (liquid) A drop or droplet is a small column of liquid, bounded completely or almost completely by free surfaces. A drop may form when liquid accumulates at the lower end of a tube or other surface boundary, producing a hanging drop called a pendant drop. Drops may also be formed by the condensation of a vapor or by atomization of a larger mass of liquid. Liquid forms drops because the liquid exhibits surface tension. A simple way to form a drop is to allow liquid to flow slowly from the lower end of a vertical tube of small diameter.
Drop (liquid)
14395922
the choice of subgrid-scale parameterization schemes can influence hurricane intensity, track, speed, and precipitation rates. Microphysical assumptions may directly or indirectly modulated storm structure, which result in small changes in the hurricane track which can have societal consequences. The shape of liquid water drops is generally spherical because of the effects of surface tension. Depending on the size of the drop the friction of the air flowing past a falling drop may squish the bottom on the drop so that it is slightly non-spherical. However, solid ice does not generally form into nice spherical shapes. Ice crystals have a preference
Hurricane dynamics and cloud microphysics
12613273
(like marbles) into a tight spherical or almost spherical bag (some stable nuclei are not quite spherical, but are known to be prolate). Models of nuclear structure include : Early models of the nucleus viewed the nucleus as a rotating liquid drop. In this model, the trade-off of long-range electromagnetic forces and relatively short-range nuclear forces, together cause behavior which resembled surface tension forces in liquid drops of different sizes. This formula is successful at explaining many important phenomena of nuclei, such as their changing amounts of binding energy as their size and composition changes (see semi-empirical mass formula), but
Atomic nucleus
517870
the surface tension of a body of liquid makes possible to reduce or prevent noise due to droplets falling into it. This would involve adding soap, detergent or a similar substance to water. The reduced surface tension reduces the noise from dripping. The classic shape associated with a drop (with a pointy end in its upper side) comes from the observation of a droplet clinging to a surface. The shape of a drop falling through a gas is actually more or less spherical for drops less than 2 mm in diameter. Larger drops tend to be flatter on the bottom
Drop (liquid)
517863
The surface tension of the liquid causes the liquid to hang from the tube, forming a pendant. When the drop exceeds a certain size it is no longer stable and detaches itself. The falling liquid is also a drop held together by surface tension. Some substances that appear to be solid, can be shown to instead be extremely viscous liquids, because they form drops and display droplet behavior. In the famous pitch drop experiments, pitch - a substance somewhat like solid bitumen - is shown to be a liquid in this way. Pitch in a funnel slowly forms droplets, each
Drop (liquid)
1064403
forces, including gravity, drops of virtually all liquids would be approximately spherical. The spherical shape minimizes the necessary "wall tension" of the surface layer according to Laplace's law. Another way to view surface tension is in terms of energy. A molecule in contact with a neighbor is in a lower state of energy than if it were alone (not in contact with a neighbor). The interior molecules have as many neighbors as they can possibly have, but the boundary molecules are missing neighbors (compared to interior molecules) and therefore have a higher energy. For the liquid to minimize its energy
Surface tension
383909
the sphere. Alternatively, the area element on the sphere is given in spherical coordinates by . In Cartesian coordinates, the area element is For more generality, see area element. The total area can thus be obtained by integration: The sphere has the smallest surface area of all surfaces that enclose a given volume, and it encloses the largest volume among all closed surfaces with a given surface area. The sphere therefore appears in nature: for example, bubbles and small water drops are roughly spherical because the surface tension locally minimizes surface area. The surface area relative to the mass of
Sphere
6811100
will have. Consequently, interfaces are very important in systems with large interface area-to-volume ratios, such as colloids. Interfaces can be flat or curved. For example, oil droplets in a salad dressing are spherical but the interface between water and air in a glass of water is mostly flat. Surface tension is the physical property which rules interface processes involving liquids. For a liquid film on flat surfaces, the liquid-vapor interface keeps flat to minimize interfacial area and system free energy. For a liquid film on rough surfaces, the surface tension tends to keep the meniscus flat, while the disjoining pressure
Interface (matter)
5471383
model based on experiments with glass beads coated with paraffin or PTFE telomer. The self-cleaning property of ultrahydrophobic micro-nanostructured surfaces was studied by Wilhelm Barthlott and Ehler in 1977, who described such self-cleaning and ultrahydrophobic properties for the first time as the "lotus effect"; perfluoroalkyl and perfluoropolyether ultrahydrophobic materials were developed by Brown in 1986 for handling chemical and biological fluids. Other biotechnical applications have emerged since the 1990s. The high surface tension of water causes droplets to assume a nearly spherical shape, since a sphere has minimal surface area, and this shape therefore demands least solid-liquid surface energy. On
Lotus effect
5715724
lead is dripped from small orifices and dropped approximately into a hot liquid, where it is then rolled along an incline and then dropped another . The temperature of the liquid controls the cooling rate of the lead, while the surface tension of the liquid and the inclined surface(s) work together to bring the small droplets of lead into highly regular balls of lead in spherical form. The size of the lead shot that is produced is determined by the diameter of the orifice used to drip the lead, ranging from approximately for #9 lead shot to about for #6
Shot (pellet)
1064402
of same type are called cohesive forces while those acting between the molecules of different types are called adhesive forces. When cohesive forces are stronger than adhesives forces, the liquid acquires a convex meniscus (as mercury in a glass container). On the other hand, when adhesive forces are stronger, the surface of the liquid curves up (as water in a glass). Surface tension is responsible for the shape of liquid droplets. Although easily deformed, droplets of water tend to be pulled into a spherical shape by the imbalance in cohesive forces of the surface layer. In the absence of other
Surface tension
16502561
mass conservation yields Note that the viscous terms cancel during substitution. Separating variables and integrating from the bubble boundary formula_52 to formula_53 gives Let formula_56 be the normal stress in the liquid that points radially outward from the center of the bubble. In spherical coordinates, for a fluid with constant density and constant viscosity, Therefore at some small portion of the bubble surface, the net force per unit area acting on the lamina is where formula_59 is the surface tension. If there is no mass transfer across the boundary, then this force per unit area must be zero, therefore formula_60
Rayleigh–Plesset equation
12378276
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. The density of a liquid is usually close to that of a solid, and much higher than in a gas. Therefore, liquid and solid are both termed condensed matter. On the other hand, as liquids and gases share the ability to flow, they are both called fluids. Although liquid water is abundant on Earth,
Liquid
20487907
and Coulomb energies of the undistorted spherical drops, respectively, and formula_7 is the quadrupole distortion parameter. When the changes in the Coulomb and surface energies (formula_8, formula_9) are equal, the nucleus becomes unstable with respect to fission. At that point, the relationship between the undistorted surface and Coulomb energies becomes: where formula_11 is called the fissionability parameter. If formula_12, the Liquid Drop energy decreases with increasing formula_7, which leads to fission. If formula_14, then the Liquid Drop energy decreases with decreasing formula_7, which leads to spherical shapes of the nucleus. The Coulomb and surface energies of a uniformly charged sphere
Fission barrier
517873
diameter, in such a way that 1 millilitre is equivalent to 20 drops. When smaller amounts are necessary (such as paediatrics), microdroppers or paediatric infusion sets are used, in which 1 millilitre = 60 microdrops. Drop (liquid) A drop or droplet is a small column of liquid, bounded completely or almost completely by free surfaces. A drop may form when liquid accumulates at the lower end of a tube or other surface boundary, producing a hanging drop called a pendant drop. Drops may also be formed by the condensation of a vapor or by atomization of a larger mass of
Drop (liquid)
7788018
total volume of liquid water per volume of air is increased twofold. In other words, this excessive cloud seeding from the ship causes the clouds to retain more water. Normally, rain forms when cloud drops coagulate and reach a size at which gravity can pull them to the ground. Yet, in ship tracks, the cloud seeding makes the drops so small that they can no longer easily merge to reach the size needed to escape. Since no drizzle comes out of the seeded clouds, the liquid water just keeps building in the cloud. This makes the cloud brighter and more
Ship tracks
10425235
more strongly than fine matter. Due to centrifugal force, matter tends towards the outer edges of the vortex, which causes a condensation of this matter there. The rough matter cannot follow this movement due to its greater inertia—so due to the pressure of the condensed outer matter those parts will be pushed into the center of the vortex. According to Descartes, this inward pressure is nothing else than gravity. He compared this mechanism with the fact that if a rotating, liquid filled vessel is stopped, the liquid goes on to rotate. Now, if one drops small pieces of light matter
Mechanical explanations of gravitation
17394861
compression causes the spaghetti phase rods to fuse and form sheets of nuclear matter called the lasagna phase. Further compression of the lasagna phase yields the uniform nuclear matter of the outer core with intermittent holes of neutron (and possibly proton) liquid. Progressing deeper into the inner crust, those holes in the nuclear pasta change from being cylindrical, called by some the bucatini phase or antispaghetti phase, into scattered spherical holes, which can be called the Swiss cheese phase. The nuclei disappear at the crust–core interface, transitioning into the liquid core of the star. For a typical neutron star of
Nuclear pasta
13898209
pouring velocity that is too fast. The pouring velocity can be reduced by redesigning the gating system to use larger runners or multiple gates. A related source of defects are "drops", in which part of the molding sand from the cope drops into the casting while it is still a liquid. This also occurs when the mold is not properly rammed. The second type of defect is "metal penetration", which occurs when the liquid metal penetrates into the molding sand. This causes a rough surface finish. This is caused by sand particles which are too coarse, lack of mold wash,
Casting defect
20496360
and pushes the total volume out, so no liquid is left behind. Volatile liquids such as acetone, hexane, and methanol, evaporate continuously in air displacement pipettes. Some volatile liquids expand so quickly that they expand the air column in the pipette, which causes leakage: The pipette will lose drops and dispense liquid imprecisely. As drops leak out, they can contaminate the bench, ultimately causing cross-contamination from sample to sample. These drops can also produce a health hazard. Because there is no air cushion in a positive displacement pipette, liquids do not evaporate or leak. Drops will not fall from the
Positive displacement pipette
9498456
painting. A surface impingement nozzle causes a stream of liquid to impinge on a surface resulting in a sheet of liquid that breaks up into drops. This flat fan spray pattern nozzle is used in many applications ranging from applying agricultural herbicides to row crop to painting. The impingement surface can be formed in a spiral to yield a spiral shaped sheet approximating a full cone spray pattern or a hollow-cone spray pattern. The spiral design generally produces a smaller drop size than pressure swirl type nozzle design, for a given pressure and flow rate. This design is clog resistant
Spray nozzle
1930607
R. Meaning that from the top of the bubble to the bottom of the bubble the radius of curvature increases. Therefore, without neglecting gravity the bubbles cannot be spherical. In addition, as z increases, this causes the difference in R and R too, which means the bubble deviates more from its shape the larger it grows. Foam destabilization occurs for several reasons. First, gravitation causes drainage of liquid to the foam base, which Rybczynski and Hadamar include in their theory; however, foam also destabilizes due to osmotic pressure causes drainage from the lamellas to the Plateau borders due to internal
Foam
8931272
of New York from 1966 to 1968. Kim Tschang Yeul's time spent in New York City allowed him to interact with and be inspired by the Pop art movement, which was a significant influence on him. Because of his years abroad, Kim Tschang-Yeul developed his art outside of the Seoul and Tokyo art scene, developing his unique style parallel to the Dansaekhwa movement. In 1969, Kim moved from New York City to Paris, where he continued depicting opaque abstract liquid forms. WIth time, the liquid abstract forms transformed into spherical, transparent 'water drops', which have become his distinctive, trademark style
Kim Tschang-yeul
517871
part due to the pressure of the gas they move through. As a result, as drops get larger, a concave depression forms which leads to the eventual breakup of the drop. Raindrop sizes typically range from 0.5 mm to 4 mm, with size distributions quickly decreasing past diameters larger than 2-2.5 mm. Scientists traditionally thought that the variation in the size of raindrops was due to collisions on the way down to the ground. In 2009 French researchers succeeded in showing that the distribution of sizes is due to the drops' interaction with air, which deforms larger drops and causes
Drop (liquid)
20402923
which still provides a very high heat transfer coefficient, formula_53 at BWR compared to formula_54 at PWR. The film of liquid is continuously fed with drops from the agent suspension. A further increase in surface temperature leads to a temporary interruption of continuity of the liquid film adhering to the cooled surface. Watering of the surface continues, however, by the drops of liquid in the suspension that are present in the cooling agent as long as the heat flow remains below a value that depends on local conditions (value that is called critical flux). Over this flux there is a
Nuclear reactor heat removal
6742546
hydrophobic compound is added to stop this process from taking place. Diffusional growth of larger drops in liquid water clouds in the atmosphere at the expense of smaller drops is also characterized as Ostwald Ripening. Ostwald ripening Ostwald ripening is an observed phenomenon in solid solutions or liquid sols that describes the change of an inhomogeneous structure over time, i.e., small crystals or sol particles dissolve, and redeposit onto larger crystals or sol particles. Dissolution of small crystals or sol particles and the redeposition of the dissolved species on the surfaces of larger crystals or sol particles was first described
Ostwald ripening
2676176
drug filled capsule. The lifetime of surface antibubbles can be prolonged indefinitely by making the water under them vibrate. These are called "walking bubbles" and are used as a model of quantum mechanical behavior. Antibubble An antibubble is a droplet of liquid surrounded by a thin film of gas, as opposed to a gas bubble, which is a sphere of gas surrounded by a liquid. Antibubbles are formed when liquid drops or flows turbulently into the same or another liquid. They can either skim across the surface of a liquid such as water, in which case they are also called
Antibubble
5238847
Drizzle Drizzle is a light liquid precipitation consisting of liquid water drops smaller than those of rain – generally smaller than in diameter. Drizzle is normally produced by low stratiform clouds and stratocumulus clouds. Precipitation rates from drizzle are on the order of a millimetre per day or less at the ground. Owing to the small size of drizzle drops, under many circumstances drizzle largely evaporates before reaching the surface and so may be undetected by observers on the ground. The METAR code for drizzle is DZ and for freezing drizzle is FZDZ. While most drizzle has only a minor
Drizzle
10256382
Cryophorus A cryophorus is a glass container containing liquid water and water vapor. It is used in physics courses to demonstrate rapid freezing by evaporation. A typical cryophorus has a bulb at one end connected to a tube of the same material. When the liquid water is manipulated into the bulbed end and the other end is submerged into a freezing mixture (such as liquid nitrogen), the gas pressure drops as it is cooled. The liquid water begins to evaporate, producing more water vapor. Evaporation causes the water to cool rapidly to its freezing point and it solidifies suddenly. Wollaston's
Cryophorus
9886283
polar, they are easily attract to partially positive or partially negative charges. On a neutral surface, water molecules bunch up and attract each other, creating a spherical droplet of water. These droplets can then evaporate off the concrete surface rather than be absorbed into the capillaries of the concrete. The exact structure and composition of the crystals used in hydrophobic concrete is not public information; due to its properties, however, it can be assumed that it is a non-polar molecule. The property to repel water gives hydrophobic concrete the ability to avoid contamination by particles dissolved in water drops. Because
Hydrophobic concrete
20837772
number of these droplets is less than the theoretical curve. Carlton W. Ulbricht developed a more general formula in 1983 taking into account that a drop is spherical if D <1 mm and an ellipsoid whose horizontal axis gets flattened as D gets larger. It is mechanically impossible to exceed D = 10 mm as the drop breaks at large diameters. From the general distribution, the diameter spectrum changes, μ = 0 inside the cloud, where the evaporation of small drops is negligible due to saturation conditions and μ = 2 out of the cloud, where the small drops evaporate
Raindrop size distribution
7131665
drops, causing the pressurised gas and beer inside the widget to jet out from the hole. This agitation on the surrounding beer causes a chain reaction of bubble formation throughout the beer. The result, when the can is then poured out, is a surging mixture in the glass of very small gas bubbles and liquid. This is the case with certain types of draught beer such as draught stouts. In the case of these draught beers, which before dispensing also contain a mixture of dissolved nitrogen and carbon dioxide, the agitation is caused by forcing the beer under pressure through
Widget (beer)
1754190
the meniscus. This means that any instrument is calibrated for a specific liquid, usually water. Menisci are a manifestation of capillary action, by which surface adhesion pulls a liquid up to form a concave meniscus or internal cohesion pulls the liquid down to form a convex meniscus. This phenomenon is important in transpirational pull in plants. When a tube of a narrow bore, often called a capillary tube, is dipped into a liquid and the liquid wets the tube (with zero contact angle), the liquid surface inside the tube forms a concave meniscus, which is a virtually spherical surface having
Meniscus (liquid)
12381856
drops in small regions with particularly high content of liquid water. Rain drops associated with melting hail tend to be larger than other rain drops. Intensity and duration of rainfall are usually inversely related, i.e., high intensity storms are likely to be of short duration and low intensity storms can have a long duration. The final droplet size distribution is an exponential distribution. The number of droplets with diameter between formula_1 and formula_2 per unit volume of space is formula_3. This is commonly referred to as the Marshall–Palmer law after the researchers who first characterized it. The parameters are somewhat
Rain
2676171
Antibubble An antibubble is a droplet of liquid surrounded by a thin film of gas, as opposed to a gas bubble, which is a sphere of gas surrounded by a liquid. Antibubbles are formed when liquid drops or flows turbulently into the same or another liquid. They can either skim across the surface of a liquid such as water, in which case they are also called water globules, or they can be completely submerged into the liquid to which they are directed. Antibubbles are a common but widely unrecognized phenomenon, in part because of their resemblance to air bubbles, and
Antibubble
4124943
low density of the crystal lattice – it is beneficial for the lattice to be arranged with tetrahedral angles even though there is an energy penalty in the increased volume of the crystal lattice. As a result, the large hexagonal rings leave almost enough room for another water molecule to exist inside. This gives naturally occurring ice its unique property of being less dense than its liquid form. The tetrahedral-angled hydrogen-bonded hexagonal rings are also the mechanism that causes liquid water to be densest at 4 °C. Close to 0 °C, tiny hexagonal ice I-like lattices form in liquid water,
Ice Ih
1907651
Prill A prill is a small aggregate or globule of a material, most often a dry sphere, formed from a melted liquid. Prilled is a term used in mining and manufacturing to refer to a product that has been pelletized. The pellets are a neater, simpler form for handling, with reduced dust. The material to be prilled must be in a solid state at room temperature and a low-viscosity liquid when melted. Prills are formed by allowing drops of the melted prill substance to congeal or freeze in mid-air after being dripped from the top of a tall prilling tower.
Prill
5969227
bottom of the tank. The emergency pressure relief valve in the tank is called a hydrostatic pressure relief valve. It is designed to open if the pressure in the tank is dangerously high, thus releasing some vapour to the atmosphere to reduce the pressure in the tank. The release of a small quantity of vapour reduces the pressure in the tank, which causes some of the liquid in the tank to vaporise to re-establish equilibrium between liquid and vapour. The "latent heat of vaporisation" causes the tank to cool, which reduces pressure even further. The gauge sender is usually a
Autogas
20275630
expected to be upgraded throughout their operational lives. In September 2013, Northrop Grumman revealed the development of a company-funded Directional Infrared Counter Measures system in anticipation of a requirement to protect the F-35 from heat-seeking missiles. A laser jammer is expected to be part of the F-35 Block 5 upgrade; it must meet low-observability (LO) requirements and fit in the F-35's restricted space. Called the Threat Nullification Defensive Resource (ThNDR), it is to have a small, powerful laser, beam steering and LO window, use liquid cooling, and fit alongside the distributed aperture system (DAS) to provide spherical coverage with minimal
Lockheed Martin F-35 Lightning II development
14596626
closet. Alice takes two bottles from a small box she is carrying. One contains a sparkling liquid, the other a greenish unguent. She drinks a few drops of the bright liquid before anointing her face and hands with the unguent, chanting "Emen hetan" repeatedly as she does so, before leaving the room. Curious about the liquid she had seen Alice take, Dorothy tries a few drops herself, and is instantly overcome by a "bewildering excitement". Having felt the effect of the potion herself, and wondering if it might have the power to rouse Alizon from her sleep, she rubs a
The Lancashire Witches
12591968
commonly used to determine the pressure difference in spherical shapes such as bubbles or droplets. In this case, formula_2 = formula_3: For a gas bubble within a liquid, there is only one surface. For a gas bubble with a liquid wall, beyond which is again gas, there are two surfaces, each contributing to the total pressure difference. If the bubble is spherical and the outer radius differs from the inner radius by a small distance, formula_9, we find A common example of use is finding the pressure inside an air bubble in pure water, where formula_4 = 72 mN/m at
Laplace pressure
12138007
onward, analysis of archived data continued for some years, as can be traced in the publications. Since 2012, a similar but new system called CLAS12 was constructed, which began operations with particle beams in 2017. The CLAS detector was notable among devices in the area of hadronic particle physics in that it had a very large acceptance; in other words, it measured the momentum and angles of almost all of the particles produced in the electron-proton collisions. Roughly spherical, the detector measured 30 feet across. It surrounded the physics target, which was typically a small cylinder of liquid hydrogen (hydrogen's
CLAS detector
240309
doped with a chiral material), allowing the pitch of a given material to be tuned accordingly. In some liquid crystal systems, the pitch is of the same order as the wavelength of visible light. This causes these systems to exhibit unique optical properties, such as Bragg reflection and low-threshold laser emission, and these properties are exploited in a number of optical applications. For the case of Bragg reflection only the lowest-order reflection is allowed if the light is incident along the helical axis, whereas for oblique incidence higher-order reflections become permitted. Cholesteric liquid crystals also exhibit the unique property that
Liquid crystal
517872
them to fragment into smaller drops, effectively limiting the largest raindrops to about 6 mm diameter. However, drops up to 10 mm (equivalent in volume to a sphere of radius 4.5 mm) are theoretically stable and could be levitated in a wind tunnel. The largest recorded raindrop was 8.8 mm in diameter, located at the base of a cumulus congestus cloud in the vicinity of Kwajalein Atoll in July 1999. A raindrop of identical size was detected over northern Brazil in September 1995. In medicine, this property is used to create droppers and IV infusion sets which have a standardized
Drop (liquid)
4889903
1-K pot A 1-K pot (i.e. 1-kelvin pot) is a cryogenic device used to attain temperatures down to approximately 1 kelvin. The 1-K pot is a small vessel in a cryogenic system that is filled with liquid helium. Usually it is a few cubic centimeters in size with a pickup-tube extending into the primary liquid helium bath of the dewar. When a vessel containing liquid helium is connected to a vacuum pump, the vapor pressure above the liquid surface drops, thereby allowing the more energetic helium molecules to evaporate out of the liquid. As the particles evaporate and are pumped
1-K pot
1777698
have not reached hydrostatic equilibrium. The small Solar System body 4 Vesta is large enough to have undergone at least partial planetary differentiation. Stars like the Sun are also spheroidal due to gravity's effects on their plasma, which is a free-flowing fluid. Ongoing stellar fusion is a much greater source of heat for stars compared to the initial heat released during formation. The roughly spherical shape of the Earth can be confirmed by many different types of observation from ground level, aircraft, and spacecraft. The shape causes a number of phenomena that a flat Earth would not. Some of these
Spherical Earth
1626565
altitude increases, air pressure decreases and the temperature drops (see Gas laws). The lower temperature causes water vapor to condense into tiny liquid water droplets which are heavier than the air, and fall unless supported by an updraft. A huge concentration of these droplets over a large space up in the atmosphere become visible as cloud. Some condensation is near ground level, and called fog. Atmospheric circulation moves water vapor around the globe, cloud particles collide, grow, and fall out of the upper atmospheric layers as precipitation. Some precipitation falls as snow or hail, sleet, and can accumulate as ice
Water cycle
4121868
Shivering Shivering (also called shuddering) is a bodily function in response to cold in warm-blooded animals. When the core body temperature drops, the shivering reflex is triggered to maintain homeostasis. Skeletal muscles begin to shake in small movements, creating warmth by expending energy. Shivering can also be a response to a fever, as a person may feel cold. During fever the hypothalamic set point for temperature is raised. The increased set point causes the body temperature to rise (pyrexia), but also makes the patient feel cold until the new set point is reached. Severe chills with violent shivering are called
Shivering
3285521
on smaller droplets is larger than on large droplets. The large droplets can then collide with small droplets and combine to form even larger drops. When the drops become large enough that their downward velocity (relative to the surrounding air) is greater than the upward velocity (relative to the ground) of the surrounding air, the drops can fall as precipitation. The collision and coalescence is not as important in mixed phase clouds where the Bergeron process dominates. Other important processes that form precipitation are riming, when a supercooled liquid drop collides with a solid snowflake, and aggregation, when two solid
Cloud physics
6333113
question for high rank symmetric pairs see. In the context of algebraic groups the analogs of Gelfand pairs are called spherical pair. Namely, a pair "(G,K)" of algebraic groups is called a spherical pair if one of the following equivalent conditions holds. In this case the space "G/H" is called spherical space. It is conjectured that any spherical pair (G,K) over a local field satisfies the following weak version of the Gelfand property: For any admissible representation "π" of "G", the space Hom("π",C) is finite-dimensional. Moreover, the bound for this dimension does not depend on "π". This conjecture is proven
Gelfand pair
1980857
Precipitation (chemistry) Precipitation is the creation of a solid from a solution. When the reaction occurs in a liquid solution, the solid formed is called the 'precipitate'. The chemical that causes the solid to form is called the 'precipitant'. Without sufficient force of gravity (settling) to bring the solid particles together, the precipitate remains in suspension. After sedimentation, especially when using a centrifuge to press it into a compact mass, the precipitate may be referred to as a 'pellet'. Precipitation can be used as a medium. The precipitate-free liquid remaining above the solid is called the 'supernate' or 'supernatant'. Powders
Precipitation (chemistry)
1980811
air resistance and fall as rain. Raindrops have sizes ranging from to mean diameter, above which they tend to break up. Smaller drops are called cloud droplets, and their shape is spherical. As a raindrop increases in size, its shape becomes more oblate, with its largest cross-section facing the oncoming airflow. Contrary to the cartoon pictures of raindrops, their shape does not resemble a teardrop. Intensity and duration of rainfall are usually inversely related, i.e., high intensity storms are likely to be of short duration and low intensity storms can have a long duration. Rain drops associated with melting hail
Precipitation
15380303
isolated spherical solid particle of diameter formula_1 in its own liquid, the Gibbs–Thomson equation for the structural melting point depression can be written: formula_2 Where: The "4" in the above equation comes from the spherical geometry of the solid-liquid interface. Note: formula_1 is used for the pore size rather than formula_4 for a number of reasons : Very similar equations may be applied to the growth and melting of crystals in the confined geometry of porous systems. However the geometry term for the crystal-liquid interface may be different, and there may be additional surface energy terms to consider, which can
Gibbs–Thomson equation
9293004
exhaust flow. In crosscurrent-flow spray towers, also called horizontal-spray scrubbers, the gas and liquid flow in directions perpendicular to each other. In this vessel, the gas flows horizontally through a number of spray sections. The amount and quality of liquid sprayed in each section can be varied, usually with the cleanest liquid (if recycled liquid is used) sprayed in the last set of sprays. Spray towers are low energy scrubbers. Contacting power is much lower than in venturi scrubbers, and the pressure drops across such systems are generally less than 2.5 cm (1 in) of water. The collection efficiency for
Spray tower
19784644
a given pressure exposure profile. Solubility is the property of a gas, liquid or solid substance ("the solute") to be held homogeneously dispersed as molecules or ions in a liquid or solid medium ("the solvent"). In decompression theory the solubility of gases in liquids is of primary importance, as it is the formation of bubbles from these gases that causes decompression sickness. Solubility of gases in liquids is influenced by three main factors: The presence of other solutes in the solvent can also influence solubility. Body tissues include aqueous and lipid components in varying ratios, and the solubility of the
Physiology of decompression
14703039
daily (or twice daily) dose of liquid paraffin (one or two drops placed on the tongue of the kitten, or 0.1 ml) should help to alleviate this problem. FCKS kittens who do not maintain weight are usually among the group which die, but many of them may simply be unable to feed properly due to colic, becoming increasingly weak and lethargic, and fading due to malnutrition as much as to the thoracic problems. Colic has many causes, but in a kitten with respiratory difficulty it is possible that a malfunction during the breathing process leads the kitten to swallow air
Flat-chested kitten syndrome
4247739
liquid hits a free surface can produce symmetric forms that resemble a coronet; milk is often used as it is opaque. Sand is said to splash if hit sufficiently hard (see dry quicksand) and sometimes the impact of a meteorite is referred to as splashing, if small bits of ejecta are formed. Physicist Lei Xu and coworkers at the University of Chicago discovered that the splash due to the impact of a small drop of ethanol onto a dry solid surface could be suppressed by reducing the pressure below a specific threshold. For drops of diameter 3.4 mm falling through
Splash (fluid mechanics)
1449668
samples and often use a UV-Vis absorbance detector. Narrow-bore columns (1–2 mm) are used for applications when more sensitivity is desired either with special UV-vis detectors, fluorescence detection or with other detection methods like liquid chromatography-mass spectrometry Capillary columns (under 0.3 mm) are used almost exclusively with alternative detection means such as mass spectrometry. They are usually made from fused silica capillaries, rather than the stainless steel tubing that larger columns employ. Most traditional HPLC is performed with the stationary phase attached to the outside of small spherical silica particles (very small beads). These particles come in a variety of
High-performance liquid chromatography
8108276
arc will then appear projected on the wall. Using a spherical projection screen instead will result in a closer analogy to the natural halo counterpart. Other artificial halos can be created by similar means. Circumhorizontal arcs, especially when only fragments can be seen, are sometimes confused with cloud iridescence. This phenomenon also causes clouds to appear multi-coloured, but it originates from diffraction (typically by liquid water droplets or ice crystals) rather than refraction. The two phenomena can be distinguished by several features. Firstly, a circumhorizon arc always has a fixed location in the sky in relation to the Sun or
Circumhorizontal arc
1650719
to 50 µL of liquid stimulus is presented to the anterior and posterior tongue using a pipette, soaked filter-paper disks, or cotton swabs. In whole mouth testing, small quantities (2-10 mL) of solution are administered, and the patient is asked to swish the solution around in the mouth. Threshold tests for sucrose (sweet), citric acid (sour), sodium chloride (salty), and quinine or caffeine (bitter) are frequently performed with natural stimuli. One of the most frequently used techniques is the "three-drop test." In this test, three drops of liquid are presented to the subject. One of the drops is of the
Dysgeusia
1905006
that must be carried, but are similar per unit mass of fuel. Computer programs that predict the performance of propellants in rocket engines are available. With liquid and hybrid rockets, immediate ignition of the propellant(s) as they first enter the combustion chamber is essential. With liquid propellants (but not gaseous), failure to ignite within milliseconds usually causes too much liquid propellant to be inside the chamber, and if/when ignition occurs the amount of hot gas created can exceed the maximum design pressure of the chamber, causing a catastrophic failure of the pressure vessel. This is sometimes called a "hard start"
Rocket engine
19284543
reddish or pinkish drops appearing on the stipe. The spores of "S. lanuginosus" are roughly spherical, covered in small warts (tubercules), and measure 4.5–6 by 4.5–5 µm. Sarcodon lanuginosus Sarcodon lanuginosus is a species of tooth fungus in the family Bankeraceae. It was described as new to science in 1961 by mycologist Kenneth A. Harrison, who initially called it "Hydnum lanuginosum". He transferred it to the genus "Sarcodon" in 1984. It is found in Nova Scotia, Canada, where it fruits on the ground singly or in groups under spruce and fir. The type collection was made in Cape Split, Kings
Sarcodon lanuginosus
13360917
Pill (textile) A pill, colloquially known as a bobble, fuzzball, or lint ball is a small ball of fibers that forms on a piece of cloth. 'Pill' is also a verb for the formation of such balls. Pilling is a surface defect of textiles caused by wear, and is considered unsightly to some. It happens when washing and wearing of fabrics causes loose fibers to begin to push out from the surface of the cloth, and, over time, abrasion causes the fibers to develop into small spherical bundles, anchored to the surface of the fabric by protruding fibers that haven't
Pill (textile)
9695052
releases energy suddenly. Moreover, in some cases, the eruption is caused by volatiles dissolved in the magma. Approaching the surface, pressure decreases and the volatiles evolve creating bubbles that circulate in the liquid. The bubbles are connected together forming a network. This especially increments the fragmentation into small drops or spray or coagulate clots in gas. Generally, 95-99% of magma is liquid rock. However, the small percentage of gas present, represents a very large volume when it expands on reaching atmospheric pressure. Gas is a preponderant part in a volcano system because it generates explosive eruptions. Magma in the mantle
Volatiles
13172410
strikes an anvil at the end of the bore, generating a large amplitude acoustic pulse that is transmitted to the liquid metal in the compression chamber via the piston anvil. To create a spherical wave, the timing of these strikes must be controlled to within 10 µs of each other. The company has recorded sequences of consecutive shots with impact velocities of 50 m/s and timing synchronization within 2 µs. A proof-of-concept prototype compression system was constructed in 2013 with 14 full size pistons around 1 meter diameter spherical compression chamber to demonstrate pneumatic compression and collapse of a liquid
General Fusion
11755018
the particle. In spherical coordinates this velocity at infinity can be written as The last expression suggest an expansion on spherical harmonics for the liquid velocity and the pressure Substitution in the Navier-Stokes equations produces a set of ordinary differential equations for the coefficients. <div class="references"> Vector spherical harmonics In mathematics, vector spherical harmonics (VSH) are an extension of the scalar spherical harmonics for use with vector fields. The components of the VSH are complex-valued functions expressed in the spherical coordinate basis vectors. Several conventions have been used to define the VSH. We follow that of Barrera "et al.". Given
Vector spherical harmonics
5258223
liquid volumes there are typically multiple nucleation events, and it is difficult to disentangle the effects of nucleation from those of growth of the nucleated phase. These problems can be overcome by working with small droplets. As nucleation is stochastic, many droplets are needed so that statistics for the nucleation events can be obtained. Nucleation occurs in different droplets at different times, hence the fraction is not a simple step function that drops sharply from one to zero at one particular time. The red curve is a fit of a Gompertz function to the data. This is a simplified version
Nucleation
3890045
cable or liquid light guide might be used to direct the laser light to the experimental setup. The optics consist of a spherical lens and cylindrical lens combination. The cylindrical lens expands the laser into a plane while the spherical lens compresses the plane into a thin sheet. This is critical as the PIV technique cannot generally measure motion normal to the laser sheet and so ideally this is eliminated by maintaining an entirely 2-dimensional laser sheet. It should be noted though that the spherical lens cannot compress the laser sheet into an actual 2-dimensional plane. The minimum thickness is
Particle image velocimetry
20105118
Williams spray equation In combustion, the Williams spray equation, also known as the Williams–Boltzmann equation, describes the statistical evolution of sprays contained in another fluid, analogous to the Boltzmann equation for the molecules, named after Forman A. Williams, who derived the equation in 1958. The sprays are assumed to be spherical with radius formula_1, even though the assumption is valid for solid particles(liquid droplets) when their shape has no consequence on the combustion. For liquid droplets to be nearly spherical, the spray has to be dilute(total volume occupied by the sprays is much less than the volume of the gas)
Williams spray equation
240315
lattice. This is called the middle soap phase. At still higher concentration, a lamellar phase (neat soap phase) may form, wherein extended sheets of amphiphiles are separated by thin layers of water. For some systems, a cubic (also called viscous isotropic) phase may exist between the hexagonal and lamellar phases, wherein spheres are formed that create a dense cubic lattice. These spheres may also be connected to one another, forming a bicontinuous cubic phase. The objects created by amphiphiles are usually spherical (as in the case of micelles), but may also be disc-like (bicelles), rod-like, or biaxial (all three micelle
Liquid crystal
12678969
60 square miles. The M143 was a spherical bomblet that had a diameter of 8.6 centimeters (cm). Designed to carry a liquid biological agent, the M143 carried a 0.5 gram explosive charge meant to disseminate the agent upon impact. Eight percent of the liquid released from the M143 was in the form of an inhalable aerosol. When filled, the bomblet had a mass of .34 kg and 190 milliliters (ml) of liquid agent could contain 6 X 10 anthrax spores. The M143 demonstrates the lethality of even a small amount of biological agent, the amount of anthrax contained in the
M143 bomblet
2615228
the column of liquid in the downtake tube less the gravitational force in the uptake tube causes the liquid to move. The liquid is therefore in tension and sustains a longitudinal strain which, in the absence of disturbing factors, is insufficient to break the column of liquid". But for siphons of small uptake height working at atmospheric pressure, he concluded that: "... the tension of the liquid column is neutralized and "reversed" by the compressive effect of the atmosphere on the opposite ends of the liquid column." Potter and Barnes at the University of Edinburgh revisited siphons in 1971. They
Siphon
6265347
the inner core over several decades, using the aforementioned property that it transmits waves more quickly in some directions. Estimates of this super-rotation are around one degree of extra rotation per year. Growth of the inner core is thought to play an important role in the generation of Earth's magnetic field by dynamo action in the liquid outer core. This occurs mostly because it cannot dissolve the same amount of light elements as the outer core and therefore freezing at the inner core boundary produces a residual liquid that contains more light elements than the overlying liquid. This causes it
Inner core
7378191
coastline and near various promontories. Sea surface temperatures along the coast are generally year-round. When the marine layer encounters the colder waters along the California coast, it cools to its dewpoint, and if small particles called condensation nuclei are present, liquid water drops will form. Condensation nuclei in coastal fog are mostly composed of salt from surf and spray, with lesser amounts of iodine from kelp. These nuclei are so effective that condensation can occur even before the dewpoint is reached. The prevailing wind along the California coast is from the northwest owing to the normal location of the North
San Francisco fog
2518424
fall. The inflorescence is made up of a few spherical flower heads each around a centimeter wide. The female flower heads develop into spherical fruit clusters each made up of many hairy, maroon-red-woolly achenes. The tough and coarse-grained wood is difficult to split and work. It has various uses, including acting as a meat preparation block for butchers. Many small birds feed on its fruit, and several mammals eat its twigs and bark. The pollen and the hairs on leaves and flowers can be allergens for some people. New leaves are susceptible to anthracnose canker, which, when it causes a
Platanus racemosa
11787860
already formed. Clouds that have low densities, such as cirrus clouds, contain very little water, thus resulting in relatively low liquid water content values of around .03 g/m. Clouds that have high densities, like cumulonimbus clouds, have much higher liquid water content values that are around 1-3 g/m, as more liquid is present in the same amount of space. Below is a chart giving typical LWC values of various cloud types (Thompson, 2007). Maritime clouds tend to have fewer water droplets than continental clouds. The majority of maritime clouds have droplet concentrations between 100 drops/cm and about 200 drops/cm (Wallace,
Liquid water content
692668
refrigerated until it liquefies. Next, the pressure is reduced. When this occurs some liquid carbon dioxide vaporizes, causing a rapid lowering of temperature of the remaining liquid. As a result, the extreme cold causes the liquid to solidify into a snow-like consistency. Finally, the snow-like solid carbon dioxide is compressed into small pellets or larger blocks of dry ice. Dry ice is typically produced in three standard forms: large blocks, cylindrical small ( diameter) pellets and cylindrical tiny ( diameter), high surface to volume pellets that float on oil or water and do not stick to skin because of their
Dry ice
12960951
a general spatial movement is called a "spatial mechanism." An example is the RSSR linkage, which can be viewed as a four-bar linkage in which the hinged joints of the coupler link are replaced by rod ends, also called spherical joints or ball joints. The rod ends let the input and output cranks of the RSSR linkage be misaligned to the point that they lie in different planes, which causes the coupler link to move in a general spatial movement. Robot arms, Stewart platforms, and humanoid robotic systems are also examples of spatial mechanisms. Bennett's linkage is an example of
Mechanism (engineering)
16502558
the dynamic parameter. Consider a spherical bubble with time-dependent radius formula_14, where formula_15 is time. Assume that the bubble contains a homogeneously distributed vapor/gas with a uniform temperature formula_16 and pressure formula_17. Outside the bubble is an infinite domain of liquid with constant density formula_18 and dynamic viscosity formula_19. Let the temperature and pressure far from the bubble be formula_20 and formula_21. The temperature formula_20 is assumed to be constant. At a radial distance formula_23 from the center of the bubble, the varying liquid properties are pressure formula_24, temperature formula_25, and radially outward velocity formula_26. Note that these liquid properties
Rayleigh–Plesset equation
6418336
Mints are small, Tic-Tac-like mints. They are described by the manufacturer as a "breath-freshening mint" rather than simply a "breath mint," one of the two descriptions used for standard Certs. Cadbury-Adams also offers "Certs Cool Mint Drops," described as a "breath "drop."" These medium sized oval-shaped mints are available in flavors named Cinnamint, Freshmint, and Peppermint. Certs Cool Mint Drops are packaged in slide top paper boxes and feature a liquid center which is claimed to be "intensely flavorful." At the end of 2014, Mondelēz International stopped the production of the Classic Fruit flavor in Canada. A Facebook page was
Certs
15943960
in with a long knife and a tall head-dress. Fred then drops his phone into a pot of boiling liquid, freezing on Devlin, and the image of Devlin in his headdress causes everyone watching the video to think that he is a vampire. But after Devlin explains every weird hobby he has, Fred starts to relate to him, and he comes to realize Devlin is not a vampire, just an eccentric and cultural music teacher. Everyone at Fred's school has seen his video, which makes everyone believe that Devlin is a vampire. Fred runs to Devlin's house to apologize, but
Fred 2: Night of the Living Fred
17710290
upon the surface roughness and the contact angle between the drop and the surface. On superhydrophobic surfaces, liquid drops are observed to bounce off of the solid surface. Richard and Quéré showed that a small liquid drop was able to bounce off of a solid surface over 20 times before coming to rest. Of particular interest is the length of time that the drop remains in contact with the solid surface. This is important in applications such as heat transfer and aircraft icing. To find a relationship between drop size and contact time for low Weber number impacts (We «
Drop impact
6505401
Lateral and subjacent support Lateral and subjacent support, in the law of property, describes the right a landowner has to have that land physically supported in its natural state by both adjoining land and underground structures. If a neighbor's excavation or excessive extraction of underground liquid deposits (crude oil or aquifers) causes subsidence, such as by causing the landowner's land to cave in, the neighbor will be subject to strict liability in a tort action. The neighbor will also be strictly liable for damage to buildings on the landowner's property if the landowner can show that the weight of the
Lateral and subjacent support
15774129
formula_98 can be expressed as a sum of vector spherical harmonics Where formula_101 are the normalized vector spherical harmonics and formula_102 and formula_103 are spherical Hankel functions. See spherical Bessel functions. The differential operator formula_104 is the angular momentum operator with the property formula_105. The coefficients formula_106 and formula_107 correspond to expanding and contracting waves respectively. So formula_108 for radiation. To determine the other coefficients, the Green's function for the wave equation is applied. If the source equation is then the solution is: The Green function can be expressed in vector spherical harmonics. Note that formula_112 is a differential operator
Multipole radiation
17673272
main droplet detaches from the surface. The filament cannot retract sufficiently rapidly to the faucet to prevent breakup and thus disintegrates into several small satellite drops. Air bubbles are another common breakup phenomenon. As air enters a tank of liquid, like a fish tank, the thread again necks at the base to produce a bubble. Blowing bubbles from a straw into a glass behaves in much the same manner. The pitch drop experiment is a famous fluid breakup experiment using high viscous tar pitch. The rate of breakup is slowed to such a degree that only 11 drops have fallen
Fluid thread breakup
10624223
not form. Early results from the clinical use of this new amalgam showed an improvement in marginal integrity. About 10 years later, another alloy, called Tytin, was introduced by adding significant amount of CuSn together with AgSn, in the form of a unicompositional spherical particle to eliminate the γ phase. Both of these relatively new alloys raised the copper content from 5%, present in the older balanced composition alloy, to about 13% for the newer alloys. Dental amalgam is produced by mixing liquid mercury with an alloy made of silver, tin, and copper solid particles. Small quantities of zinc, mercury
Amalgam (dentistry)
13484262
nor neo-darwinism. Coryanthes speciosa Coryanthes speciosa, the bat orchid, is a species of orchid found in Brazil, Colombia, Costa Rica, French Guiana, Guatemala, Guyana, Honduras, Mexico, Nicaragua, Panama, Peru, Suriname, Venezuela, the Caribbean and Belize. As noted by the position of the "bucket", liquid drops in from above by a special stem gland. The bucket fills, nectar drinking organisms such as bees are attracted to the sweet drops forming aove the bucket. As the bees jostel for position, some bees inadvertantly fall into the bucket. The bucket's fluid levels are regulated by a spout that allows overflowing liquid to be
Coryanthes speciosa
13484260
Coryanthes speciosa Coryanthes speciosa, the bat orchid, is a species of orchid found in Brazil, Colombia, Costa Rica, French Guiana, Guatemala, Guyana, Honduras, Mexico, Nicaragua, Panama, Peru, Suriname, Venezuela, the Caribbean and Belize. As noted by the position of the "bucket", liquid drops in from above by a special stem gland. The bucket fills, nectar drinking organisms such as bees are attracted to the sweet drops forming aove the bucket. As the bees jostel for position, some bees inadvertantly fall into the bucket. The bucket's fluid levels are regulated by a spout that allows overflowing liquid to be released. This
Coryanthes speciosa
9159689
protective cover over the eye. Any lasting sensitivity can be reversed using short-term use of steroid eye drops such as those containing loteprednol. Punctal plug A punctal plug, also known as tear duct plug or lacrimal plug, is a small medical device that is inserted into the tear duct (puncta) of an eye to block the duct. This prevents the drainage of liquid from the eye. They are used to treat dry eye. Artificial tears are usually still required after punctal plug insertion. A temporary punctal occlusion can be inserted and tried first. These are made of collagen and are
Punctal plug
14395926
and/or entrainment mixing are efficient methods for the removal of liquid water. They noted that the effective radius started to decrease at altitudes above 2–4 km above cloud base, which they attribute to the warm rain process. Ice processes became important at temperatures between -4 °C and -10 °C, and they photographed different shapes including needles, frozen drops, and sheaths. In growing clouds, it was noted that the particle size often grew by riming. Tokay et al. (2008) studied the raindrop size distribution in topical cyclones. They found high concentrations of small and middle sized drops regardless if larger drops
Hurricane dynamics and cloud microphysics
20185489
Reverse spherification Reverse spherification is a method of molecular gastronomy. This method is similar to spherification, different by that it is used to enclose liquid containing alcohol content, as well as liquid with calcium content such as milk and yogurt. When the liquid containing alcohol or calcium salt got dropped into an alginate bath, the liquid will draw itself into a spherical shape and got encapsulated by the gel-like membrane formed by the cross-linking of the calcium ions and the alginate polymer strands. Larger spheres can be created using reverse spherification. After removing the jelly from the alginate bath, calcium
Reverse spherification
7939024
roots growing along the stem make contact with the surface and extend root hairs that range from 20-400 μm in length. These tiny hairs grow into any small crevices available, secrete glue-like nanoparticles, and lignify. As they dry out, the hairs shrink and curl, effectively pulling the root closer to the surface. The glue-like substance is a nano composite adhesive that consists of uniform spherical nanoparticles 50-80 nm in diameter in a liquid polymer matrix. Chemical analyses of the nanoparticles detected only trace amounts of metals, once thought to be responsible for their high strength, indicating that they are largely
Hedera helix
6412001
complete atomic model, irregularities observed in numerical energy solutions of the Thomson problem have been found to correspond with electron shell-filling in naturally occurring atoms throughout the periodic table of elements. The Thomson problem also plays a role in the study of other physical models including multi-electron bubbles and the surface ordering of liquid metal drops confined in Paul traps. The generalized Thomson problem arises, for example, in determining the arrangements of the protein subunits which comprise the shells of spherical viruses. The "particles" in this application are clusters of protein subunits arranged on a shell. Other realizations include regular
Thomson problem
2492380
a long period of time with liquid water, possibly of high salinity and acidity. Features that suggest this include cross-bedded sediments, the presence of many small spherical pebbles that appear to be concretions, vugs inside rocks, and the presence of large amounts of magnesium sulfate and other sulfate-rich minerals such as jarosite. "Opportunity" rover found that the soil at Meridiani Planum was very similar to the soil at Gusev Crater and Ares Vallis; however in many places at Meridiani the soil was covered with round, hard, gray spherules that were named “blueberries.” These blueberries were found to be composed almost
Meridiani Planum
3327696
Now, let all of formula_32 but one and then divide both sides by the corresponding differential of that coordinate parameter, we find: formula_33 Del in cylindrical and spherical coordinates This is a list of some vector calculus formulae for working with common curvilinear coordinate systems. formula_12 formula_13 The expressions for formula_14 and formula_15 are found in the same way. formula_16 formula_17 formula_18 formula_19 formula_20 formula_21 formula_22 formula_23 formula_24 formula_25 The unit vector of a coordinate parameter u is defined in such a way that a small positive change in u causes the position vector formula_26 to change in formula_27 direction.
Del in cylindrical and spherical coordinates
18199957
formulas as the standard Mercator as used for small-scale maps. However, the Web Mercator uses the spherical formulas at all scales whereas large-scale Mercator maps normally use the ellipsoidal form of the projection. The discrepancy is imperceptible at the global scale but causes maps of local areas to deviate slightly from true ellipsoidal Mercator maps at the same scale. This deviation becomes more pronounced further from the equator, and can reach as much as 40 km on the ground. While the Web Mercator's formulas are for the spherical form of the Mercator, geographical coordinates are required to be in the
Web Mercator projection
10955227
where the micellar aggregates are forced to be disposed regularly in space. For amphiphiles that consist of a single hydrocarbon chain the concentration at which the first liquid crystalline phases are formed is typically in the range 25–30 wt%. The simplest liquid crystalline phase that is formed by spherical micelles is the 'micellar cubic', denoted by the symbol I. This is a highly viscous, optically isotropic phase in which the micelles are arranged on a cubic lattice. At higher amphiphile concentrations the micelles fuse to form cylindrical aggregates of indefinite length, and these cylinders are arranged on a long-ranged hexagonal
Lyotropic liquid crystal
15380304
be written as a wetting angle term formula_6. The angle is usually considered to be near 180°. In cylindrical pores there is some evidence that the freezing interface may be spherical, while the melting interface may be cylindrical, based on preliminary measurements for the measured ratio for formula_7 in cylindrical pores. Thus for a spherical interface between a non-wetting crystal and its own liquid, in an infinite cylindrical pore of diameter formula_1, the structural melting point depression is given by: formula_9 The Gibbs–Thomson equation may be written in a compact form: formula_10 where the Gibbs–Thomson Coefficient formula_11 assumes different values
Gibbs–Thomson equation
12381855
up. Smaller drops are called cloud droplets, and their shape is spherical. As a raindrop increases in size, its shape becomes more oblate, with its largest cross-section facing the oncoming airflow. Large rain drops become increasingly flattened on the bottom, like hamburger buns; very large ones are shaped like parachutes. Contrary to popular belief, their shape does not resemble a teardrop. The biggest raindrops on Earth were recorded over Brazil and the Marshall Islands in 2004 — some of them were as large as . The large size is explained by condensation on large smoke particles or by collisions between
Rain
16502560
of the liquid relative to the bubble at formula_36, then the mass entering the bubble is given by with formula_38 being the surface area of the bubble. Now by conservation of mass formula_39, therefore formula_40. Hence Therefore In many cases, the liquid density is much greater than the vapor density, formula_43, so that formula_29 can be approximated by the original zero mass transfer form formula_32, so that Assuming that the liquid is a Newtonian fluid, the incompressible Navier–Stokes equation in spherical coordinates for motion in the radial direction gives Substituting kinematic viscosity formula_48 and rearranging gives whereby substituting formula_26 from
Rayleigh–Plesset equation