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Perrin Friction Factors
In hydrodynamics, the Perrin friction factors are multiplicative adjustments to the translational and rotational friction of a rigid spheroid, relative to the corresponding frictions in spheres of the same volume. These friction factors were first calculated by Jean-Baptiste Perrin. These factors pertain to spheroids (i.e., to ellipsoids of revolution), which are characterized by the axial ratio ''p = (a/b)'', defined here as the axial semiaxis ''a'' (i.e., the semiaxis along the axis of revolution) divided by the equatorial semiaxis ''b''. In prolate spheroids, the axial ratio ''p > 1'' since the axial semiaxis is longer than the equatorial semiaxes. Conversely, in oblate spheroids, the axial ratio ''p < 1'' since the axial semiaxis is shorter than the equatorial semiaxes. Finally, in s, the axial ratio ''p = 1'', since all three semiaxes are equal in length. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hydrodynamics
In physics, physical chemistry and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids – liquids and gases. It has several subdisciplines, including (the study of air and other gases in motion) and (the study of water and other liquids in motion). Fluid dynamics has a wide range of applications, including calculating forces and moments on aircraft, determining the mass flow rate of petroleum through pipelines, predicting weather patterns, understanding nebulae in interstellar space, understanding large scale geophysical flows involving oceans/atmosphere and modelling fission weapon detonation. Fluid dynamics offers a systematic structure—which underlies these practical disciplines—that embraces empirical and semi-empirical laws derived from flow measurement and used to solve practical problems. The solution to a fluid dynamics problem typically involves the calculation of various properties of the fluid, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jean-Baptiste Perrin
Jean Baptiste Perrin (; 30 September 1870 – 17 April 1942) was a French atomic physicist who, in his studies of the Brownian motion of minute particles suspended in liquids (sedimentation equilibrium), verified Albert Einstein's explanation of this phenomenon and thereby confirmed the atomic nature of matter. For this achievement, he was honoured with the Nobel Prize in Physics in 1926. Biography Early years Born in Lille, France, Perrin attended the École normale supérieure, the elite ''grande école'' in Paris. He became an assistant at the school during the period of 1894–97 when he began the study of cathode rays and X-rays. He was awarded the degree of '' docteur ès sciences'' in 1897. In the same year, he was appointed as a lecturer in physical chemistry at the Sorbonne, Paris. He became a professor at the university in 1910, holding this post until the German occupation of France during World War II. Research and achievements In 1895, Perrin showed that ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spheroid
A spheroid, also known as an ellipsoid of revolution or rotational ellipsoid, is a quadric surface (mathematics), surface obtained by Surface of revolution, rotating an ellipse about one of its principal axes; in other words, an ellipsoid with two equal semi-diameters. A spheroid has circular symmetry. If the ellipse is rotated about its major axis, the result is a ''prolate spheroid'', elongated like a rugby ball. The ball (gridiron football), American football is similar but has a pointier end than a spheroid could. If the ellipse is rotated about its minor axis, the result is an ''oblate spheroid'', flattened like a lentil or a plain M&M's, M&M. If the generating ellipse is a circle, the result is a sphere. Due to the combined effects of gravity and rotation of the Earth, rotation, the figure of the Earth (and of all planets) is not quite a sphere, but instead is slightly flattening, flattened in the direction of its axis of rotation. For that reason, in cartography and geode ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ellipsoid
An ellipsoid is a surface that can be obtained from a sphere by deforming it by means of directional Scaling (geometry), scalings, or more generally, of an affine transformation. An ellipsoid is a quadric surface; that is, a Surface (mathematics), surface that may be defined as the zero set of a polynomial of degree two in three variables. Among quadric surfaces, an ellipsoid is characterized by either of the two following properties. Every planar Cross section (geometry), cross section is either an ellipse, or is empty, or is reduced to a single point (this explains the name, meaning "ellipse-like"). It is Bounded set, bounded, which means that it may be enclosed in a sufficiently large sphere. An ellipsoid has three pairwise perpendicular Rotational symmetry, axes of symmetry which intersect at a Central symmetry, center of symmetry, called the center of the ellipsoid. The line segments that are delimited on the axes of symmetry by the ellipsoid are called the ''principal ax ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Axial Ratio
Axial ratio, for any structure or shape with two or more axes, is the ratio of the length (or magnitude) of those axes to each other - the longer axis divided by the shorter. In ''chemistry'' or ''materials science'', the axial ratio (symbol P) is used to describe rigid rod-like molecules. It is defined as the length of the rod divided by the rod diameter. In ''physics'', the axial ratio describes electromagnetic radiation with elliptical, or circular, polarization. The axial ratio is the ratio of the magnitudes of the major and minor axis defined by the electric field vector. See also * Aspect ratio * Degree of polarization , or , is a property of transverse waves which specifies the geometrical orientation of the oscillations. In a transverse wave, the direction of the oscillation is perpendicular to the direction of motion of the wave. One example of a polarize ... References Ratios Polymer physics {{materials-sci-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Prolate Spheroid
A spheroid, also known as an ellipsoid of revolution or rotational ellipsoid, is a quadric surface obtained by rotating an ellipse about one of its principal axes; in other words, an ellipsoid with two equal semi-diameters. A spheroid has circular symmetry. If the ellipse is rotated about its major axis, the result is a ''prolate spheroid'', elongated like a rugby ball. The American football is similar but has a pointier end than a spheroid could. If the ellipse is rotated about its minor axis, the result is an ''oblate spheroid'', flattened like a lentil or a plain M&M. If the generating ellipse is a circle, the result is a sphere. Due to the combined effects of gravity and rotation, the figure of the Earth (and of all planets) is not quite a sphere, but instead is slightly flattened in the direction of its axis of rotation. For that reason, in cartography and geodesy the Earth is often approximated by an oblate spheroid, known as the reference ellipsoid, instead of a sp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Oblate Spheroid
A spheroid, also known as an ellipsoid of revolution or rotational ellipsoid, is a quadric surface obtained by rotating an ellipse about one of its principal axes; in other words, an ellipsoid with two equal semi-diameters. A spheroid has circular symmetry. If the ellipse is rotated about its major axis, the result is a ''prolate spheroid'', elongated like a rugby ball. The American football is similar but has a pointier end than a spheroid could. If the ellipse is rotated about its minor axis, the result is an ''oblate spheroid'', flattened like a lentil or a plain M&M. If the generating ellipse is a circle, the result is a sphere. Due to the combined effects of gravity and rotation, the figure of the Earth (and of all planets) is not quite a sphere, but instead is slightly flattened in the direction of its axis of rotation. For that reason, in cartography and geodesy the Earth is often approximated by an oblate spheroid, known as the reference ellipsoid, instead of a sphe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sphere
A sphere (from Ancient Greek, Greek , ) is a surface (mathematics), surface analogous to the circle, a curve. In solid geometry, a sphere is the Locus (mathematics), set of points that are all at the same distance from a given point in three-dimensional space.. That given point is the center (geometry), ''center'' of the sphere, and the distance is the sphere's ''radius''. The earliest known mentions of spheres appear in the work of the Greek mathematics, ancient Greek mathematicians. The sphere is a fundamental surface in many fields of mathematics. Spheres and nearly-spherical shapes also appear in nature and industry. Bubble (physics), Bubbles such as soap bubbles take a spherical shape in equilibrium. The Earth is spherical Earth, often approximated as a sphere in geography, and the celestial sphere is an important concept in astronomy. Manufactured items including pressure vessels and most curved mirrors and lenses are based on spheres. Spheres rolling, roll smoothly in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stokes' Law
In fluid dynamics, Stokes' law gives the frictional force – also called drag force – exerted on spherical objects moving at very small Reynolds numbers in a viscous fluid. It was derived by George Gabriel Stokes in 1851 by solving the Stokes flow limit for small Reynolds numbers of the Navier–Stokes equations.Batchelor (1967), p. 233. Statement of the law The force of viscosity on a small sphere moving through a viscous fluid is given by: :_ = - 6 \pi \mu R where (in SI units): * _ is the frictional force – known as Stokes' drag – acting on the interface between the fluid and the particle (newtons, kg m s−2); * (some authors use the symbol ) is the dynamic viscosity ( Pascal-seconds, kg m−1 s−1); * is the radius of the spherical object (meters); * is the flow velocity relative to the object (meters per second). Note the minus sign in the equation, the drag force points in the opposite direction to the relative velocity: drag opposes the motion. Stokes' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Einstein Relation (kinetic Theory)
In physics (specifically, the kinetic theory of gases), the Einstein relation is a previously unexpected connection revealed independently by William Sutherland in 1904, Albert Einstein in 1905, and by Marian Smoluchowski in 1906 in their works on Brownian motion. The more general form of the equation in the classical case is D = \mu \, k_\text T, where * is the diffusion coefficient; * is the "mobility", or the ratio of the particle's terminal drift velocity to an applied force, ; * is the Boltzmann constant; * is the absolute temperature. This equation is an early example of a fluctuation-dissipation relation. Note that the equation above describes the classical case and should be modified when quantum effects are relevant. Two frequently used important special forms of the relation are: * Einstein–Smoluchowski equation, for diffusion of charged particles: D = \frac * Stokes–Einstein–Sutherland equation, for diffusion of spherical particles through a li ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ultracentrifuge
An ultracentrifuge is a centrifuge optimized for spinning a rotor at very high speeds, capable of generating acceleration as high as (approx. ). There are two kinds of ultracentrifuges, the preparative and the analytical ultracentrifuge. Both classes of instruments find important uses in molecular biology, biochemistry, and polymer science.Susan R. Mikkelsen & Eduardo Cortón. Bioanalytical Chemistry, Ch. 13. Centrifugation Methods. John Wiley & Sons, Mar 4, 2004, pp. 247-267. History In 1924 Theodor Svedberg built a centrifuge capable of generating 7,000 g (at 12,000 rpm), and called it the ultracentrifuge, to juxtapose it with the Ultramicroscope that had been developed previously. In 1925-1926 Svedberg constructed a new ultracentrifuge that permitted fields up to 100,000 g (42,000 rpm). Modern ultracentrifuges are typically classified as allowing greater than 100,000 g. Svedberg won the Nobel Prize in Chemistry in 1926 for his research on colloids and proteins using the ultrac ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dynamic Light Scattering
Dynamic light scattering (DLS) is a technique in physics that can be used to determine the size distribution profile of small particles in suspension or polymers in solution. In the scope of DLS, temporal fluctuations are usually analyzed using the intensity or photon autocorrelation function (also known as photon correlation spectroscopy – PCS or quasi-elastic light scattering – QELS). In the time domain analysis, the autocorrelation function (ACF) usually decays starting from zero delay time, and faster dynamics due to smaller particles lead to faster decorrelation of scattered intensity trace. It has been shown that the intensity ACF is the Fourier transform of the power spectrum, and therefore the DLS measurements can be equally well performed in the spectral domain. DLS can also be used to probe the behavior of complex fluids such as concentrated polymer solutions. Setup A monochromatic light source, usually a laser, is shot through a polarizer and into a sample. The s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
