|
Tolman Length
The Tolman length \delta (also known as Tolman's delta) measures the extent by which the surface tension of a small liquid drop deviates from its planar value. It is conveniently defined in terms of an expansion in 1/R, with R=R_ the equimolar radius (defined below) of the liquid drop, of the pressure difference across the droplet's surface: :\Delta p = \frac\left(1-\frac+\ldots\right) (1) In this expression, \Delta p = p_-p_ is the pressure difference between the (bulk) pressure of the liquid inside and the pressure of the vapour outside, and \sigma is the surface tension of the ''planar interface'', i.e. the interface with zero curvature R=\infty. The Tolman length \delta is thus defined as the leading order correction in an expansion in 1/R. The equimolar radius is defined so that the superficial density is zero, i.e., it is defined by imagining a sharp mathematical dividing surface with a uniform internal and external density, but where the total mass of the pure fluid is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Richard Tolman
Richard Chace Tolman (March 4, 1881 – September 5, 1948) was an American mathematical physicist and physical chemist who made many contributions to statistical mechanics. He also made important contributions to theoretical cosmology in the years soon after Einstein's discovery of general relativity. He was a professor of physical chemistry and mathematical physics at the California Institute of Technology (Caltech). Biography Tolman was born in West Newton, Massachusetts and studied chemical engineering at the Massachusetts Institute of Technology, receiving his bachelor's degree in 1903 and PhD in 1910 under A. A. Noyes. He married Ruth Sherman Tolman in 1924. In 1912, he conceived of the concept of relativistic mass, writing that "the expression m_0 \left(1 - \frac \right)^ is best suited for the mass of a moving body." In a 1916 experiment with Thomas Dale Stewart, Tolman demonstrated that electricity consists of electrons flowing through a metallic condu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Surface Tension
Surface tension is the tendency of liquid surfaces at rest to shrink into the minimum surface area possible. Surface tension is what allows objects with a higher density than water such as razor blades and insects (e.g. water striders) to float on a water surface without becoming even partly submerged. At liquid–air interfaces, surface tension results from the greater attraction of liquid molecules to each other (due to cohesion) than to the molecules in the air (due to adhesion). There are two primary mechanisms in play. One is an inward force on the surface molecules causing the liquid to contract. Second is a tangential force parallel to the surface of the liquid. This ''tangential'' force is generally referred to as the surface tension. The net effect is the liquid behaves as if its surface were covered with a stretched elastic membrane. But this analogy must not be taken too far as the tension in an elastic membrane is dependent on the amount of deformation of the m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Curvature
In mathematics, curvature is any of several strongly related concepts in geometry. Intuitively, the curvature is the amount by which a curve deviates from being a straight line, or a surface deviates from being a plane. For curves, the canonical example is that of a circle, which has a curvature equal to the reciprocal of its radius. Smaller circles bend more sharply, and hence have higher curvature. The curvature ''at a point'' of a differentiable curve is the curvature of its osculating circle, that is the circle that best approximates the curve near this point. The curvature of a straight line is zero. In contrast to the tangent, which is a vector quantity, the curvature at a point is typically a scalar quantity, that is, it is expressed by a single real number. For surfaces (and, more generally for higher-dimensional manifolds), that are embedded in a Euclidean space, the concept of curvature is more complex, as it depends on the choice of a direction on the surface or man ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Leading-order
The leading-order terms (or corrections) within a mathematical equation, expression or model are the terms with the largest order of magnitude.J.K.Hunter, ''Asymptotic Analysis and Singular Perturbation Theory'', 2004. http://www.math.ucdavis.edu/~hunter/notes/asy.pdf The sizes of the different terms in the equation(s) will change as the variables change, and hence, which terms are leading-order may also change. A common and powerful way of simplifying and understanding a wide variety of complicated mathematical models is to investigate which terms are the largest (and therefore most important), for particular sizes of the variables and parameters, and analyse the behaviour produced by just these terms (regarding the other smaller terms as negligible). This gives the main behaviour – the true behaviour is only small deviations away from this. This main behaviour may be captured sufficiently well by just the strictly leading-order terms, or it may be decided that slightly smaller ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Radius Of Spontaneous Curvature
In classical geometry, a radius ( : radii) of a circle or sphere is any of the line segments from its center to its perimeter, and in more modern usage, it is also their length. The name comes from the latin ''radius'', meaning ray but also the spoke of a chariot wheel. as a function of axial position ../nowiki>" Spherical coordinates In a spherical coordinate system, the radius describes the distance of a point from a fixed origin. Its position if further defined by the polar angle measured between the radial direction and a fixed zenith direction, and the azimuth angle, the angle between the orthogonal projection of the radial direction on a reference plane that passes through the origin and is orthogonal to the zenith, and a fixed reference direction in that plane. See also *Bend radius *Filling radius in Riemannian geometry *Radius of convergence * Radius of convexity *Radius of curvature *Radius of gyration *Semidiameter In geometry, the semidiameter or semi-diameter of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Thermodynamic Free Energy
The thermodynamic free energy is a concept useful in the thermodynamics of chemical or thermal processes in engineering and science. The change in the free energy is the maximum amount of work that a thermodynamic system can perform in a process at constant temperature, and its sign indicates whether the process is thermodynamically favorable or forbidden. Since free energy usually contains potential energy, it is not absolute but depends on the choice of a zero point. Therefore, only relative free energy values, or changes in free energy, are physically meaningful. The free energy is a thermodynamic state function, like the internal energy, enthalpy, and entropy. The free energy is the portion of any first-law energy that is available to perform thermodynamic work at constant temperature, ''i.e.'', work mediated by thermal energy. Free energy is subject to irreversible loss in the course of such work. Since first-law energy is always conserved, it is evident that free energy ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Laplace Equation
In mathematics and physics, Laplace's equation is a second-order partial differential equation named after Pierre-Simon Laplace, who first studied its properties. This is often written as \nabla^2\! f = 0 or \Delta f = 0, where \Delta = \nabla \cdot \nabla = \nabla^2 is the Laplace operator,The delta symbol, Δ, is also commonly used to represent a finite change in some quantity, for example, \Delta x = x_1 - x_2. Its use to represent the Laplacian should not be confused with this use. \nabla \cdot is the divergence operator (also symbolized "div"), \nabla is the gradient operator (also symbolized "grad"), and f (x, y, z) is a twice-differentiable real-valued function. The Laplace operator therefore maps a scalar function to another scalar function. If the right-hand side is specified as a given function, h(x, y, z), we have \Delta f = h. This is called Poisson's equation, a generalization of Laplace's equation. Laplace's equation and Poisson's equation are the simplest exa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gibbs Isotherm
The Gibbs adsorption isotherm for multicomponent systems is an equation used to relate the changes in concentration of a component in contact with a surface with changes in the surface tension, which results in a corresponding change in surface energy. For a binary system, the Gibbs adsorption equation in terms of surface excess is: :-\mathrm\gamma\ = \Gamma_1\mathrm\mu_1\, + \Gamma_2\mathrm\mu_2\,, where :\gamma\,\! is the surface tension, :\Gamma\,\!i is the surface excess concentration of component i, :\mu\,\!i is the chemical potential of component i. Adsorption Different influences at the interface may cause changes in the composition of the near-surface layer.Shchukin, E.D., Pertsov, A.V., Amelina E.A. and Zelenev, A.S. Colloid and Surface Chemistry. 1st ed. Mobius D. and Miller R. Vol. 12. Amsterdam: Elsevier Science B.V. 2001. Substances may either accumulate near the surface or, conversely, move into the bulk. The movement of the molecules characterizes the phenom ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Willard Gibbs
Josiah Willard Gibbs (; February 11, 1839 – April 28, 1903) was an American scientist who made significant theoretical contributions to physics, chemistry, and mathematics. His work on the applications of thermodynamics was instrumental in transforming physical chemistry into a rigorous inductive science. Together with James Clerk Maxwell and Ludwig Boltzmann, he created statistical mechanics (a term that he coined), explaining the laws of thermodynamics as consequences of the statistical properties of ensembles of the possible states of a physical system composed of many particles. Gibbs also worked on the application of Maxwell's equations to problems in physical optics. As a mathematician, he invented modern vector calculus (independently of the British scientist Oliver Heaviside, who carried out similar work during the same period). In 1863, Yale awarded Gibbs the first American doctorate in engineering. After a three-year sojourn in Europe, Gibbs spent the rest of his ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Shipley Rowlinson
Sir John Shipley Rowlinson (12 May 1926 – 15 August 2018) was a British chemist. He attended Oxford University, where he completed his undergraduate studies in 1948 and doctoral in 1950. He then became research associate at University of Wisconsin (1950–1951), lecturer at University of Manchester (1951–1961), Professor at Imperial College London (1961–1973) and back at Oxford from 1974 to his retirement in 1993. His works covered a wide range of subjects, including on capillarity (the ability of a liquid to flow in narrow spaces without the assistance of, or even in opposition to, external forces like gravity) and cohesion (forces that make similar molecules stick together). In addition, he wrote about the history of science, including multiple works on the Dutch physicist Johannes Diderik van der Waals (1837–1923). He was a Fellow of the Royal Society and the Royal Academy of Engineering. He received a Faraday Lectureship Prize in 1983 and was knighted in 2000. Early ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Physical Chemistry
Physical chemistry is the study of macroscopic and microscopic phenomena in chemical systems in terms of the principles, practices, and concepts of physics such as motion, energy, force, time, thermodynamics, quantum chemistry, statistical mechanics, analytical dynamics and chemical equilibria. Physical chemistry, in contrast to chemical physics, is predominantly (but not always) a supra-molecular science, as the majority of the principles on which it was founded relate to the bulk rather than the molecular or atomic structure alone (for example, chemical equilibrium and colloids). Some of the relationships that physical chemistry strives to resolve include the effects of: # Intermolecular forces that act upon the physical properties of materials ( plasticity, tensile strength, surface tension in liquids). # Reaction kinetics on the rate of a reaction. # The identity of ions and the electrical conductivity of materials. # Surface science and electrochemistry of cell membrane ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
